4410-68-X VESIAC Special Report TABLES OF AMPLITUDE AND ENERGY RATIOS FOR PLANE SV WAVES JOHN, K. OSTAIN KENNETWC.- COOK S. T. ALGERMISSEN Department of GeophysicsUniversity of Utah Salt Lake City December 1963 Acoustics and Seismics Laboratory 4f4tUtce i& Scee aaW 7ee4449 THE UNIVERSITY OF MICHIGAN Ann Arbor, Michigan

Institute of Science and Technology The University of Michigan NOTICES Sponsorship. The work reported herein is being published by the Institute of Science and Technology for the Advanced Research Projects Agency of the Office of the Secretary of Defense under Contract SD-78. Contracts and grants to the University of Michigan for the support of sponsored research by the Institute of Science and Technology are administered through the Office of the Vice-President for Research. Acknowledgments. Messrs. Bongil Jeong and Roy E. Willie,Jr., graduate students in the Department of Geophysics, University of Utah, assisted in the compiling and execution phases of the computer programs. Financial support was provided from research contract No. AF 19(628)-201 with the Air Force Cambridge Research Laboratories of the U. S. Air Force under project VELA UNIFORM of the Advanced Research Projects Agency of the Department of Defense. DDC Availability. Qualified requesters may obtain copies of this document from: Defense Documentation Center Cameron Station Alexandria, Virginia Final Disposition. After this document has served its purpose, it may be destroyed. Please do not return it to the Institute of Science and Technology. ii

Institute of Science and Technology The University of Michigan PREFACE VESIAC, the VELA Seismic Information Analysis Center, is an information collection, analysis, and dissemination facility established at the Institute of Science and Technology of The University of Michigan. The contract is sponsored by the Advanced Research Projects Agency under the Office of the Secretary of Defense. The purpose of VESIAC is to analyze the research information related to the VELA UNIFORM Program of Project VELA and to function as a central facility for this information. The facility will serve all authorized recipients of VELA UNIFORM research information by issuing subject bibliographies with abstracts and special reports as required. In addition, VESIAC will periodically summarize the progress of the research being conducted. VESIAC is under the technical direction of the Acoustics and Seismics Laboratory of the Institute. In its operation VESIAC draws upon members of this laboratory and other members of the Institute and University. iii

Institute of Science and Technology The University of Michigan CONTENTS Notices...................................... ii Preface..................................iii Abstract................................... vii 1. Introduction................................ vii 2. General Method of Computation and Accuracy of Data.......... vii 3. Energy and Amplitude Ratios....................... viii 4. Format of Tables............................... x References................................... xii Energy Ratios For an Incident SV Wave, Poisson's Ratio.250........ 1 Velocity Ratio.700, Density Ratio.700.................. 1 Velocity Ratio.800, Density Ratio.700................. 7 Velocity Ratio.900, Density Ratio.700....................13 Velocity Ratio.700, Density Ratio.800..................19 Velocity Ratio.800, Density Ratio.800..................25 Velocity Ratio.900, Density Ratio.800..................31 Velocity Ratio.700, Density Ratio.900....................37 Velocity Ratio.800, Density Ratio.900..................43 Velocity Ratio.900, Density Ratio.900.................49 Velocity Ratio.700, Density Ratio 1.000..................55 Velocity Ratio.800, Density Ratio 1.000..................61 Velocity Ratio.900, Density Ratio 1.000..................67 Amplitude Ratios For an Incident SV Wave, Poisson's Ratio.250.......73 Velocity Ratio.700, Density Ratio.700...............73 Velocity Ratio.800, Density Ratio.700..................78 Velocity Ratio.900, Density Ratio.700..................83 Velocity Ratio.700, Density Ratio.800..................88 Velocity Ratio.800, Density Ratio.800..................93 Velocity Ratio.900, Density Ratio.800............... 99 Velocity Ratio.700, Density Ratio.900..............107 Velocity Ratio.800, Density Ratio.900................. 113 Velocity Ratio.900, Density Ratio.900............... 119 Velocity Ratio.700, Density Ratio 1.000................ 124 Velocity Ratio.800, Density Ratio 1.000................. 130 Velocity Ratio.900, Density Ratio 1.000................ 135 V

Institute of Science and Technology The University of Michigan Amplitude Ratios For an Incident SV Wave, Poisson's Ratio.400...... 141 Velocity Ratio.700, Density Ratio.700................. 141 Velocity Ratio.800, Density Ratio.700................. 145 Velocity Ratio.900, Density Ratio.700................. 149 Velocity Ratio.700, Density Ratio.800............... 151 Velocity Ratio.800, Density Ratio.800................. 153 Velocity Ratio.900, Density Ratio.800................. 155 Velocity Ratio.700, Density Ratio.900................. 157 Velocity Ratio.800, Density Ratio.900................ 159 Velocity Ratio.900, Density Ratio.900..................161 Velocity Ratio.700, Density Ratio 1.000.............. 163 Velocity Ratio.800, Density Ratio 1.000.................165 Velocity Ratio.900, Density Ratio 1.000................ 167 vi

TABLES OF AMPLITUDE AND ENERGY RATIOS FOR PLANE SV WAVES ABSTRACT This report presents tabulations of energy ratios calculated from Knott's energy equation, and amplitude ratios calculated from the Zeoppritz equations, for a plane SV wave incident on a plane elastic discontinuity. All computations were programmed in FORTRAN for an IBM 1620 digital computer. Incident angles were varied from 00 to 90~ in increments of 20 except near the critical angles, where the ratios were calculated in increments of 0.250 generally. Both real and imaginary coefficients were considered in the calculations. The varying parameters were the velocity ratio and density ratio across each interface, and the angle of incidence. Energy ratios were computed for a Poisson's ratio of 0.25 only, and amplitude ratios were computed for Poisson's ratios of both 0.25 and 0.40. Compressional velocity ratios (transmitted/incident) of 0.7, 0.8, and 0.9, and density ratios (transmitted/incident) of 0.7, 0.8, 0.9, and 1.0 were used. The data are presented in 36 tables, 12 for energy ratios and 24 for amplitude ratios. 1 INTRODUCTION Energy ratios from Knott's energy equation and amplitude ratios from the Zoeppritz equations are presented in tabular form for a plane SV wave incident on a plane elastic discontinuity. All computations were programmed in FORTRAN for an IBM 1620 digital computer with a core storage of 60,000 bits. Both real and imaginary coefficients were considered in the calculations. The velocity ratio, the density ratio, and the angle of incidence were varied across each interface. Compressional velocity ratios (transmitted/incident) of 0.700, 0.800, and 0.900, and density ratios (transmitted/incident) of 0.700, 0.800, 0.900, and 1.000, are used. With the exception of the amplitude-ratio data for Poisson's ratio equal to 0.400, all of the data presented herein in tabular form are shown as curves in a recent publication [1], for which Poisson's ratio was kept constant at 0.25. 2 GENERAL METHOD OF COMPUTATION AND ACCURACY OF DATA The determination of the relative energies and amplitudes of waves derived from a plane SV wave incident on a plane interface involves the solution of four simultaneous linear equations [2, 3] with real and imaginary coefficients. The equations were solved in the real and complex domains by the Crout method [4], which was programmed in FORTRAN I and FORTRAN II. The vii

Institute of Science and Technology The University of Michigan variable-field-length capability of the 1620 FORTRAN II system provided a means of checking the accuracy of the solutions, most of which were obtained by using a floating-point precision of eight decimal places. Those solutions which were obtained in FORTRAN II by using a floating-point precision of sixteen decimal places differed only in the seventh decimal place from those obtained by using a precision of eight decimal places. A conservation-of-energy check on all solutions was satisfied in every set of computations to at least the sixth decimal place in FORTRAN I, and to the fourteenth decimal place when the higher precision was used in FORTRAN II. The numerical results presented in the tables are accurate to the sixth decimal place. 3 ENERGY AND AMPLITUDE RATIOS Amplitude ratios were determined from the Zoeppritz equations for a plane SV wave of amplitude B incident on a plane interface. These equations are [5, pp. 670-673]: (B + D) sin b + C cos a - E cos e - F sin f = 0 (B - D) cos b + C sin a + E sin e - F cos f = 0 (B + D) cos 2b - C(V/U) sin 2a + EK(Z2/VY) sin 2e - FK(Z/V) cos 2f = 0 (1) -(B - D) sin 2b + C(U/V) cos 2b + EK(Y/V) cos 2f + FK(Z/V) sin 2f = 0 where the angles and the velocities U, V, Y, and Z are as defined in Figure 1. The angle a is the angle of incidence of a compressional wave of velocity U which would generate four waves with the same reference angles as shown in Figure 1. K is the density contrast, equal to P1/P2, where p1 and P2 are the densities of the upper and lower media, respectively. SV P Y = LONGITUDINAL VELOCITY IN MEDIUM I Y.V Z eZ = SHEAR VELOCITY MEDIUM I IN MEDIUM I MEDIUM II_______ MEDIUM 2 U = LONGITUDINAL VELOCITY U,V j \ ^^^ IN MEDIUM 2 P V = SHEAR VELOCITY b/,~ \^ IN MEDIUM 2 INCIDENT / e SV SV FIGURE I viii

Institute of Science and Technology The University of Michigan With B set equal to unity, the equations were solved for C, D, E, and F, which are the amplitudes of the reflected P, reflected S, transmitted P, and transmitted S waves, respectively. The quantities are complex after the first critical angle of 35.2640, for a Poisson's ratio of 0.250. For velocity ratios Y/U equal to 0.700, 0.800, and 0.900, second critical angles occur at 55.567, 46.194, and 39.904 degrees, respectively, for Poisson's ratio of 0.250. Both the real and the imaginary parts of the complex amplitudes are printed out in the tables. The physically significant quantity is the modulus of the complex amplitude, which is the square root of the sum of the squares of the real and imaginary parts of the complex amplitudes. The phase shifts associated with the complex domain can be determined from the entries in the tables. Beyond the first critical angle, the amplitudes of the derived waves are complex, and all derived wave amplitudes will generally undergo phase changes. The complex amplitudes computed from the Zoeppritz equations are printed out in the form a + ib. The phase angle i of the derived wave is given by -1 b - = tan - a The quantities a and b identify the quadrant and thus the phase angle of the derived wave. The distribution of energy among the four waves derived from a plane incident SV wave can be obtained from Knott's energy equation for an incident SV wave [6, p. 173, Equation 7.80], which can be written in the form: ~2 ~l2 f)(tE 22 2 2 Pi t c) C 2 P(cot (cot f) F Z +D + + (2) (cot d) V p2(cot d) V p2(cot d) V The terms on the right-hand side of this equation represent the energies of the reflected P, reflected S, transmitted P, and transmitted S waves, respectively, relative to the energy of an incident SV wave of amplitude B, with B set equal to unity. The energy ratios were obtained by determining the amplitudes C, D, E, and F from the Zoeppritz equations, inserting these values in Equation 2, and then evaluating each term in the equation. These individual ratios were then printed out as the energies of the reflected P, reflected S, transmitted P, and transmitted S waves, respectively, relative to the energy of an incident SV wave. The computed energy ratios from Equation 2 serve as a useful check on the accuracy of the amplitudes determined from the Zoeppritz equations. The sum of the terms on the right-hand side of Equation 2 differs from unity only in the seventh decimal place at worst, when a floatingpoint precision of eight decimal places was used in the computations. ix

Institute of Science and Technology The University of Michigan In applying the conservation-of-energy equation for angles greater than 35.264 degrees, for Poisson's ratio of 0.250, the terms on the right-hand side of Equation 2 are complex. The imaginary parts of all of these terms must add up to zero and the real parts to unity, in every set of computations. The sum of the moduli of the complex energies of those derived waves whose angles of reflection or refraction are not imaginary will be unity. The moduli of those waves showe angles of reflection or refraction are imaginary are not included in the summation. 4 FORMAT OF TABLES The velocity ratio (transmitted/incident), Poisson's ratio for the incident medium, Poisson's ratio for the transmitted medium, and the density ratio (transmitted/incident) are listed above each set of computations for both energy ratios and amplitude ratios. Energy ratios computed in the real domain are presented in the following format: ANGLE ERP ERS ETP ETS ENERGY 2.00.00126547.11566885.00025266.88281290.99999988 where ANGLE refers to the angle of incidence, in degrees, of the plane SV ray, and ERP, ERS, ETP, and ETS are the energy ratios of the reflected P, reflected S, transmitted P, and transmitted S waves, respectively, to the energy of a plane SV wave. The ENERGY column is the conservation-of-energy check; for the energy computations, it is the sum of ERP, ERS, ETP, and ETS for a particular angle of incidence. Energy ratios computed in the complex domain are presented in the following format: ANGLE ERP ERS ETP ETS ENERGY 37.00.03779700.04416885.08750717.83052694.99999997.01022057J.00826448J.08019472J -.09867977J.00000000.03915448M.04493539M.11869582M.83636875M For each angle of incidence, the imaginary part of the complex energy is followed by the letter J, and the real part is printed above this. The modulus is the square root of the sum of the squares of these first two entries, and is followed by the letter M. The first line in the ENERGY column for each angle of incidence is the algebraic sum of the real parts of the complex energies of the derived waves, and the second line in the ENERGY column is the algebraic sum of the imaginary parts of the complex energies of the derived waves. Theoretically, the former should be exactly unity, and the latter should be zero. X

Institute of Science and Technology The University of Michigan When the coefficient of a derived wave in the Zoeppritz equations becomes imaginary-that is, when the angle of reflection or refraction of that wave becomes imaginary-the computer is programmed to print the word IMAGINARY in the column corresponding to that particular derived wave just after the last set of computations for which the angle was real, that is, for which the derived wave existed physically. An example appears on the second page of the tabular material. In determining a conservation-of-energy check for those waves which do exist, only the moduli of coefficients not preceded anywhere in the column by the word IMAGINARY are used. Such calculations were not printed out explicitly, since the real and imaginary parts of the complex energies were always checked. The sum of the moduli of waves whose coefficients are not imaginary, however, should be unity. Amplitude ratios computed in the real domain are presented in the following format: ANGLE RP RS TP TS ENERGY 26.00.25561126 -.02091038.23283892 1.29804660.99999988 where ANGLE refers to the angle of incidence in degrees of the plane SV ray, and RP, RS, TP, and TS are the amplitudes of the reflected P, reflected S, transmitted P, and transmitted S waves, respectively, relative to the amplitude of an incident SV wave of unit amplitude. Sign changes in the real domain correspond to phase shifts of 1800 with respect to the incident wave. The ENERGY column is the conservation-of-energy check, and is the algebraic sum of each of the terms in Equation 2. Amplitude ratios computed in the complex domain are presented in the following format: ANGLE RP RS TP TS ENERGY 36.00.29276898.17911049.27812276 1.27313730 1.00000000 -.13548989J.02127643J.13531673J -.06442387J -O00000000.32260065M.18036977M.30929417M 1.27476620M For each angle of incidence, the imaginary part of the complex amplitude is followed by the letter J, and the real part is printed above this. The modulus is the square root of the sum of the squares of these first two entries, and is followed by the letter M. The first line in the ENERGY column for each angle of incidence is the algebraic sum of the real parts of each term in Equation 2; the second line is the algebraic sum of the imaginary parts of the terms. The word IMAGINARY is inserted by the computer, as described above, whenever a coefficient becomes imaginary. Phase angles can be determined from the real and imaginary parts of the complex amplitudes a + ib by the relation -1 b f = tan - xi

Institute of Science and Technology The University of Michigan A later modification of the FORTRAN program provided for the computation of these phase angles by use of the relation above. Amplitude ratios for a velocity ratio of 0.900, a density ratio of 0.800, and Poisson's ratio of 0.250 were computed by using this modified program. Phase angles are followed by the letters PA. In most computations, this angle must be added to or subtracted from 1800 to identify the phase angle with the proper quadrant. REFERENCES 1. J. K. Costain, K. L. Cook, and S. T. Algermissen, "Amplitude, Energy, and Phase Angles of Plane SV Waves and Their Application to Earth Crustal Studies," Bull. Seis. Soc Am., 1963, Vol. 53, pp. 1039-1074. 2. C. G. Knott, "Reflexion and Refraction of Elastic Waves, with Seismological Applications," Phil. Mag. London, 1899, Vol. 48, pp. 64-97 and 567-569. 3. Karl Zoeppritz, 1919, "Uber Erdbebenwellen VIIB: Uber Reflexion and Durchgang Seismischer Wellen durch Unstetigkeitsflischen," Nachr. der Kbniglichen Gesell. d. Wissen, Gbttingen, math.-phys. Kl., 1919, p. 66-84. 4. P. D. Crout, "A Short Method for Evaluating Determinants and Solving Systems of Linear Equations with Real or Complex Coefficients," Trans. Am. Inst. Elec. Eng., 1941, Vol. 60, pp. 1235-1240. 5. C. F. Richter, Elementary Seismology, W. H. Freeman and Co., San Francisco, 1958. 6. J. B. Macelwane, Introduction to Theoretical Seismology, Part 1: Geodynamics, St. Louis University, St. Louis, 1932. xii

Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC) *700.250.250.700 ANGLE ERP ERS ETP ETS ENERGY.uU.00000000.11715687.00000000 *88284302.99999989 1.Oo.00031745 *11678379.00006315.88283545 *99999984 2.0o.00126547.11566885.00025266.88281290.99999988 3.00.00283102.11382515.00056865.88277505.99999987 4.00.00499257.11127462.00101133.88272144.99999996 5.00.00772020.10804750.00158096.88265131.99999997 6.00.01097597.10418214.00227790.88256388.99999989 7.00.01471420.09972482.00310259.88245825.99999987 8.OU.01888198.09472927.00405549.88233319.99999994 9.00.02341964.08925600.00513714.88218710 *99999988 10.00.02826131.08337186.00634812.88201872 1.00000000 11.00.03333564 *07714950.00768903.88182568.99999985 12.0u.03856646.07066654.00916047.88160628.99999975 13.00.04387361.06400488.01076303 *88135841.99999994 14.00.04917375.05724973.01249726.88107901.99999975 15.00.05438135.05048902.01436362.88076575.9999974 16.00.05940949.04381217.01636242.88041568.99999976 17,00.06417106.03730936.01849380.88002563.99999985 18.00.06857968.03107032 *02075756 *87959224.99999981 19.00.07255093.02518344.02315315.87911232 *99999984 20.00.07600332.01973455.02567941.87858259.99999989 21.00.07885959.01480585.02833441.87800001.99999986 1

Institute of Science and Technology The University of Michigan 22.00.08104787.01047472.03111513.87736216.99999989 23.00.08250283.00681257.03401695.87666763.99999999 24.00.08316689.00388352.03703309.87591643.99999994 25.00.08299139.00174318 *04015349.87511175.99999981 26.00.08193759.00043724.04336327 o87426172.99999983 27.ou.07997740.00000001.04664017.87338228 999999987 28.00.07709389.00045272.04995020.87250295.99999977 29.00.07328073.00180141.05323975.87167798.99999988 30.00.06853912.00403399.05642089.87100589.99999990 31.00.06286998.00711533.05934044.87067424 1.00000000 32.00.05624974.01097730.06170804.87106496 1~00000000 33.00.04855165.01549239.06289728.87305869 1.00000000 34.00.03918888.02037436.06120665.87922992.99999981 35.00.02327763.02432781.04809952.90429488.99999986 35.25.00734361.02319058.03119010.93827562.99999992 IMAGINARY 35.5u.01432570.02511924.02850934.93204580 1.0000000.02657883J.00480707J.02868851J -.06007442J.00000000.03019371M.02557507M.04044519M.93397981M 35.75.02520644.02836078.03496344.91146926.99999993.02949627J.00657728J.04366246J -.07973602J.00000000.03879942M.02911348M.05593615M.91495029M 36.00.03243845.03162788.04345066.89248302 1.00000000.02754074J.00762166J.05539313J -.09055553J.00000000.04255286M.03253325M.07040141M.89706534M 37.00.03779700.04416885.08750717.83052694.99999997.01022057J.00826448J.08019472J -.09867977J.00000000.03915448M.04493539M.11869582M.83636875M 38.00.02639527.05492118.13211251.78657095.99999991 -.00088263J.00619907J.07855035J -.08386678J.00000000.02641002M.05526992M.15370059M.79102938M 39.00.01336902.06360601.16737181.75565297.99999981 -.00352893J.00348849J.061115973 -.06107552J.00000000.01382693M.06370160M.17818104M.75811715M 2

Institute of Science and Technology The University of Michigan 40.00.00430558.07048978.19114991.73405478 1.00000000 -.00200109J.00126061J.03637358J -.03563310J.00000000.00474789M.07050105M.19457987M.73491913M 41.00.00030389.07595315.20461330.71912978 1.00000010 -.00019805J.00009996J.00986229J -.00976421J -.00000000 *00036273M.07595321M.20485084M.71919605M 42.00.00072634.08031694.20992227.70903442 *99999998 -.00060418J.00026775J -.015264903 *01560133J -.00000000 *00094478M *08031739M.21047654M.70920604M 43.00 *00448902.08379486.20922335.70249266.99999989 -.00452474J.00184514J -.03744223J.04012183J -.00000000.00637374M.08381517M.21254724M.70363747M 44.00.01058416.08649614.20429686.69862283 1.00000000 -.01249868J.00481869J -.05604982J.06372980J -.00000000.01637808M.08663026M.21184614M.70152358M 45.00.01824465.08844394.19649411.69681743 1.00000010 -.02462734J.00912701J -.07098406J.08648440J.00000001.03064919M.08891362M.20892264M.70216385M 46.00.02695958.08959429.18678174.69666438.99999999 -.04079050J.01468402J -.082394093.10850058J.00000001.04889462M.09078963M.20414750M.70506285M 47.00.03643768.08985170.17581369.69789701 1.00000000 -.06077591J.02138893J -.09052780J.12991479J.00000001.07086195M.09236240M.19775170M.70988596M 48.00.04655982.08907895.16399724.70036400 1.00000000 -.08435441J.02912917J -.09564428J.15086951J -.00000001.09635084M.09372069M.18984973M.71642957M 49.00.05733573.08710264.15154277.70401898 1.00000010 -.11132387J.03777925J -.09796221J.17150684J.00000001.12522136M.09494284M.18044890M.72460838M 50.00.06886986.08371217.13849180.70892620 1.00000000 -.14154196J.04719777J -.09762404J.19196826J.000000003.15740769M.09610076M.16944153M.73445773M 51.00.08133581.07864972.12471668.71529774.99999995 -.17496428J.05722284J -.09465694J.21239835J -.00000003.19294562M.09726372M.15657007M.74616614M 52.00.09495888.07158247.10987544.72358329 1.00000000 -.21171523J.06766637J -.08890531J.23295417J.00000000.23203561M.09850273M.14133918M.76015815M 53.00.11000543.06202701.09325962.73470794 1.00000000 -.25226381J.07830634J -.07986859J.25382602J -.00000004.27520578M.09989611M.12278578M.77731808M 3

Institute of Science and Technology The University of Michigan 54.00.12677562.04910613.07328218.75083612 1.00000000 -,29798460J *08887559J -.06618618J.27529519J.00000000.32383156M.10153956M.09874659M.79971389M 55.00.14556326.03025690.04473519 *77944464.99999999 -.35418057J *09905513J -.04286956J.29799494J -.00000006.38292628M.10357315M *06195996M.83446685M 55.25.15056396 *02339158.03367479.79236963.99999996 -.37267679J.10151004J -.03294014J.30410686J -.00000003.40194214M.10417031M.04710673M.84872292M 55.50.15550075.01312809.01564181.81572942 1.00000000 -.39899226J.10399035J -.01581703J.31081897J.00000003.42822342M.10481573M.02224510M.87293924M IMAGINARY 55.75.13154457.00447633.02751256.83646663 1.00000000 -.42081791J.11846619J.02436510J.27798666J.00000004.44089871M.11855072M.03675050M.88144937M 56.00.12237973.00268010.04238401.83255629 1.00000010 -.42571568J.12696390J.03608675J.26266503J *00000000.44295669M.12699218M.05566559M.87300795M 57.00.11388840 -.00678991.07690186.81599966 1.00000000 -.44807438J *14993976J.06046715J.23766740J -.00000007.46232154M.15009341M.09782726M.84990660M 5.8.00.12027522 -.01906275.09958867.79919904 1.00000010 -,47242504J.16728980J.07516643J.22996881J.00000000.48749516M *16837239M.12477137M.83162777M 59.00.13424903 -.03390088.11738382.78226798.99999995 -.49767483J.18163331J.08657072J.22947077J -.00000003.51546390M.18476993M.14585421M.81523004M 60.00.15391673 -.05122148.13216700.76513778 1.00000000 -.52316412J.19340018J.09640754J.23335633J -.00000007.54533573M.20006816M.16359257M.79993186M 61.00.17848834 -.07094651.14474593.74771222.99999998 -.54832380J.20254676J.10544454J.24033246J -.00000004.57664293M.21461266M.17908080M.78538732M 62.00.20755048 -.09296532.15553079.72988399.99999994 -.57260145J.20884093J.11410028J.24966013J -.00000011.60905633M.22859808M.19289557M.77140185M 63.00.24083414 -.11711441.16474302.71153718.99999993 -.59543242J.21195091J.12262894J.26085249J -.00000008.64229342M.24215485M.20537312M.75784508M 4

Institute of Science and Technology The University of Michigan 64.00.27811624 -.14316299.17249945.69254737 1.00000000 -.61622862J *21148417J.13119262J *27355191J *00000008.67608161M.25538440M.21672001M.74461567M 65.00.31916679 -.17079948.17885171.67278094.99999996 -.63437449J.20701043J.13989367J.28747041J.00000002.71013972M *26837619M.22706424M.73162382M 66.00.36371376 -.19961856.18380816.65209668 1.00000000 -.64922605J.19807936J.14879101J *30235561J -.00000007.74416541M.28121700M.23648299M.71878299M 67.00.41141536 -.22910745.18734545 *63034660.99999996 -.66011446J.18423752J.15790722J.31796964J -.00000008.77782626M.29399606M.24501634M.70600391M 68.00.46183888 -.25863347.18941716.60737740.99999997 -.66635437J.16504782J.16723194J.33407455J -.00000006.81075477M.30680947M.25267643M.69319052M 69.00.51443941 -.28743198.18995954.58303314 1.00000010 -.66725462J.14011166J.17672219J.35042072J -.00000005.84254177M.31976306M.25945203M.68023695M 70.00.56853973 -.31459560.18889695.55715903 1.00000010 -.66213481J.10909628J *18630131J.36673713J -.00000009.87273130M.33297505M.26531158M.66702496M 71.00.62331152 -.33906578.18614694.52960738 1.00000000 -.65034635J.07176669J.19585669J.38272303J.00000006.90081497M.34657762M.27020460M.65342245M 72.00.67775994 -.35962980.18162665.50024330 1*00000000 -.63130151J.02802520J.20523672J.39803952J -*00000007.92622898M.36072011M.27406267M.63927992M 73.00.73070895 -.37492290.17525944.46895444.99999993 -.60450705J -.02204391J.21424749J.41230340J -.00000007.94834821M.37557037M.27679930M.62442962M 74.00.78079248 -.38343952.16698403.43566293.99999992 -.56960855J -.07812142J.22264995J.42508004J.00000002.96648372M.39131677M.27831037M.60868319M 75.00.82645303 -.38355704.15676483.40033909.99999991 -.52644170J -.13959513J.23015694J.43587984J -.00000005.97988033M.40817006M.27847339M.59182989M 76.00.86595054 -.37357527.14460518.36301959 1.00000000 -.47509168J -.20549621J.23643273J.44415520J.00000004.98771576M.42636506M.27714814M.57363495M 77.00.89738675 -.35177587.13056216.32382708 1.00000010 -.41596066J -.27443497J.24109376J.44930188J.00000001.98910376M.44616231M.27417636M.55383766M 5

Institute of Science and Technology The University of Michigan 78.00.91874359 -.31650504.11476458.28299694 1.00000000 -.34984161J -.34453699J,24371344J.45066520J *00000004.98309660M.46784738M.26938290M.53215259M 79.00.92795125 -.26628643.09743255.24090275 1.00000010 -.27799321J -.41339008J.24383129J.44755208J.00000008.96869692M.49173145M *26257722M.50826861M 80.00.92297978 -.19996146.07889751.19808424 1.00000000 -.20220737J -.47801180J *24096795J.43925120J -.00000002.94487009M.51815042M.25355545M.48184954M 81.00.90196341 -.11686515.05962304.15527875 1.00000000 -.12487233J -.53484147J.23464847J.42506544J.00000011.91056635M.54746037M.24210495M.45253963M 82.00.86335914 -.01702528.04022197.11344415.99999998 -.04900240J -.57978411J.22443299J.40435359J.00000007.86474865M.58003402M.22800871M.41996595M 83.00.80613572.09861738.02146815.07377880 1.00000000.02176433J -.60831085J.20995843J.37658809J.00000000.80642946M.61625276M.21105312M.38374718M 84.00.72998785.22798775.00429806.03772644 1.00000010.08322521J -.61563809J.19098824J.34142466J.00000002.73471674M.65649727M.19103659M.34350266M 85.00.63555954.36767743 -.01020116.00696409.99999989.13074052J -.59699503J.16747033J.29878425J.0000007.64886748M.70113462M.16778073M.29886539M 86.00.52465713.51280213 -.02082353 -.01663579 1.00000000 ~15944487J -.54798572J.13959884J.24894206J *00000005.54835003M.75050274M.14114338M.24949729M 87.00.40041753.65695654 -.02629855 -.03107547 1.00000010.16454909J -.46503849J *10787307J.19261636J.00000003.43290945M.80489297M.11103248M.19510701M 88.00.26739750.79230939 -.02537099 -.03433588 1.00000010.14172501J -.34591719J.07314621J.13104600J.00000003.30263410M.86453043M.07742129M.13546957M 89.00.13154206.90987745 -.01690385 -.02451564 1.00000010.08755419J -.19024842J.03665210J.06604215J.00000002.15801598M.92955442M.04036232M.07044559M 90.00 -.00000044 1.00000020.00000008.00000007.99999995 -.00000037J.00000078J -.00000015J -.00000028J -.00000002.00000058M OO00000Q1M o00000017M.00000029M 6

Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).800.250 *250.700 ANGLE ERP ERS ETP ETS ENERGY.00.00000000.07955294.00000000.92044712 1.00000000 1.00.00021203.07930729.00003151.92044907.99999991 2.00.00084535.07857311.00012609.92045536.99999993 3.00 *00189166.07735867.00028380.92046571.99999985 4.00.00333717.07567776.00050479.92048009.99999982 5.00.00516277.07354951.00078923.92049838.99999989 6.00.00734414.07099817.00113735.92052031.99999998 7.00.00985200.06805303.00154943.92054544.99999991 8.00.01265233.06474814.00202577.92057368.99999992 9.00.01570667.06112191.00256673.92060465.99999996 10.00.01897246.05721698.00317267.92063783.99999994 11.00.02240343.05307969.00384398.92067270.99999980 12.00.02594999.04875976.00458105.92070914.99999995 13.00.02955973.04430983.00538428.92074602.99999987 14.00.03317783.03978488.00625399.92078319.99999989 15.00.03674773.03524187.00719047.92081976.99999984 16.00.04021155.03073915.00819393.92085508.99999972 17.00.04351078.02633576.00926442.92088894.99999991 18.00.04658687.02209099.01040182.92092015.99999983 19.00.04938195.01806363.01160570.92094867.99999996 20.00.05183941.01431137.01287530.92097375.99999984 21.00.05390477.01089008.01420932.92099574.99999992 7

Institute of Science and Technology The University of Michigan 22.00.05552621 *00785303.01560574.92101483.99999982 23.00.05665558,00525027 *01706154.92103258,99999997 24.00.05724900 *00312771.01857226.92105096.99999994 25.00.05726769.00152636,02013144.92107438,99999988 26.00.05667865.00048139.02172952.92111024 *99999980 27.00,05545538 *00002116.02335240.92117099.99999994 28.00.05357828,00016609.02497877.92127679.99999994 29.00.05103452,00092725.02657536.92146280.99999993 30.00.04781670.00230443.02808814.92179073 1.00000000 31.00.04391813.00428311.02942384.92237496 1.00000000 32.00.03931831.00682843.03040709.92344610.99999994 33.00,03393279.00987004.03066144.92553571.99999999 34.00,02737914.01324540,02916974.93020567.99999996 35.00.01636597.01621066.02091213.94651113.99999989 35.25.00524338.01572861.01119798.96782996.99999995 IMAGINARY 35.50.01078471.01709862.00824543,96387117.99999994.01858441J.00281914J.01607993J -.03748349J.00000000.02148698M.01732947M.01807073M.96459973M 35.75.01863886.01923270.01115803.95097048 1.00000000.01991626J.00380115J.02582792J -.04954534J.00000000.02727754M.01960473M.02813509M.95226025M 36.00.02352831.02136440.01599775.93910952.99999999.01782621J.00433656J.03383078J -.05599355J.00000001.02951873M.02180007M.03742258M.94077731M 37.00.02489900.02940872,04475668.90093571 1,00000010.00449194J.00435064J.05038249J -.05922509J -.00000000.02530094M.02972879M.06739106M.90288025M 38.00.01495509.03617221,07388965.87498307 1.00000000 -.00213901J..00287552J,04676005J -.04749655J.00000000.01510728M.03628632M.08744245M.87627124M 39.00.00567021.04156506.09448329.85828149 1,00000000 -.00231346J.00124867J.03149831J -.03043352J -.00000000.00612400M.04158381M.09959536M.85882088M 8

Institute of Science and Technology The University of Michigan 40.00 *00074761.04579190.10484125.84861915.99999991 -.00049466J.00019183J.01185864J -.01155581J *00000000.00089644M.04579230M.10550978M *84869782M 41.00.00029432.04908396.10612748.84449431 1.00000000 -.00027303J *00008894J -.00743188J.00761597J.00000000.00040146M *04908404M.10638737M *84452864M 42.00.00317954.05159237.10020870 *84501947 1.00000000 -*00390009J.00114302J -.02365536J *02641244J.00000000.00503192M.05160503M.10296290M.84543214M 43.00 *00803847.05334682 *08871419.84990040.99999989 -.01275472J.00348405J -.03528062J *04455129J -.00000000.01507647M.05346047M.09547214M.85106727M 44.00.01357026.05421009.07259191.85962772.99999999 -.02800221J.00726118J -.04116570J.06190674J.00000000.03111713M.05469423M.08345179M.86185396M 45.00.01834643.05370901.05148872.87645596 1000000010 -.05173065J.01280920J -.03940333J.07832478J -.00000000.05488763M.05521534M.06483603M.87994875M 46.00.01834267.04954683.01887664.91323392 1.00000000 -.09403383J.02181384J -.02058112J.09280111J.00000000.09580613M.05413624M.02792687M.91793694M IMAGINARY 46.25 -.00028939.04724661.01199311.94104961.99999995 -.11574988J.02962569J.00865114J.07747303J -.00000001.11575023M.05576669M.01478773M.94423325M 46.50 -.01436391.05089843.02682241.93664302.99999995 -.11209466J.03448802J.01831726J.05928936J -.00000000.11301121M.06148230M.03248021M.93851764M 46.75 -.02188434.05342887.03533948.93311592.99999993 -.11122594J.03797064J.02328634J.04996894J -.00000001.11335843M.06554704M.04232178M.93445289M 47.00 -.02736555.05559575.04189491.92987483.99999994 -.11134675J.04104946J *02679784J.04349943J -.00000000.11466024M.06910822M.04973237M.93089172M 48.00 -.04151879.06273099.06077454.91801322.99999996 -.11641155J.05207478J.03533962J.02899714J.00000000.12359392M.08152889M.07030245M.91847106M 49.00 -.05043819.06856454.07501851.90685528 1.00000010 -.12553449J.06262983J.04030484J.02259979J -.00000001.13528828M.09286330M.08516019M.90713684M 9

Institute of Science and Technology The University of Michigan 50.00 -.05679395.07344886.08735988 *89598531 1.00000010 -.13734938J.07332478J *04371657J *02030801J -.00000001 *14862841M.10378467M *09768771M,89621542M 51.00 -.06134919.07740476.09866521 *88527922 1.00000000 -.15136881J.08434138J.04624664J.02078077J -.00000001 *16332862M.11447692M *10896594M.88552308M 52.00 -.06436652.08036251.10931332.87469079 1.00000000 -.16734995J.09573933J *04822013J.02339049J.00000000.17930157M.12499661M.11947628M.87500347M 53.00 -.06591305.08221542 *11949699.86420061 *99999996 -.18514362J.10752195J.04983221J.02778943J -.00000001.19652656M.13535266M.12947115M.86464729M 54.00 -.06596117.08283876.12932335.85379901.99999994 -.20463936J.11965694J.05121927J.03376315J.00000000.21500731M.14553364M.13909687M.85446632M 55.00 -.06442979.08209828.13885488.84347668 1.00000000 -.22574090J.13208368J.05248761J.04116960J -.00000000.23475551M.15551921M.14844401M.84448081M 56.00 -.06120461.07985521.14812865.83322073.99999997 -.24835174J.14471539J.05372726J.04990907J -.00000001.25578231M.16528580M.15757130M.83471413M 57.00 -.05614838.07596990.15716615.82301232.99999998 -.27236734J.15743932J.05501861J.05990943J.00000002.27809460M.17481007M.16651800M.82518992M 58.00 -.04910772.07030508.16597833.81282415 *99999983 -.29766769J.17011516J.05643634J.07111617J -.00000001.30169126M.18407056M.17531076M.81592929M 59.00 -.03991731.06272914.17456796.80262032 1.00000010 -.32411332J.18257349J.05805162J.08348819J -.00000001.32656213M.19304927M.18396728M.80695083M 60.00 -.02840349.05311965.18293097.79235278.99999991 -.35154010J.19461336J.05993326J.09699345J -.00000002.35268568M.20173263M.19249866M.79826728M 61.00 -.01438789.04136783.19105672.78196335 1.00000000 -.37975467J.20599964J.06214862J.11160642J.00000001.38002713M.21011222M.20091072M.78988775M 62.00.00230977.02738345.19892746.77137928.99999996 -.40853115J.21646088J.06476374J.12730652J -.00000001.40853767M.21818608M.20920438M.78181387M 63.00.02186693.01110099.20651779.76051416.99999987 -.43760505J.22568608J.06784370J.14407524J -.00000003.43815104M.22595892M.21737609M.77404099M 10

Institute of Science and Technology The University of Michigan 64.00.04445370 -.00751274.21379330.74926573.99999999 -.46666922J.23332257J.07145228J.16189437J.00000000.46878170M.23344348M.22541739M *76655652M 65.00.07022723 -.02844994.22070910.73751366 1.00000000 -.49536945J *23897422J.07565144J.18074378J -.00000001.50032264M *24066174M *23331448M *75933833M 66.00.09932445 -.05165114.22720833.72511835.99999999 -.52329865J.24219993J.08050053J.20059822J.00000003.53264136M.24764621M.24104763M.75235381M 67.00.13185215 -.07699145.23321993.71191937 1.00000000 -.54999175J.24251349J.08605494J.22142334J.00000002.56557573M.25444149M.24858999M.74555850M 68.00.16787621 -.10426578.23865652.69773300.99999995 -.57492087J.23938508J.09236432J.24317152J.00000005.59892940M.26110643M.25590643M.73889357M 69.00.20740748 -.13317009.24341219.68235048 1.00000000 -.59749104J *23224543J.09946979J.26577581J -.00000001.63246612M.26771666M.26295196M.73228338M 70.00.25038433 -.16328023.24735973.66553622 1.00000000 -.61703682J.22049322J.10740055J.28914305J.00000000.66590295M.27436780M.26966963M.72563224M 71.00.29665007 -.19402645.25034870.64702775 1.00000000 -.63282043J.20350718J.11616909J.31314417J.00000001.69890125M.28117865M.27598863M.71882138M 72.00.34592837 -.22466598.25220288.62653475 1.00000000 -.64403415J.18066554J.12576503J.33760358J.00000000.73105843M.28829644M.28182110M.71170356M 73.00.39779139 -.25425184.25271903.60374134.99999992 -.64980593J.15137337J.13614723J.36228531J -.00000002.76189614M.29590183M.28705918M.70409818M 74.0U.45162213 -.28159954.25166654.57831075.99999988 -.64921222J.11510244J.14723364J.38687603J -.00000011.79084705M.30421517M.29157124M.69578472M 75.00.50657183 -.30525471.24878883.54989400.99999995 -.64130077J.07144604J.15888895J.41096590J.00000012.81724029M.31350434M.29519752M.68649572M 76.0u.56151323 -.32346375.24380756.51814307 1.00000010 -.62512667J.02019272J.17090915J.43402486J.00000006.84028593M.32409341M.29774496M.67590666M 77.00.61498909 -.33415393.23643166.48273317.99999999 -.59980578J -.03857613J.18300398J.45537801J.00000008.85905677M.33637324M.29898225M.66362673M 11

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Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).900.250.250.700 ANGLE ERP ERS ETP ETS ENERGY.00.00000000 *05152624.00000000.94847382 1.00000000 1.00.00013410.05137761.00000996.94847824.99999992 2.00.00053487.05093333.00003985.94849191.99999996 3.00.00119758.05019794 *00008969.94851454.99999975 4.00.00211444.04917915.00015949.94854677.99999986 5.00.00327463.04788771.00024928.94858834.99999996 6.00.00466433.04633707.00035909.94863948.99999998 7.00.00626688.04454373.00048897.94870015.99999973 8.00.00806285.04252677.00063893.94877146 1.00000000 9.00.01003023.04030784.00080900.94885276.99999984 10.00.01214452 *03791098.00099920.94894519.99999989 11.00.01437898.03536250.00120952.94904883 *99999983 12.00.01670478.03269065.00143991.94916451.99999985 13.00.01909124.02992555.00169030.94929290 1.00000000 14.00.02150601.02709880.00196055.94943442.99999979 15.00.02391542.02424338.00225045.94959051.99999978 16.00.02628465.02139328.00255969.94976216.99999979 17.00.02857804.01858324.00288781.94995077.99999986 18.00.03075939.01584843.00323421.95015785.99999989 19.00.03279224.01322415.00359802.95038556.99999998 20.00.03464023.01074551.00397811.95063599.99999985 21.00.03626735.00844703.00437294.95091261.99999994 13

Institute of Science and Technology The University of Michigan 22.00 *03763835.00636230 *00478044.95121879 *99999989 23.00.03871903.00452361.00519783.95155938.99999986 24.00.03947655.00296144.00562138.95194039.99999978 25.0o.03987979.00170413.00604599.95236988.99999980 26.u0.03989959.00077727.00646468.95285834.99999989 27.0G.03950898.00020318.00686767.95342004 *99999988 28.00.03868319 *00000020.00724099.95407551.99999989 29.00.03739940.00018183.00756404.95485481 1.00000000 30.00.03563546.00075544.00780524.95580390 1.00000000 31.00.03336663.00172018.00791326.95699984.99999992 32.00.03055530.00306285.00779772.95858409.99999997 33.Ou.02711565.00474741.00727875.96085815.99999997 34.0.02273907 *00667607.00591667.96466803.99999986 35.0O.01472569.00835091.00203751.97488583.99999995 35.25.00508183.00792192.00000261.98699351.99999987 IMAGINARY 35.5u.01255732.00880410 -.00588844.98452699.99999996.01682674J.00198233J.00202829J -.02083737J -00000000.02099585M.00902451M.00622798M.98474747M 35.75.02071481.01024414 -.00821930.97726023.99999988.01581397J.00265950J.00844599J -.02691946J.00000000.02606118M.01058373M.01178523M.97763091M 36.0U.02485273.01168719 -.00738552.97084555.99999994.01176509J.00299655J.01490666J -.02966831J -.00000000.02749682M.01206522M.01663594M.97129875M 37.00.02009937.01696374.01009422.95284257.99999991 -.00303871J.00265563J.02781728J -.02743421J.00000000.02032778M.01717035M.02959213M.95323742M 38.00.00724475.02088873.02635143.94551496.99999987 -.00476673J.00125396J.02053107J -.01701830J -.00000000.00867226M.02092633M.03340543M.94566810M 39.0.00044394.02321776.02770189.94863632.99999993 -.00064614J.00011945J.00491972J -.00439302J.00000000.00078396M.02321807M.02813536M.94864648M 14

Institute of Science and Technology The University of Michigan IMAGINARY 40*00 -.00429272.02295396.00443313.97690547.99999984 -.00562937J.00244023J.00783769J -.00464855J -.00000000.00707935M.02308330M.00900455M.97691652M 41.00 -.01230400.02825040.01321764.97083603 1.00000000 -.00158868J.00600687J.01898655J -.02340475J -.00000000.01240614M.02888196M.02313429M.97111810M 42.00 -.01716979.03337653.01877174.96502140.99999988 -.00054829J.00863869J.02304400J -.03113440J.00000000.01717854M.03447637M.02972211M.96552351M 43.00 -.02170927.03871534.02401031.95898358.99999997 -,00083774J.01131220J.02570526J -.03617972J.00000000.02172542M.04033415M.03517464M.95966581M 44.0u -.02620891.04427228.02924882.95268783 1.00000000 -.00213524J.01417470J.02764310J -.03968256J.00000000.02629574M.04648609M.04024468M.95351392M 45.u0 -.03073504.05001433.03457198.94614873 1.0000000 -.00433199J.01728900J.02907161J -.04202862J.00000000.03103882M.05291826M.04517057M.94708173M 46.UU -.03529493.05589471.04000418.93939612 1.00000000 -.00739322J.02069427J.03008458J -.04338564J.00000000.03606094M.05960261M.05005414M.94039745M 47.00 -.03987236.06185864.04554806.93246571 1.00000000 -.01131732J.02442051J.03073260J -.04383579J.00000000.04144740M.06650453M.05494651M *93349551M 48.00 -.04443864.06784522.05119715.92539611.99999984 -.01611956J.02849319J.03104833J -.04342194J.00000000.04727190M.07358557M.05987610M.92641428M 49.00 -.04895696.07378819.05694115.91822773 1.O00U0010 -.02182450J.03293484J.03105654J -.04216688J.00000000.05360124M.08080470M.06485988M.91919540M 50.00 -.05338429.07961652.06276855.91099919.99999996 -.02846192J.03776563J.03077881J -.04008253J -.00000000.06049763M.08811942M.06990869M.91188054M 51.00 -.05767205.08525452.06866789.90374954.99999990 -.03606406J *04300309J.03023581J -.03717483J.00000000.06801972M.09548612M.07502989M.90451378M 52.00 -.06176649.09062209.07462878.89651562 1.00000000 -.04466410J.04866173J.02944848J -.03344612J -.00000001.07622323M.10286072M.08022884M.89713928M 53.00 -.06560866.09563474.08064231.88933154.99999992 -.05429508J.05475245J.02843860J -.02889598J -.00000000.08516133M.11019906M.08550986M.88980085M 15

Institute of Science and Technology The University of Michigan 54U00 -.06913433.10020351 *08670145.88222940 1.00000000 -~06498839J ~06128154J ~02722928J -~02352244J -.00000000 *09488439M.11745710M *09087670M.88254292M 55.00 -.07227373.10423536.09280136.87523693.99999992 -~07677354J ~06824998J.02584498J -.01732142J -.0000000.10544036M.12459161M.09633304M.87540831M 55.25 -.07298949.10514806.09433233.87350922 1.00000010 -.07989346J.07006018J ~02547461J -.01564132J ~00000000 *10821474M *12635087M.09771153M.87364924M 55.50 -.07367516 ~10601959.09586565.87178996 1.00000000 -.088308378J 07189742J.02509531J -.01390893J ~00000001.11104478M.12809914M.09909590M.87190090M 55.75 -.07432946.10684827.09740129.87008006 1.00000010 -.08634455J.07376134J.02470760J -.01212440J -~00000001.11393090M.12983561M.10048620M.87016453M 56.00 -.07495113.10763262.09893928.86837920.99999997 -.08967637J.07565187J.02431182J -.01028733J -.00000001.11687396M.13155982M.10188251M.86844012M 57.00 -.07708462.11029364.10511485.86167636 1.00000020 -.10371951J.08347378J.02265739J -.00241164J.00000002.12922761M.13832049M.10752901M.86167973M 58.00 -.07858537.11211219.11132977.85514349 1.00000000 -.11892002J.09169256J.02091110J.00631635J.00000000.14253993M.14483324M.11327661M.85516681M 59.00 -.07935736.11297806.11758794.84879153 1.00000010 -.13528955J.10027433J.01910426J.01591097J.00000002.15684658M.15105953M.11912974M.84894063M 60.0U -.07929661.11277696.12389517.84262434 *99999986 -.15283243J.10917210J.01727014J.02639019J.00000000.17217928M.15696238M.12509304M.84303749M 61.0u -.07829064.11139099.13025882.83664099 1.00000010 -.17154440J.11832367J.01544440J.03777635J.00000003.18856538M.16250675M.13117122M.83749340M 62.00 -.07621774 ~10869917.13668761.83083096 1.00000000 -.19141197J.12764945J.01366508J.05009742J -.00000000.20602836M.16766004M.13736898M.83233997M 63.00 -.07294642.10457841.14319126.82517682 1.00000000 -.21240896J ~13704911J.01197354J.06338633J.00000003.22458572M.17239229M.14369099M.82760775M 64.00 -.06833465.09890457.14977945.81965062.99999998 -.23449525J.14639823J.01041441J.07768262J.00000002.24424914M.17667641M.15014108M.82332358M 16

Institute of Science and Technology The University of Michigan 65.00 -.06222931.C9155468.15646183 *81421283 1.00000000 -.25761377J.15554483J *00903660J *09303235J3 00000001.26502328M *18048948M.15672257M.81951054M 66.00 -.05446573.08240935 *16324650 *80880992 1.00000000 -.28168683J.16430438J *00789373J *10948874J.00000002 *28690413M.18381303M *16343723M *81618703M 67.00 -.04486738.07135674.17013915.80337151 1.00000000 -.30661194J *17245492J *00704507J.12711190J -.00000005.30987733M *18663462M *17028494M.81336536M 68,Uu -.03324628.05829773.17714128.79780729 1.00000000 -.33225630J.17973090J *00655655J.14596.887J.00000002.33391549M.18894925M.17726257M.81105078M 69.00 -.01940348.04315326.18424876.79200153 1.00000000 -.35845074J.18581678J.00650131J.16613261J -.00000004.35897551M.19076183M.18436342M.80923819M 70.00 -.00313077.02587407.19144865.78580812 1.00000000 -.38498138J *19033956J.00696106J.18768078J.00000002.38499410M.19209012M.19157516M.80790993M 71.00.01578581.00645424.19871618.77904366 *99999990 -.41157921J.19286020J.008026823.21069212J -.00000007.41188182M.19296816M.19887822M.80703170M 72.00.03756129 -.01505040.20601088.77147829 1.00000000 -~43790911J.19286679J.00979947J *23524283J -00000002 *43951705M *19345312M *20624381M.80654691M 73.00.06240360 -.03849859.21327037.76282458 *99999996 -.46355433J.18976532J *01239013J.26139889J *00000001.46773585M *19363113M.21362997M.80636884M 74.00.09050051 -.06362995.22040376.75272552.99999984 -.48799913J.18287461J.01591940J.28920511J -.00000001.49631994M.19362823M.22097792M.80637168M 75.U0.12200039 -.09002184 *22728227.74073907.99999989 -.51060720J.17142306J.02051556J.31866853J -*00000005.52497980M *19362281M.22820630M.80637708M 76.00.15698425 -.11703178.23372750.72632010 1.00000000 -.53059837J.15455380J.02631007J.34973450J.00000000.55333414M.19386416M.23520366M.80613591M 77.00.19542526 -.14372251.23949736.70879993 1.00000000 -.54702268J.13134188J *03342974J.38225103J -.00000003.58088281M.19469681M.24181921M.80530316M 78.00.23712594 -.16876429.24426782.68737051.99999998 -.55873147J.10083144J.041983613.41591644J.00000002.60696751M.19659187M.24784953M.80340818M 17

Institute of Science and Technology The University of Michigan 79.00.28163419 -.19031300.24761241.66106642 1.00000000 -.56435495J.06210967J *05204002J *45020534J.00000008 *63072523M *20019153M *25302187M *79980851M 80.00,32812220 -.20586202.24897874.62876109 1,00000000 -.56229003J,01443311J *06359223J *48426467J -.00000002,65102554M *20636735M.25697156M.79363264M 81.00.37521576 -*21206965.24766571.58918816.99999998 -.55071284J -.04255695J *07650400J *51676581J,00000002 *66638689M.21629754M.25921258M.78370248M 82,00.42076870 -.20458334.24280771.54100687 *99999994 -.52764386J -.10849103J.09042779J *54570714J.00000004,67487357M *23156996M *25909992M *76843002M 83,00,46156624 -.17789856.23337689 *48295549 1.00000000 -.49110545J -.18173640J.10468651J.56815529J -,00000005.67396435M *25431479M.25578123M.74568521M 84,00.49296416 -.12534179.21822661.41415096.99999994 -.43943836J -.25859696J.11810698J,57992840J.00000006.66039361M.28737249M.24813728M *71262751M 85.00,50849872 -.03934622.19621651.33463094.99999995 -.37188143J -.33217400J.12880120J.57525433J.00000010.62997361M.33449617M.23471401M.66550387M 86.00.49957319.08768531.16647834.24626323 1.00000000 -.28954392J -.39086255J.13390675J.54649971J -,00000001 *57741583M *40057738M.21364937M.59942263M 87,OU.45545412.26146054.12891601.15416929.999999996 -.19692329J -,41660792J.12934047J.48419079J.00000005.49620282M.49185746M.18261515M.50814258M 88.00.36403519,48218526.08503892.06874064 1,00000000 -.10404014J -,38341613J.10970406J.37775222J *00000001.37861057M.61604427M.13880417M.38395573M 89,00.21409884,73864356.03918592.00807172 1,00000000 -.02898508J -.25731222J *06862584J.21767149J,00000003.21605195M.78217893M.07902558M.21782109M 90.00 -.00000074 1.0000080 -*00000010 -.00000013.99999990 -.00OU0000.00000119J -.00000031J -.00000098J -.00000011.00000074M 1.00000070M.00000033M,00000099M 18

Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).700 *250 *250.800 ANGLE ERP ERS ETP ETS ENERGY.00.00000000.07955294.00000000.92044709 1.00000000 1.00.00021679.07928824.00006304 *92043174.99999982 2.00.00086398.07849737.00025225 *92038631.99999991 3.00.00193204.07718999.00056780.92031002.99999987 4.00.00340520.07538233.00101003.92020219.99999976 5.00.00526158.07309668.00157938.92006230.99999995 6.00.00747345.07036139.00227644 *91988858.99999987 7.00.01000748.06721060.00310189.91967987.99999985 8.00.01282504.06368391.00405658.91943424.99999979 9.00.01588270.05982589.00514147.91914976.99999983 10o.U.01913256.05568584.00635762.91882401 1.00000000 11.00.02252284.05131714.00770625.91845365.99999989 12.Ou.02599842.04677683.00918867.91803585.99999977 13.00.02950143.04212495.01080630.91756714.99999983 14.00.03297193.03742396.01256069.91704314.99999973 15.00.03634863.03273812.01445346.91645950.99999972 16.00.03956963.02813267.01648634.91581118.99999984 17.00.04257320.02367318.01866109.91509228.99999977 18.00.04529862.01942479.02097954.91429678.99999974 19.00.04768711.01545133.02344350.91341787.99999982 20.00.04968261.01181457.02605473.91244790.99999982 19

Institute of Science and Technology The University of Michigan 21.00.05123288.00857332.02881482.91137900 1.00000000 22.00.05229036.00578263 *03172517.91020173.99999990 23.00.05281319.00349280.03478663.90890723.99999986 24.00.05276624.00174852.03799934.90748566.99999977 25.00.05212210.00058795.04136222.90592747.99999975 26.0o.05086214 *00004171.04487213.90422368.99999967 27.00.04897746 *00013191.04852263.90236788.99999989 28.00.04646960.00087104.05230153.90035778.99999996 29.00.04335120.00226073.05618647.89820151.99999991 30.00.03964547.00429024.06013617.89592799.99999987 31.00.03538362.00693420.06407132.89361073.99999989 32.00.03059589.01014853.06782835.89142712.99999990 63.0o.02527888.01386042.07102543.88983516.99999991 34.00.01924483.01793115.07254005.89028376.99999979 35.00.01048251.02182664.06611291.90157778.99999986 35.25.00318572.02196365.05349703.92135355.99999996 IMAGINARY 35.50.00578515.02345455.05482919.91593106.99999996.01138242J.00195713J *02381884J -.03715840J.00000000.01276823M.02353606M.05977941M.91668448M 35.75.01000344.02544590.06297199.90157873 1.00000000.01255665J.00256417J.03389595J -*04901677J.00000000.01605423M.02557477M.07151508M.90291021M 36.00.01261955.02739845.07177186.88821008.99999994.01166201J.00284804J.04073747J -.05524752J.00000000.01718300M.02754607M.08252722M.88992664M 37.00.01307633.03463050.10875032.84354280.9999995.00441829J.00257032J.05023585J -.05722447J.00000001.01380260M.03472575M.11979262M.84548157M 38.00.00723015.04075488.14145328.81056159.99999991.00028470J.00146097J.04176537J -.04351105J -.00000000.00723576M.04078106M.14749025M.81172858M 20

Institute of Science and Technology The University of Michigan 39.00.00205207.04580078.16570081.78644629.99999995 -.00037165J.00044631J.02372506J -.02379973J -.00000000.00208545M.04580295M.16739066M.78680632M 40.00.00001048.04993137.18109017.76896793.99999995 -.00000386J.00000249J.00175307J -.00175170J.00000000.00001117M.04993137M.18109865M.76896992M 41.0u.00141132.05331469.18882309.75645104 1.00000010 -.00076226J.00037036J -.02058861J.02098051J.00000000.00160402M.05331598M.18994222M.75674193M 42.00.00571471.05607308.19054687.74766537 1.00000000 -.00401505J.00165401J -.04127101J.04363206J.00000000.00698416M *05609747M.19496514M.74893742M 43.00.01218063.05827189.18782845.74171907 1.00000000 -.01047170J.00387971J -.05927936J.06587135J.00000000.01606314M.05840090M.19696083M.74463830M 44.00.02014270.05992367.18196449.73796911.99999998 -.02040299J.00703042J -.07421414J.08758670J -.00000000.02867072M.06033468M.19651670M.74314859M 45.00.02909787.06099711.17394881.73595629 1.00000000 -.03382396J.011064383 -.08601967J.10877926J.00000001.04461778M.06199248M.19405559M.74395200M 46.00.03871476.06142549.16450102.73535869.99999997 -.05062024J.01592442J -.09481196J.12950780J *00000001.06372787M.06345611M.18986809M.74667574M 47.00.04881094.06111364.15411389.73596173 1.00000020 -.07062750J.02154148J -.10077354J.14985957J.00000002.08585308M.06479902M.18413689M.75106428M 48.00.05932309.05994147.14309612.73763928.99999997 -.09368091J 02783514J -.10409010J.16993588J.00000001.11088437M.06608915M.17694984M.75696096M 49.00.07027846.05776543.13160570.74035038.99999997 -.11964772J.03471221J -.10490980J.18984528J -.00000003.13876108M.06739274M.16830367M.76430355M 50.00.08177168.05441539.11966751.74414544 1.00000000 -.14845573J.04206438J -.10331115J.20970249J -.00000001.16948661M.06877825M.15809334M.77312843M 51.00.09394612.04968490.10716981.74919926 1.00000010 -.18013222J.04976489J -.09926397J.22963130J.0000000.20315878M.07032164M.14607773M.78360070M 52.00u.10697907.04330686.09382508.75588904 1.00000000 -.21487883J.05766430J -.09255964J.24977415J -.00000002.24003631M.07211557M.13179694M.79608753M 21

Institute of Science and Technology The University of Michigan 53.00.12106692.03488976.07904413.76499921 1.000000 -.25325646J *06558489J -.08264379J.27031534J -.00000002 *28070631M *07428778M *11435895M.81135329M 54.u0.13639464.02371481.06151737.77837316.99999998 -.29677128J *07331300J -.06808982J.29154811J.00000001.32661397M *07705316M.09176388M.83118294M 55.00.15295557.00766219 *03698720.80239492.99999988 -.35101377J *08060185J -.04378548J *31419735J -.00000005.38289172M.08096522M.05731685M.86171780M 55.25.15713875 *00186979 *02766293 *81332865 1*00000010 -.36917405J.08233959J -.03354908J.32038355J.00000001.40122569M.08236081M.04348308M.87415622M 55.50.16086678 -.00673668 *01270293.83316698 1.00000000 -~39542358J.08411291J -.01603039J.32734103J -.00000003.42689334M..08438225M.02045331M.89516443M IMAGINARY 55.75.13486435 -.01392192.02730151.85175598.99999992 -.41572510J.09579728J.01946922J.30045853J -.00000007.43705348M.09680361M.03353242M.90319630M 56.00.12486796 -.01547916.04174476.84886656 1.00000010 -.41917876J.10247839J.02880192J.28789840J -.00000005.43738178M.10364084M.05071662M.89635925M 57.00.11342418 -.02364480.07469580.83552483 1.00000000 -.43696021J.12007437J.04834412J.26854168J -.00000004.45144132M.12238026M.08897537M.87761971M 58.00.11658723 -.03407617.09611770.82137121.99999997 -.45726431J.13297301J.06037342J.26391785J -.00000003.47189324M.13726982M.11350578M.86273013M 59.0C.12686050 -.04652993.11292032 *80674908.99999997 -.47871780J.14333519J.06992247J.26546012J -.00000002.49524166M.15069841M.13281623M.84930156M 60.00.14229185 -*06091450.12695843.79166414.99999992 -.50064524J.15151808J.07833678J.27079034J -.00000004.52047346M.16330433M.14918141M.83669558M 61.0U.16206520 -.07714889.13902321.77606044.99999996 -.52252301J.15749088J.08621049J.27882162J -.00000002.54707898M.17537197M.16358393M.82462797M 62.00.18575868 -.09512919.14951392.75985648.99999989 -.54387102J.16106943J.09386728J.28893423J -.00000008.57471903M.18706395M.17653747M.81293594M 22

Institute of Science and Technology The University of Michigan 63.00.21310978 -.11471057.15864491.74295579.99999991 -.56421311J.16198899J.10150463J.30071937J -.00000012.60311872M,19849168M.18833851M.80150822M 64.00.24391752 -.13569527,16652855.72524927 1.00000000 -.58306081J.15993599J,10924995J.31387490J,00000003.63202504M.20974443M.19916653M.79025562M 65.00.27799143 -.15782150.17321421.70661583.99999997 -.59990605J.15456636J.11718526J,32815438J -.00000005.66118567M.22090356M.20913045M.77909641M 66.00.31511827 -.18075241.17870930.68692481.99999997 -.61421720J.14551946J.12535961J.34333802J -.00000011.69033491M.23205031M.21829348M.76794966M 67.00.35503810 -.20406497.18299055.66603630.99999998 -.62543985J.13243137J,13379399J.35921440J -.00000009.71918499M.24327059M.22668562M.75672937M 68.00,39742469 -.22723944.18601177.64380295.99999997 -.63300095J.11494991J,14248364J.37556736J -.00000004.74741994M.25465907M.23431168M.74534091M 69.00.44186758 -.24964871.18770909.62007208 1,00000000 -.63631536J.09275168J.15139761J.39216600J -.00000007.77468974M.26632189M.24115542M.73367809M 70.00.48785413 -.27054881.18800534.59468937 1.00000000 -.63479590J.06556337J.16047757J.40875492J -.00000004.80060444M.27837962M.24718223M.72162041M 71.00.53475238 -.28907026.18681418.56750375 1.00000000 - 62786814J.03318671J.16963495J.42504640J -000000008.82472935M.29096902M.25234015M.70903099M 72.00.58179601 -.30421381.18404487.53837299 1.00000000 -.61498982J -.00447038J.17874795J.44071226J.00000001.84658081M.30424665M.25656060M.69575339M 73.00.62806925 -.31484896.17960755.50717213.99999997 -.59567592J -.04735804J.18765762J.45537628J -.00000006.86562161M.31839071M.25975806M,68160922M 74.00.67249375 -.31971925.17342026.47380519.99999995 -.56952986J -.09524171J.19616427J.46860724J -.00000006.88125597M.33360362M.26183011M.66639636M 75.00.71382138 -.31745644.16541723.43821769.99999986 -.53628251J -,14765380J.20402351J.47991266J -.00000014.89282690M.35011459M.26265653M.64988529M 76.00.75063250 -.30660660.15555951.40041459 1.00000000 -.49583892J -.20383972J.21094379J.48873485J.00000000.89961401M.36818233M.26209930M.63181768M 23

Institute of Science and Technology The University of Michigan 77.00.78134382 -.28567111.14384771.36047966 1.00000000 -.448332123 -.26270072J.21658447J.49444830J -.00000007 *90083287M.38809747M.26000191M *61190253M 78.00.80422632 -.25316623.13033739.31860244.99999992 -.39418508J -.32273429J.22055664J.49636270J -.00000003 *89563488M.41018356M.25618951M.58981644M 79.00.81744394 -.20770727.11515732.27510606 1.00000000 -.33417872J -.38197853J.22242741J.49372994J.00000010 *88311382M.43479870M.25046988M.56520137M 80.00.81911062 -.14811674.09852867.23047744.99999999 -.26951897J -.43796851J.22172803J.48575938J -.00000007.86231240M.46233643M.24263391M.53766349M 81.00.80737255 -.07356520.08078721.18540550 1.00000000 -.20190741J -.48770581J.21796947J.47164376J.00000001.83223616M.49322286M.23245916M.50677710M 82.00.78052280.01626191.06240405.14081125 1.00000000 -.13359511J -.52766452J.21066410J.45059554J.00000001.79187340M.52791504M.21971260M.47208488M 83.00.73714396.12097012.04400485.09788107 1.00000000 -.06742061J -.55383724J.19935788J.42189999J.00000002.74022074M.56689457M.20415678M.43310541M 84.00.67628469.23924529.02638301.05808694.99999993 -.00681106J -.56184270J.18367119J.38498260J.00000003.67631898M.61065990M.18555637M.38934006M 85.00.59765890.36864142.01050410.02319559 1.00000000.04426089J -.54710674J.16335115J.33949475J.00000005.59929556M.65971378M.16368852M.34028623M 86.0u.5U186032.50539220 -.00250497 -.00474761 1.00000000.08138888J -.50513205J.13833122J.28541191J -.00000004.50841708M.71454857M.13835389M.28545139M 87.0u.39057048 *64427808 -.01138522 -.02346333 1.00000000.09991948J -.43185918J.10879651J.22314321J.00000002.40314910M.77562657M.10939060M.22437339M 88.00.26673182.77858977 -.01479959 -.03052198 1.00000010.09522526J -.32411353J.07524806J.15364025J.00000004.28322025M.84335734M.07668963M.15664264M 89.00.13465187.90023125 -.01141320 -.02346991 1.00000000.06306315J -.18011410J.03855729J.07849366J.00000000.14868788M.91807264M.04021102M.08192736M 90.00 -.00000034 1.00W0Q2.O0000005 -.00000007.99999988 -.00000022J.000000673 -.00000017J -.0000036J -.00000008.00000041M 1.OOOOO0M.000O 8M.008M 00000037M 24

Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).800.250.250.800 ANGLE ERP ERS ETP ETS ENERGY.00.000 0000.04818561.00000000.95181440 1.00000000 1.00.00012920.04802924.00003040.95181105.99999990 2.00.00051500.04756199.00012165.95180117.99999981 3.00.00115188.04678933.00027387.95178471.99999980 4.00 *00203076.04572048.00048728.95176133.99999986 5.00.00313900.04436816.00076217.95173042.99999976 6.00.00446056.04274851.00109893.95169203 1.00000000 7.00.00597613.04088101.00149802.95164469.99999986 8.00.00766330.03878832.00196001.95158832.99999995 9.00.00949679.03649595.00248551.95152169.99999995 10.00.01144863.03403221.00307527.95144392 1.00000000 11,0.01348850.03142784.00373009.95135351.99999995 12.00.01558398.02871582.00445085.95124923.99999989 13.00.01770087.02593093.00523855.95112955.99999990 14.00.01980355.02310954.00609422.95099253.99999985 15.00.02185540.02028925.00701901.95083623.99999990 16.00.02381912.01750845.00801412.95065816.99999985 17.00.02565724.01480595.00908080.95045591.99999991 18.00.02733254.01222062.01022040.95022625.99999981 19.00.02880853.00979083.01143425.94996622.99999984 20.00.03005000.00755413.01272371.94967198.99999984 25

Institute of Science and Technology The University of Michigan 21.0U.03102354.00554670.01409014.94933943 *99999982 22.00 *03169807.00380285.01553478.94896407 *99999978 23.00.03204552 *00235456.01705871.94854114.99999994 24.00.03204144.00123092.01866273.94806475.999999=4 25.00.03166561 *00045754.02034708.94752959.99999983 26.00.03090287.00005603 *02211114.94692982.99999987 27.00 *02974378.00004332.02395278.94626010.99999999 28.0U *02818539.00043100.02586730.94551624.99999994 29.uO.02623199 *00122453.02784523.94469813.99999989 30.00.02389549.00242229.02986817.94381408 1.0000000 31.00.02119509.00401426.03189945.94289113.99999993 32.00.01815394.00597994.03386065.94200530.99999985 33.uu.01478495.00828370.03556247.94136892 1.00000000 34.0u.01101765.01085887.03642653.94169733.99999979 35.0.00584056.01346850.03306811.94762284 1.00000000 35.25.00178182.01377256.02612727.95831830.99999996 IMAGINARY 35.5U.00337672.01469957.02704833.95487540 1.00000000.00616042J.00085210J.01339267J -.02040519J.00000000.00702517M.01472424M.03018238M *95509339M 35.75.00565133.01583851.03196464.94654542..99999990.00647521J.00108226J.01903959J -.02659707J.00000000.00859452M.01587544M.03720543M.94691901M 36.00.00687182.01694810.03735066.93882947 1.00000000.00567876J.00116122J.02271896J -.02955895J -.00000000.00891461M.01698783M.04371754M.93929468M 37.00.00575270.02101816.05968898.91354011.99999996.00140420J.00085867J.02572262J -.02798549J.00000000.00592160M.02103569M.06499560M.91396865M 38.00.00197290.02444794.07772381.89585546 1.00000010 -.00014191J.00030928J.01686654J -.01703391J -.00000000.00197800M.02444990M.07953283M.89601738M 26

Institute of Science and Technology The University of Michigan 39.00.00003596.02728610.08844721 *88423079 1.00000000 -.00001164J.00000624J.00240546J -.00240006J -.00000000 *00003780M.02728610M.08847991M *88423404M 40.00.00106757.02962359.09184114.87746756.99999987 -.00059743J.00021056J -.01331297J.01369984J.00000000.00122337M.02962434M.09280102M.87757449M 41.00.00470080.03153053.08904048.87472834 1.00000010 -.00377104J.00107026J -.02753483J *03023561J.00000000.00602646M.03154869M.09320072M.87525074M 42.00.01005430.03302894.08138932.87552744 1.00000000 -.01076734J.00267952J -.03862578J.04671360J.00000000.01473176M.03313746M.09008980M.87677275M 43.00.01614790.03407651.07000514.87977052 1.00000000 -.02246731J.00512184J -.04555862J.06290410J.00000000.02766830M.03445927M.08352429M.88201649M 44.0U.02197409.03453512.05554538.88794541 1.00000000 -.03984541J.00851923J -.04737313J.07869931J -.00000000.04550294M.03557038M.07300344M.89142617M 45.00.02617942.03405306.03782082.90194665.99999995 -.06495961J.01315481J -.04219315J.09399795J.00000000.07003651M.03650561M.05666283M.90683150M 46.00.02394318.03106652.01271501.93227542 1.00000010 -,10793589J.02042284J -.02069367J.10820671J -.00000001.11055962M.03717824M.02428785M.93853404M IMAGINARY 46.25.00328605.02981545.01156710.95533139.99999999 -.12840431J /.02633398J.00529952J.09677079J -.00000001.12844635M.03977989M.01272331M.96022009M 46.50 -.01045550.03261690.02546974.95236883..99999997 -.12314100J.02964025J.01109647J.08240425J -.00000001.12358407M.04407275M.02778200M.95592722M 46.75 -.01768878.03448623.03324805.94995441.99999991 -.12128731J.03203940J.01403347J.07521441J -.00000001.12257040M.04707253M.03608838M.95292737M 47.00 -.02290447.03605167.03913465.94771801.99999986 -,12060012J.03417568J.01609592J.07032851J.00000000.12275587M.04967595M.04231548M.95032390M 48.00 -.03613979.04103283.05566149.93944534.99999987 -.12294631J.04189668J.02109277J.05995685J -.00000000.12814788M.05864320M.05952400M.94135666M 27

Institute of Science and Technology The University of Michigan 49.0 -.04434259,04494504.06782492.93157263 1.00000000 -.12944705J.04933669J.02400760J.05610275J -.00000000 *13683130M *06673954M.07194849M *93326045M 50.00 -.05019519.04810931.07825589.92383000 1.00000000 -.13846038J *05688569J.02602806J.05554660J -000000001 o14727808M.07450159M *08247087M.92549840M 51.00 -.05449049.05056816.08778805.91613424.99999996 -.14941444J.06465356J.02754165J.05721919J -.0000003.15904052M *08208058M *09200698M.91791937M 52.00 -.05752766.05228765.09678727.90845291 1.00000010 -.16203373J.07267031J.02873474J.06062867J -.00000000.17194290M.08952637M.10096267M.91047378M 53.00 -.05941441.05320259.10544109.90077065.99999993 -.17615855J.08092871J.02971995J.06550984J -.00000003.18590832M.09685026M.10954952M.90314965M 54.00 -.06016667.05323247.11385456.89307960.99999996 -.19168094J.08939769J.03057746J.07170577J -.00000001.20090199M.10404635M.11788910M.89595361M 55.00 -.05974950.05228864.12208969.88537105.99999989 -.20851662J.09802698J.03137165J.07911797J -.00000001.21690823M.11110081M.12605582M.88889906M 56.00 -.05809661.05027848.13018371.87763442 1.00000000 -.22658972J.10674839J.032158913.08768240J -.00000001.23391904M.11799637M.13409695M.88200361M 57.00 -.05512059.04710831.13815879.86985333 *99999984 -.24582453J.11547593J.03299154J *09735701J -.00000004.25192852M.12471520M.14204327M.87528463M 58.00 -.05071908.04268598.14602692.86200612.99999995 -.26613849J.12410458J.03391995J.10811392J -.00000004.27092825M.13124039M.14991472M.86875955M 59.00 -.04477831.03692326.15379256.85406243.99999995 -.28743874J.13250928J.03499394J.11993551J -.00000001.29090569M.13755739M.15772358M.86244254M 60.00 -.03717620.02973857.16145417.84598334.99999989 -.30961788J.14054311J *03626336J.13281138J -.00000003.31184179M.14365496M.16547652M.85634494M 61.00 -.02778477.02106017.16900474.83771987 1.00000000 -.33254993J.14803549J.03777860J.14673581J -.00000003.33370863M.14952603M.17317570M.85047396M 62.00 -.01647200.01082966.17643167.82921061.99999994 -.35608831J.15479063J.03959076J.16170686J -.00000006.35646907M.15516900M.18081914M.84483095M 28

Institute of Science and Technology The University of Michigan 63.00 -.00310480 -.00099354.18371649.82038172 *99999986 -.38006095J *16058515J *04175181J *17772398J -.00000001.38007362M.16058822M *18840106M *83941168M 64*00.01244836 -*01442690.19083390 *81114461.99999997 -.40426717J.16516653J *04431437J.19478629J.00000002 *40445877M.16579541M.19591156M *83420457M 65.00.03031412 -.02945854.19775093.80139356 1.00000000 -.42847437J.16825174J.04733149J.21289118J.00000004.42954537M.17081116M.20333642M.82918893M 66.00.05061021 -.04603970.20442543.79100400.99999994 -.45241349J.16952580J.05085609J *23203157J -.00000003.45523549M.17566630M.21065635M.82433365M 67.00.07343921 -.06407506.21080458.77983128 1.00000000 -.47577427J.16864137J.05494026J.25219263J -000000001.48140883M.18040378M.21784628M.81959621M 68.00.09888258 -.08341214.21682277.76770678.99999999 -.49820135J.16521940J *05963406J *27334794J.00000005.50791962M.18508115M.22487404M.81491888M 69.00.12699181 -.10382792.22240008.75443614 1.00000010 -.51928954J.15885114J.06498374J.29545464J -.00000002.53459194M.18977334M.23169955M.81022671M 70.00.15777812 -.12501347.22743897.73979641 1.00000000 -.53857960J.14910248J.07102966J.31844746J.00000000.56121468M.19457625M.23827231M.80542380M 71.00.19119778 -.14655512.23182282.72353457 1.00000000 -.55555362J.13552109J.07780295J.34222954J -.00000004.58753417M.19961054M.24453040M.80038948M 72.00.22713688 -.16791402.23541235.70536486 1.00000000 -.56963315J *117648303.08532159J.36666325J -.00000001.61324798M.20502741M.25039718M.79497265M 73.00.26539000 -.18840179.23804373.68496806 1.00000000 -.58017781J.09503633J.09358453J.39155699J.0000004.63799540M.21101454M.25577896M.78898550M 74.00.30563437 -.20715371.23952599.66199329.99999994 -.58648707J.06727361J.10256474J.41664871J -.00000001.66134668M.21780357M.26056136M.78219643M 75.00.34739919 -.22310023.23963968.63606132.99999996 -.58780675J.03402045J.11219965J.44158660J -.00000005.68279058M.22567920M.26460524M.77432081M 76.00.39002975 -.23493834.23813640.60677223 1.00000000 -.58334260J -.00494165J.12237930J.46590504J.00000009.70172059M.23499030M.26774173M.76500983M 29

Institute of Science and Technology The University of Michigan 77.00.43264517 -.24110540.23474131.57371899 1.00000000 -*57228379J -.04964342J.13293168J.48899551J -.00000002.71741938M *24616312M *26976714M *75383691M 78.00.47408772 -.23975861 *22915790.53651284.99999985 -.55383867J -.09983934J *14360424J *51007363J -.00000014.72903802M.25971539M.27043579M.74028449M 79.00.51287313 -.22877107.22108022.49481793 1.00000020 -.52729255J -.15489198J.15404285J.52814172J.00000004.73557887M 2762747M.26945438M.72372540M 80,00 *54713767 -.20574982.21020958.44840265 1.00000000 -.49208659J -.21362933J.16376651J.54194949J.00000008.73587284M.29659817M.26647239M.70340186M 81.00.57459013 -.16809632.19628535.39722074 *99999990 -.44793437J -.27416322J.17214105J.54995652J -.00000002.72855955M.32159266M.26107562M.67840731M 82.00.59248474 -.11312739 *17912850.34151419 1.00000000 -.39497398J -.33368297J.17835337J.55030354J -.0000004.71206924M.35233807M.25277845M.64766189M 83.00.59762464 -.03828484.15870366.28195664 1.00000010 -*33396956J -.38822446J.18138982J.54080415J -.000000005.68461002M.39010761M.24101684M.60989234M 84.00.58642874.05853179.13520420.21983531 1.00000000 -.26656046J -.432442243.18002890J.51897384J.00000004.64416856M.43638544M.22514568M.56361459M 85.00.55508711.17847539.10916292.i5727444.99999986 -.19555424J -.45942475J.17285681J.48212215J -.00000003.58852626M.49287377M.20444074M.50712622M 86.00.49985685.32107410.08158361 *09748541.99999997 -.12523664J -.46062862J.15832516J.42754008J -.00000002.51530678M.56148669M.17810879M.43851330M 87.00.41753331.48336312.05408671.04501675.99999989 -.06165563J -.42603489J.13486873J.35282181J *00000002.42206097M.64431796M.14530982M.35568206M 88.00.30614062.65886419.02904610.00594913 1.00000000 -.01279207J -.34467315J.10110780J.25635742J.00000000.30640776M.74357353M.10519725M.25642643M 89.00.16584060.83654468.00967443 -.01205969 1.00000000.01150834J -.20567564J.05615095J.13801637J.00000002.16623942M.86145775M.05697828M.13854224M 90.00 -.00000046 1.00000040 -.00000001 -.00000013.99999990 -e00000008J.00000082J -.00000024J -.00000060J -.00000010.00000047M 1.0000003QM *.00000024M.00000061M 30

Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).900.250.250.800 ANGLE ERP ERS ETP ETS ENERGY.00.00000000.02650081.00000000 *97349922 1.00000000 1.00.00006921.02642082.00000890 *97350088.99999983 2.00.00027599.02618167.00003562.97350663.99999993 3.00.00061769.02578596.00008021.97351588.99999975 4.00.00108997.02523802.00014271.97352907.99999978 5.00.00168675.02454382 *00022321.97354590.99999969 6.00.00240033.02371092.00032181.97356680.99999987 7.0U.00322138.02274856.00043865.97359123.99999984 8.00.00413907.02166741.00057388.97361955.99999992 9.00.00514110.02047959.00072766.97365148.99999985 10.00.00621382.01919853.00090019.97368723.99999978 11.00.00734234.01783897.00109166.97372681.99999979 12.00.00851061.01641669.00130229.97377009.99999968 13.00.00970158.01494848.00153230.97381754.99999991 14.00.01089733.01345198.00178193.97386865.99999991 15.00.01207921.01194561.00205140.97392369.99999992 16.00.01322800.01044827.00234092.97398261.99999981 17.00.01432408.00897931.00265068.97404567.99999976 18.00.01534758.00755824.00298083.97411317.99999983 19.00.01627863.00620469.00333145.97418511.99999990 20.00.01709748.00493807.00370255.97426181.99999992 31

Institute of Science and Technology The University of Michigan 21.00 001778475.00377750.00409399 *97434359.99999983 22.00.01832161.00274149.00450547.97443120.99999978 23.00.01869011.00184781.00493639.97452553 *99999984 24*00.01887323 *00111320.00538582.97462758 *99999984 25.00.01885532.00055314.00585227.97473910 *99999984 26.00.01862224.00018158.00633346.97486268.99999996 27.00.01816165.00001063.00682590.97500169.99999988 28.00.01746328.00005027.00732424.97516209.99999988 29.00.01651919.00030785.00782001.97535305 1.00000010 30.00.01532369.00078766.00829948.97558919 1.00000000 31.00.01387311 *00149014.00873878.97589797 1.00000000 32.00.01216351.00241062.00909282.97633286.99999981 33.00.01018181.00353661.00926318 *97701838.99999999 34.00.00785835.00483887.00897293.97832959.99999976 35.00.00446104.00619468.00671910.98262521 1.00000000 35.25.00145623 *00634522.00367294.98852544.99999985 IMAGINARY 35.50.00331421.00685744.00307554.98675272.99999991.00470382J.00047678J.00551572J -.01069633J -.00000000.00575413M.00687399M.00631522M.98681069M 35.75.00526775.00748795.00473937.98250481.99999989.00434842J.00059153J.00867978J -.01361975J.00000000.00683067M.00751128M.00988940M.98259920M 36.00.00603598.00809746.00714364.97872289.99999998.00319954J.00061518J.01091568J -*01473041J.00000000.00683155M.00812079M *01304545M.97883373M 37.00.00344513.01026030.01834714.96794739.99999998 -.00031593J.00035048J.01161783J -.01165238J *00000000.00345959M.01026629M.02171616M.96801752M IMAGINARY 38.00.00028536.01192496.02415005.96363937.99999974 -.00016501J.00003599J.00367998J -.00355096J.00000000.00032964M.01192501M.02442881M.96364591M 32

Institute of Science and Technology The University of Michigan 39.00.00071978.01304404.02000708.96622911 1.00000000 -.00095140J.00013625J -.00533655J.00615170J.00000000 *00119300M.01304475M *02070657M *96624868M 39.25 *00131553.01321096 *01708401 *96838956 1.00000000 -,00219864J.00029451J -.00671921J.00862335J.00000000 *00256216M.01321424M *01835787M *96842795M 39.50.00193444.01330051.01314202.97162315 1.00000010 -.00436921J.00055118J -.00723551J.01105354J.00000000.00477830M.01331192M.01500218M *97168602M 39.75.00220526.01323593.00754234.97701652 1.00000000 -.00838345J.00099801J -.00596940J.01335484J.00000000.00866865M.01327350M.00961876M.97710778M IMAGINARY 40.00 -.00500477.01353115.00524481.98622885 1.00000000 -.01329874J.00242541J.00393807J.00693525J.00000000.01420930M.01374680M.00655869M.98625322M 41.00 -.01311256.01699178.01364627.98247446.99999995 -.00873390J.00424265J.00935600J -.00486475J -.00000000.01575501M.01751344M.01654556M.98248649M 42.00 -.01703724.02009349.01787574.97906794.99999993 -.00785991J.00571142J.01127724J -.00912875J.00000000.01876288M.02088944M.02113571M.97911049M 43.00 -.02041911.02325352.02158947.97557609 *99999998 -.00814170J.00724104J.01250622J -.01160556J.00000000.02198243M.02435485M.02495017M.97564511M 44.00 -.02365724.02650561.02519778.97195390 1.00000000 -.00918394J.00889460J.01336430J -.01307496J -.00000000.02537735M.02795821M.02852249M.97204183M 45.00 -.02686343.02984245.02882187.96819904.99999993 -.01085420J.01069966J.01395109J -.01379654J.00000000.02897340M.03170259M.03202083M.96829733M 46.00 -.03007393.03324312.03250772.96432308.99999999 -.01310221J.01267359J.01430831J -.01387969J -.00000000.03280410M.03557703M.03551731M.96442295M 47.00 -.03329646.03667973.03627393.96034289 1.00000000 -.01591204J.01482948J.01445687J -.01337430J.00000000.03690322M.03956408M.03904867M.96043601M 48.00 -.03652519.04011965.04012723.95627842 1.00000010 -.01928458J.01717809J.01440895J -.01230245J.00000000.04130356M.04364256M.04263581M.95635755M 33

Institute of Science and Technology The University of Michigan 49.00 -.03974648.04352637 *04406856.95215156 1.00000000 -.02322977J.01972842J.01417296J -.01067161J -.00000000,04603699M *04778865M *04629159M *95221135M 50.00 -.04294159.04686017.04809612.94798546 1.00000010 -.02776279J.02248796J.01375572J -.00848090J -.00000000.05113465M.05197676M.05002456M *94802339M 51.00 -.04608776.05007819 *05220665.94380289.99999997 -.03290164J.02546246J.01316374J -.00572458J -.000000001.05662685M.05617973M.05384068M.94382025M 52.00 -.04915888.05313474.05639648.93962790 1.00000020 -.03866585J.02865572J.01240385J -.00239373J -*00000000.06254313M.06036929M.05774443M.93963094M 53.00 -.05212579.05598130.06066197.93548241 *99999989 -.04507579J.03206929J.01148342J.00152307J -.00000000.06891244M.06451624M.06173932M.93548364M 54.00 -.05495629.05856660.06499986.93138985 1.00000000 -.05215152J.03570187J.01041087J.00603878J.00000001.07576262M.06859060M.06582832M.93140942M 55.00 -.05761528.06083688.06940767.92737056.99999983 -.05991273J.03954898J.00919553J *01116819J -.00000002.08312074M.07256203M.07001416M.92743780M 56.00 -.06006456.06273583.07388371 *92344530 1.00000020 -.06837770J.04360216J.00784813J.01692738J -.00000001.09101242M *07639982M.07429936M.92360042M 57.00 -.06226277.06420471.07842726 *91963071.99999991 -.07756362J.04784843J.00638032J.02333485J -.00000001.09946239M.08007320M.07868636M.91992670M 58.00 -.06416508.06518248.08303867.91594383.99999990 -.08748517J.05226926J.00480537J.03041054J.00000000.10849338M.08355137M.08317760M.91644852M 59.00 -.06572320.06560620.08771943.91239749.99999993 -.09815492J.05683991J.00313792J.03817712J.0000003 011812674M.08680408M.08777554M.91319585M 60.00 -.06688484.06541099.09247208.90900151.9999974 -.10958213J.06152811J.00139412J.04665989J.00000000.12838156M.08980148M.09248258M.91019826M 61.00 -.06759362.06453065 *09730009.90576291 1.00000000 -.12177210J.06629287J -.00040801J.05588725J.00000000.13927434M.09251459M.09730095M.90748544M 62.00 -.06778866.06289821.10220809.90268233.99999997 -.13472641J.07108340J -.00224875J.06589175J -.00000000.15081945M.09491593M.10223282M.90508403M 34

Institute of Science and Technology The University of Michigan 63.00 -.06740425.06044652.10720129.89975645 1.00000000 -*14844048J.07583696J -.00410597J *07670951J.00000002.16302732M.09697952M.10727989M.90302049M 64.00 -,06636943.05710950.11228549.89697456 1.00000010 -.16290367J.08047738J -.00595526J.08838159J.00000003 ~17590482M.09868183M.11244330M *90131829M 65.00 -.06460771.05282342.11746672.89431751.99999995 -.17809746J.08491274J -.00776937J.10095409J.00000000.18945411M.10000244M.11772337M.89999751M 66.00 -.06203668.04752893.12275095.89175679 1.00000000 -o19399400J.08903310J -.00951772J.11447861J -000000001.20367184M.10092518M.12311938M.89907481M 67.00 -.05856758.04117371.12814317.88925067.99999998 -.21055392J.09270756J -.01116606J.12901240J -.00000002.21854774M.10143946M.12862874M.89856048M 68.00 -.05410534.03371593.13364686.88674256 1.00000000 -.22772384J.09578104J -.01267572J.14461854J.00000002.23406310M.10154197M.13424662M.89845806M 69.00 -.04854828.02512917.13926314.88415612 1.00000010 -.24543347J.09807107J -.01400315J.16136552J -.00000003.25018897M.10123936M.13996538M.89876074M 70.00 -.04178842.01540868.14498890.88139086 1.00000000 -.26359149J.09936366J -.01509899J.17932678J -.00000004.26688339M.10055131M.14577297M.89944868M 71.00 -.03371235.00458001.15081538.87831689.99999993 -.28208026J.09940910J -.01590732J.19857846J -.00000002.28408765M.09951455M.15165197M.90048540M 72.00 -.02420233 -.00728944.15672603.87476576 1.00000000 -.30075069J.09791833J -.01636501J.21919735J -.00000002.30172293M.09818929M.15757811M.90181073M 73.00 -.01313854 -.02007570.16269287.87052130.99999992 -.31941398J.09455852J -.01640080J.24125626J.00000000.31968407M.09666617M.16351744M.90333377M 74.00 -.00040337 -.03357752 *16867279.86530800.99999990 -.33783203J.08895033J -.01593490J.26481658J -.00000002.33783226M.09507687M.16942382M.90492306M 75.00.01411256 -.04748978.17460179.85877539.99999996 -.35570535J.08066643J -.01487876J.28991764J -.00000004.35598519M.09360744M.17523459M.90639251M 76.00.03050088 -.06136808.18038803.85047922 1.00000000 -.37265882J.06923420J -.01313563J.31656022J -.00000003.37390493M.09251711M.18086565M.90748293M 35

Institute of Science and Technology The University of Michigan 77.00.04882163 -.07458218.18590305.83985759 1.00000000 -.38822457J,05414465J -.01060264J.34468252J -.00000004 *39128234M *09216368M,18620515M *90783633M 78.00.06907980 -.08625418.19096848.82620580.99999991 -.40181795J.03487023J -.00717435J.37412203J -.0000004.40771272M.09303610M *19110319M.90696378M 79.00.09119422 -.09517920.19534172.80864336 1.00000010 -.41271421J.01090235J -.00275062J.40456247J -.00000001.42266937M.09580157M.19536108M.90419846M 80.00.11494912 -.09972293.19869486.78607895 1.00000000 -.42001823J -.01818620J.00275069J.43545376J.00000002.43546367M.10136764M.19871389M.89863234M 81.00.13992138 -.09769199.20059051.75718016 1.00000000 -.42263363J -.05263185J.00937199J.46589344J -.00000005.44519341M *11096772M.20080932M.88903233M 82.00.16537822 -.08617740.20045153.72034766 1.00000000 -.41923504J -.09230265J.01708034J.49445735J.00000000.45067501M.12627875M.20117791M.87372124M 83.00.19012356 -.06137285.19752739.67372199 1.00000000 -.40825144J -.13641096J.02571085J.51895144J -.00000011.45035119M.14958133M.19919366M.85041867M 84.00.21228105 -,01838830.19085979.61524734.99999988 -.38787836J -,18305857J.03487762J.53605925J -.00000006.44216836M.18397980M.19402037M.81602010M 85.u0.22898603.04889383.17925918,54286094.99999998 -.35615625J -.22852846J.04383615J.54084863J.00000007.42341689M.23370037M.18454122M.76629970M 86.00.23596532,14781270.16131148.45491047,99999997 -.31117137J -.26620975J.05127668J.52610448J.00000004.39052176M.30449339M,16926514M.69550662M 87.00.22699033.28655410.13545949.35099607.99999999 -.25149128J -.28501411J.05502267J.48148269J -.00000003.33878085M.40416121M.14620795M.59583875M 88.0'.19323668.47298933.10023880.23353519 1.00000000 -.17700906J -.26716551J.05161596J.39255856J -.00000005.26205461M.54322768M.11274761M.45677226M 89.00.12269096.71198671.05480859.11051378 1.00000000 -.09046526J -.18538981J.03579915J.24005596J.00000004.15243699M.73572716M.06546419M.26427288M 90.00 -.00000075 1.00000100 -.00000026 -.00000020.99999990.000000403.00000109J -.000000193 -.00000120J.00000009.00000086M 1.00O00090M.00000033M.00000122M 36

Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).700.250.250.900 ANGLE ERP ERS ETP ETS ENERGY ~00 ~.00000000 05152621.00000000.94847369.99999990 1.00.00014197.05134447.00006238.94845091.99999974 2.00.00056561 ~05080152.00024962 ~94838320.99999996 3.00.00126412.04990444.00056197.94826924.99999977 4.00.00222621.04866492.00099986.94810896.99999996 5.uO.00343627.04709920.00156390.94790048.99999986 6.O0.00487451.04522773.00225489.94764274.99999988 7.u00.0651720 *04307531.00307378.94733349.99999978 8.00.00833686.04067052.00402173.94697080.99999992 9.00.01030268.03804560.00510009.94655143.99999981 10.00.01238074.03523609.00631043.94607255.99999981 11.0'.01453452.03228051.00765449.94553033.99999986 12.00.01672525.02921985.00913426.94492045.99999982 13.00.01891241.02609723.01075198.94423821.99999984 14.00.02105428.02295736.01251010.94347805.99999980 15.U0.02310843.01984614.01441137.94263376.99999971 16.00.02503236.01681001.01645882.94169867.99999988 17.0u.02678412.01389547.01865583.94066437.99999979 18.0u.02832290.01114846.02100607.93952237.99999981 19.00.02960986.00861380.02351368.93826246.99999980 20.Ou.03060870.00633449.02618315.93687352.99999987 37

Institute of Science and Technology The University of Michigan 21.oU.03128654 400435118.02901955.93534273 1.00000000 22.ou.03161471.00270142.03202844.93365531.99999988 23.0U.03156947.00141904.03521601.93179540.99999992 24.00.03113303.00053346.03858914.92974425.99999989 25.00.03029438.00006899.04215547.92748100.99999985 26.0u.02905030.00004416.04592340.92498200.99999986 27.00.02740634.00047092.04990205.92222063.99999995 28.00.02537782.00135397.05410085.91916718.99999984 29.00.02299112.00268994.05852862.91579028.99999997 30.00.02028449.00446644.06319121.91205775.99999990 31.00.01730882.00666110.06808477.90794527.99999997 32.00.01412696.00923989.07317744.90345570 1.00000000 33.0u.01080723.01215424.07834870.89868968.99999985 34.00.00738561.01533152.08312430.89415841.99999985 35.0u.00340887.01859290.08415027.89384776.99999981 35.25.00097251.01919909.07770959.90211885 1.00000000 IMAGINARY 35.5U.00160015.02021206.08133254.89685516.99999992.00330803J.00052247J.01511861J -.01894911J.0000000.00367471M.02021881M.08272578M.89705531M 35.75.00260778.02134205.08901438.88703575.99999997.U0347008J.00063420J.02020905J -.02431334J.00000000.00434074M.02135147M.09127960M.88736889M 36.UU.00306855.02243630.09666262.87783238.99999986.00303948J.00064701J.02282766J -.02651415J.00000000.00431908M.02244563M.09932152M.87823270M 37.Uu.00199968.02643215.12498434.84658384 1.00000000.00079326J.00034976J.02076886J -.02191188J.00000000.00215128M.02643446M.12669818M.84686736M 38.00.00023512.02982545.14708234.82285708.99999999.00002394J.00004081J.00765196J -.00771672J.00000000.00023633M.02982547M.14728125M.82289325M 38

Institute of Science and Technology The University of Michigan 39.00,00040238.03268030.16190097.80501630.99999995 -.00004471J.00007318J -.01042339J.01039491J -.00000000 oUU040485M *03268038M *16223615M.80508340M 40,OU.00318311.03507328 *17001234.79173125,99999999 -.00091961J.00062053J -.02986528J.03016436J.00000000.00331329M.03507877M.17261555M.79230565M 41.00.00836444.03706126.17260943.78196502 1,00000010 -.00375178J.00176532J -.04852972J.05051618J.00000000.00916732M.03710328M.17930183M.78359502M 42.00.01542368.03867101.17097810.77492712.99999991 -.00922133J.00353748J -.06523866J.07092250J -.00000001.01797005M.03883247M.18300162M.77816581M 43.0.02381362.03989919.16626307.77002404.99999993 -.01764145J.00593605J -.07943190J.09113730J -.00000000.02963628M.04033835M *18426295M.77539862M 44.00.03308009.04071595.15939069.76681328 1*00000000 -.02908783J.00894126J -.09091987J.11106644J.00000000.04404991M.04168614M.18349881M.77481504M 45.00.04289514.04106924.15106625.76496942 1.00000000 -.04350210J.01252080J -.09971792J.13069921J -.00000001.06109358M.04293545M.18101015M.77605443M 46.00.05305254.04088851.14179987.76425903.99999995 -.06076373J.01663244J -.10594002J.15007134J *00000003.08066476M.04414191M.17700421M.77885381M 47,00.06344907.04008738.13193995.76452357.99999998 -.08073662J.02122460J -.10973220J.16924423J.00000001.10268489M.04535948M,17160800M.78303249M 48.00.07406334.03856437.12170226.76566998.99999996 -.10330013J.02623574J -.11123019J.18829457J -.00000001.12710741M.04664252M.16487448M.78848294M 49.00.08493582.03620236.11119186.76766999 1.00000000 -.12837223J.03159283J -.11052974J.20730914J.00000000.15392700M.04804912M *15678154M.79516934M 50,00.09615222.03286472.10041382.77056923 1.00000000 -.15593437J.03720950J -.10765953J.22638442J.0000002.18319600M.04964511M.14721925M.80313562M 51.00.10782899.02838610,08926822.77451664.99999995 -.18606985J.04298343J -.10254384J.24563026J.00000000.21505599M.05151064M.13595607M.81253323M 52.00.12009883.02255124.07751786.77983203.99999996 -.21904119J.04879330J -.09493280J.26518068J -.00000001.24980546M.05375262M.12256123M.82368609M 39

Institute of Science and Technology The University of Michigan 53.00.13308944.01504039 *06468863.78718147.99999993 -.25548129J.05449467J -.08423385J.28522046J -.00000001.28806854M.05653213M.10620716M.83726064M 54.00 *14686503 *00525735.04974226.79813533 *99999997 -.29699718J *05991546J -.06898317J.30606488J -.00000001 *33132561M *06014567M *08504687M *85480741M 55.00.16108543 -.00857817.02934892.81814374.99999992 -.34938891J *06486763J -.04403284J *32855406J -.00000006 *38473512M.06543237M.05291739M.88165012M 55.25.16440382 -.01352778.02177460.82734932.99999996 -.36718824J.06602858J -.03364362J.33480326J -.00000002.40231307M.06740011M.04007526M.89252457M 55.50.16683039 -.02084641.00985685.84415914.99999997 -.39325747J.06723803J -.01599845J.34201790J.00000001.42718123M.07039549M.01879117M.91081331M IMAGINARY 55.75.13903970 -.02686462.02677877.86104616 1*00000000 -.41177101J.07677732J.01478640J.32020731J.00000002.43461176M.08134166M.03058987M.91865837M 56.00.12843445 -.02819145.04070183.85905519 1.00000000 -.41379412J.08203693J.02182550J.30993168J -.00000001.43326778M.08674570M.04618432M.91325432M. 57.00.11470532 -.03517857.07200743.84846575.99999993 -.42719696J.09536605J.03663097J.29519987J -.00000007.44232855M.10164750M.08078922M.89835243M 58.0o.11527769 -.04401349.09215708.83657872 1.00000000 -.44370013J.1046959J-.04593077J.29307345J -.00000001.45843074M.11357120M.10296875M.88642878M 59.00.12252630 -.05444114.10794775.82396706.99999997 -.46159343J.11184676J.05349260J.29625400J -.00000007.47757845M.12439266M.12047478M.87560730M 60.00.13445892 -.06635953.12119353.81070700.99999992 -.48015749J.11712574J.06031086J.30272082J -.00000007.49862853M.13461807M.13537086M.86538184M 61.00.15023891 -.07968265.13266588 *79677781.99999995 -.49889095J.12051653J.06682187J.31155255J.00000000.52102198M.14447684M.14854426M.85552315M 62.00.16943470 -.09430885.14275397.78212009.99999991 -.51736402J.12187616J.07326332J.32222440J -.00000014.54440209M.15410372M.16045625M.84589621M 40

Institute of Science and Technology The University of Michigan 63.00.19178441 -.11010526.15166746.76665334.99999995 -.53516704J *12099603J.07978119J.33438975J -.00000007.56849364M.16359464M.17137110M.83640530M 64.00.21709853 -.12689710.15951753.75028106 1.00000000 -.55188982J.11762806J.08647089J.34779084J -.00000003.59305492M.17302957M.18144712M.82697045M 65.0C.24521081 -.14445855.16635472.73289299.99999997 -.56711038J.11149993J.09339520J.36221524J -.00000001 *61785315M.18248426M.19077881M.81751575M 66.00.27594700 -.16250371.17218942.71436729 1.00000000 -.58038969J.10232615J.10059290J.37747063J -.00000001.64264992M.19203670M.19941947M.80796330M 67.00.30910314 -.18067724.17700229.69457184 1.00000000 -.59126975J.U89818583.10808221J.39336891J -.00000005.66719162M.20177126M.20739232M.79822875M 68.00.34442859 -.19854572.18075189.67336522.99999998 -.59927496J.07369836J.11586196J.40971460J -.00000004.69120295M.21178255M.21469802M.78821746M 69.U0.38161056 -.21558853.18337890.65059909 1.0000000 -.60391547J.05370901J.12391085J.42629548J -.00000013.71438120M.22217801M.22131814M.77782197M 70.00.42025858 -.23118953.18481001.62612100 1.00000000 -.60469325J.02963329J.13218598J.44287397J -.00000001.73639065M.23308095M.22721767M.76691907M 71.00.45988937 -.24462915.18496108.59977881 1.00000010 -.60111165J.00131251J.14062020J.45917895J.00000001.75685761M.24463266M.23234595M.75536741M 72.00.49991374 -.25507936.18374059.57142509 1.00000000 -.59268832J -.03132867J.14911882J.47489818J.00000001.77536648M.25699604M.23663690M.74300397M 73.00.53962152 -.26160063.18105369.54092540.99999998 -.57897246J -.06825397J.15755610J.48967023J -.00000010.79145466M.27035808M.24000909M.72964184M 74.00.57816820 -.26314334.17680725.50816785.99999996 -.55956706J -.10928102J.16577112J.50307692J -.00000004 *80460782M.28493290M.24236515M.71506709M 75.00.61456452 -.25855563.17091609.47307490.99999988 -.53415721J -.15404198J.17356346J.51463573J.00000000.81425639M.30096502M.24359101M.69903489M 76.00.64766871 -.24659989.16331119.43562009 1.00000010 -.50254514J -.20193832J.18068945J.52379402J.00000001.81977215M.31873278M.24355537M.68126723M 41

Institute of Science and Technology The University of Michigan 77.00.67618531 -*22598047 15394960.39584558 1.00000000 -.46469119J -.25209185J *18685868J.52992429J -.00000007.82046600M *33855201M *24210874M *66144801M 78.00.69866872 -.19538499.14282715.35388909.99999997 -.42076333J -.30329114J.19173201J.53232241J -.00000005.81558553M.36077806M.23908316M *63922190M 79.00.71354161 -.15354592.12999362.31001080 1.00000010 -.37119441J -.35393828J.19492166J.53021102J -.00000001.80431767M.38580909M.23429211M.61419086M 80. U.71912633 -.09932123 *11556991.26462500 1.00000000 -.31674080J -.40200122J.19599422J.52274778J -.00000002.78579094M.41408897M.22753052M.58591094M 81.00.71369370 -.03180333.09976882.21834089 1.00000000 -.25855145J -.44497095J.19447845J.50904399J.00000004.75908336M.44610604M.21857650M.55389396M 82.CO.69553803.04954686.08291638.17199874 1.00000000 -.19822820J -.47984307J.18987860J.48819257J -.00000010.72323409M.48239429M.20719317M.51760559M 83.00.66307662.14473706.06547426.12671215 1.00000000 -.13788368J -.50312470J.18169580J.45931254J -.00000004.67726102M.52352962M.19313270M.47647032M 84.00.61498040.25305671.04805987.08390297.99999995 -.08017986J -.51088571J.16945772J.42160794J.00000009.62018521M.57012446M.17614105M.42987551M 85.00.55033372.37287363.03146280.04532990 1.00000000 -.02834034J -.49886683J.15275944J.37444772J -.00000001.55106294M.62281847M.15596587M.37718152M 86.00.46882110.50142906.01665161.01309820.99999997.01388218J -.46266084J *13131421J.31746444J -.00000001.46902657M.68226545M.13236577M.31773452M 87.00.37093045.63465487.00476803 -.01035336 1.00000000.04229238J -.39797774J.10501395J.25067140J -.00000001.37333368M.74911486M.10512213M.25088511M 88.00.25815670.76704395 -.00289821 -.02230243 1.00000000 *05241324J -.30100200J.07399696J *17459184J *00000004.26342367M.82398945M.07405369M.17601053M 89.00.13318217.89161293 -.00495814 -.01983693 1.00000010.03972687J -.16883450J.03871595J.09039168J *00000000.13898098M.90745727M.03903214M.09254274M 90.00 -.C0000070 1.00Q0020.000000Q3.00000026.99999979 -.0000002J.O0000081J -.00000015J -.00000030J.00000009.00000075M 1.OOOOOO10M.00000015M.00000040M 42

Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC) *800.250.250.900 ANGLE ERP ERS ETP ETS ENERGY.00.00000000.02650081.00000000.97349920 1.00000000 l.ou.*0007210.02640807.00002913.97349059.99999989 2.00.00028726.02613095.00011658.97346501.99999982 3.00.00064205.02567296.00026252.97342212.99999966 4.00.00113075.02504000.00046724.97336179.99999978 5.00.00174547.02424011.00073113.97328316.99999987 6.00.00247618.02328359.00105471.97318553 1.00000000 7.00.00331084.02218282.00143862.97306749.99999978 8.00.00423550.02095211.00188363.97292864.99999989 9.00.00523444.01960771.00239065.97276717.99999998 10.0.00629036.01816752.00296070.97258128.99999987 11.00.00738453.01665096.00359497.97236939.99999986 12.00.00849703.01507884.00429482.97212919.99999989 13.00.00960696.01347303.00506174.97185810.99999983 14.00.01069267.01185642.00589744.97155328.99999983 15.00.01173210.01025251.00680383.97121138.99999982 16.00.01270294.00868524.00778300.97082865.99999984 17.0U.01358308.00717874.00883735.97040069.99999987 18.0u.01435087.00575700.00996953.96992241.99999982 19.00.01498546.00444361.01118250.96938837.99999995 20.00.01546725.00326145.01247965.96879160.99999996 43

Institute of Science and Technology The University of Michigan 21.00.01577826.00223235 *01386475.96812457.99999993 22.00.01590256.00137678.01534214 *96737836.99999985 23.00.01582684.00071351.01691678.96654265.99999979 24.00.01554084.00025922.01859442.96560529.99999979 25.00.01503802.00002816.02038179.96455188.99999986 26.00.01431622.00003170.02228684 *96336508 *99999985 27.00.01337842.00027797.02431913 *96202438.99999992 28.00.01223368.00077135 *02649030.96050458.99999991 29.00.01089824.00151197 *02881464.95877511.99999997 30.00.00939690.00249516.03130992.95679799.99999998 31.00.00776469.00371070.03399793.95452667 1.00000000 32.00.00604899.00514191.03690361.95190546.99999998 33.00.00431161.00676426.04004539.94887874 1.00000000 34.00.00262622.00854260.04336934.94546167 *99999984 35.00.00098607.01041541.04589707.94270155 1.00000010 35.25.00026265 *01085267.04404146.94484319.99999998 IMAGINARY 35.50.00041235.01137867.04675239.94145663 1.00000000.00078955J.00009501J.00602487J -.00690944J *00000000.00089075M.01137907M.04713900M.94148198M 35.75.00057727.01191837.05106727.93643700.99999992.00070113J.00009915J *00744968J -.00824996J.00000000.00090820M.01191878M.0516C779M.93647333M 36.00.00055675 *01244059.05522640 *93177628 1.00000000.00049404J.00008302J.00760075J -.00817782J.00000000.00074434M.01244087M.05574699M.93181216M 37.00.00001878.01435551.06920200.91642372 1.00000000.00000563J.00U0235J.00155449J -.00156247J -.00000000.00001961M.01435551M.06921946M.91642504M 38.00.00067743.01600991.07765251.90566014 1.00000000 -.000000737J.00008572J -.00986655J.00978821J.00000000.00067747M.01601014M.07827682M.90571302M 44

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Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).900.250.250.900 ANGLE ERP ERS ETP ETS ENERGY.00.000000u0.01101920.00000000.98898084 1.00000000 1.00.00002923.01098286.00000791.98897973 *99999974 2.00.00011651.01087421.00003168.98897742.99999982 3.00.00026054.01069454.00007135.98897332.99999976 4.00.00045921.01044599.00012703.98896757 099999981 5.00.00070956.01013151.00019882.98895990.99999980 6.00.00100782.00975482.00028691.98895035.99999992 7.Ou.00134948.00932048.00039150.98893830.99999977 8.00.00172926.00883371.00051284.98892395.99999977 9.00.00214122.00830048.00065121.98890710 1.00000000 10.00.00257876.00772741.00080694.98888667.99999979 11.Uu.00303470.00712168.00098042.98886301.99999982 12.00.00350135.00649105.00117207.98883518.99999966 13.00.00397056.00584371.00138237.98880322.99999987 14.00.00443382.00518825.00161185.98876598.99999991 15.00.00488234.00453362.00186112.98872284.99999993 16.00.00530710.00388900.00213084.98867286.99999980 17.00.00569901.00326372.00242173.98861519.99999966 18.00.00604899.00266716.00273462.98854913.99999991 19.00.00634807.00210873.00307041.98847270.99999992 20.00.00658751.00159766.00343011.98838456.99999985 21.00.00675899.00114296.00381485.98828318.99999999 49

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Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).700.250 *250 1.000 ANGLE ERP ERS ETP ETS ENERGY ~00 *000 0000 *03114187.00000000.96885818 1.00000000 1.00 *00008749.03102277.00006135.96882815.99999977 2.00.00034842.03066710.00024550.96873900 1.00000000 3.00.00077806.03007980.00055279.96858911.99999977 4.00.00136864.02926925.00098373.96837833.99999995 5.00.00210938.02824678.00153908 096810467.99999992 6.00.00298667.02702693.00221981.96776647.99999989 7,00.00398418.02562713.00302715.96736137.99999983 8.00.00508310.02406753.00396254.96688670.99999988 9.00.00626238.02237079.00502769.96633898.99999985 10.00.00749892.02056185.00622460.96571447.99999986 11,00.00876801.01866767.00755554.96500856.99999979 12.00.01004353.01671691.00902312.96421621.99999977 13.00.01129838.01473958.01063029.96333154.99999980 14.00.01250490.01276671.01238039.96234776.99999976 15.00.01363524.01083002.01427719.96125736.99999983 16.00.01466188.00896145.01632497.96005145.99999976 17.00.01555807.00719278.01852853.95872045.99999984 18.00.01629836.005555516 02089336.95725281.99999970 19.00.01685922.00407874.02342570.95563611.99999978 20.00.01721950.00279211.02613270.95385557.99999989 55

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Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).800 *250.250 1.000 ANGLE ERP ERS ETP ETS ENERGY.00.00000000.01234568.00000000.98765432 1.00000000 1.00.00003468.01229667.00002779.98764074.99999989 2.00.00013807.01215035.00011125.98760010.99999979 3.00.00030820.01190878.00025059 *98753210.99999967 4.00.00054179.01157546.00044613 *98743655.99999994 5.00.00083433.01115517.00069839.98731190.99999979 6.00.00118008.01065401.00100798.98715783.99999991 7.00.00157220.01007928.00137571.98697258.99999978 8.00.00200276.00943949.00180252.98675504.99999982 9.00.00246291.00874418.00228955.98650325.99999990 10.00.00294294.00800390.00283812.98621505 1.00000000 11.00.00343241.00723003.00344973.98588768.99999986 12.00.00392033.00643471.00412614.98551858.99999977 13.00.00439529.00563075.00486933.98510448.99999985 14.00.00484560.00483133.00568157.98464124.99999976 15.00.00525958.00405004.00656545.98412475.99999983 16.00.00562564.00330059.00752391.98354968.99999983 17.00.00593260.00259664.00856032.98291025.99999982 18.00.00616988.00195172.00967854.98219971.99999986 19.00.00632779.00137891.01088304.98141013.99999987 20.00.00639780.00089072.01217898.98053246.99999996 61

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Institute of Science and Technology The University of Michigan ENERGY RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC) *900.250.250 1.000 ANGLE ERP ERS ETP ETS ENERGY.00.00000000.00277008.00000000.99722997 1.00000000 1.00,00000778.00275869.00000701.99722642.99999991 2.00.00003097.00272466.00002809.99721609.99999981 3.00.00006909 *00266849.00006329.99719881.99999969 4.00.00012139.00259100.00011273.99717477.99999990 5.00.00018677.00249332.00017658.99714315 *99999983 6.00.00026389.00237689.00025506.99710411.99999995 7.00.00035111.00224343.00034842.99705697.99999993 8.00.00044655.00209497.00045699.99700140.99999992 9.00.00054810.00193377.00058116.99693685.99999989 10.00.00065344.00176234.00072137.99686277.99999992 11.00.00076008.00158339.00087814.99677813 *99999975 12.00.00086539.00139985.00105208.99668249.99999982 13.00.00096662.00121477.00124388.99657464.99999992 14.00.00106099.00103137.00145431.99645307.99999975 15.00.00114566.00085294.00168430.99631687.99999979 16.00.00121787 *00068283.00193487.99616423 *99999982 17.00.00127492.00052443.00220723.99599331.99999990 18.00.00131428.00038107.00250277.99580160.99999973 19.00.00133367.00025607.00282309.99558718 1.00000000 20.00.00133109.00015260.00317008.99534613.99999990 67

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Institute of Science and Technology The University of Michigan 49.00 -.02024938 *00982688.02217707.98824547 1.00000000 -.02527410J *00574722J -.00753454J 02706142J -.00000000.03238546M.01138411M *02342203M.98861591M 50.00 -.02144125.01028524 *02363608 *98751987.99999995 -.02704339J.00629088J -.00817125J.02892375J -.00000000 *03451191M *01205659M.02500867M *98794335M 51.00 -.02262570.01067931 *02512613.98682013 *99999987 -.02901779J *00685825J -.00887505J.03103459J -.00000001 o03679612M.01269186M.02664750M.98730801M 52.00 -.02379934.01099827.02664799.98615315 1.00000000 -.03119495J.00744574J -.00964657J.03339576J -000000000.03923689M.01328161M.02834028M.98671845M 53.00 -.02495773.01123082.02820193.98552500 1.00000000 -.03357456J.00804897J -.01048619J.03601178J -.00000000.04183467M.01381728M.03008835M.98618272M 54.00 -.02609557.01136533.02978785.98494244 1.00000000 -.03615735J.00866247J -.01139395J.03888880J -.00000002.04459072M.01429018M.03189260M.98570986M 55.00 -.02720686.01139008.03140554.98441116.99999992 -.03894477J.00927970J -.01236963J.04203468J -.00000001.04750693M.01469173M.03375375M.98530819M 56.00 -.02828491.01129329 *03305462.98393706 1.00000000 -.04193840J.00989271J -.01341263J.04545832J -.00000000.05058523M.01501346M.03567221M.98498659M 57.00 -.02932249.01106351.03473477.98352426 1.00000000 -.04514014J.01049207J -.01452209J.04917C15J -.00000000.05382788M.01524746M.03764831M.98475259M 58.00 -.03031164.01068970.03644551.98317647 1.00000000 -.04855125J.01'106655J -.01569663J.05318131J -.00000001.05723652M.01538630M.03968198M.98461374M 59.00 -.03124388.01016172.03818649.98289561.99999995 -.05217274J.01160292J -.01693447J.05750430J.00000001.06081262M.01542363M.04177301M.98457631M 60.00 -.03211013.00947070.03995738.98268191.99999987 -.05600485J.01208571J -.018233283.06215243J.00000000.06455698M *01535443M.04392089M.98464544M 61.00 -.03290059.00860950.04175778.98253340 1.00000000 -.06004670J.01249677J -.01959008J.06714003J.00000001.06846938M.01517540M.04612465M.98482468M 62.00 -.03360491.00757350.04358736.98244402.99999998 -.06429661J.01281515J -.02100137J.07248283J.00000000.07254891M.01488577M.04838301M.98511421M 70

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Institute of Science and Technology The University of Michigan 77.00 -.02453225 -.00428446.07258304.95623375 1.00000000 -.14241076J -.02139421J -.04224154J.20604651J.00000000 *14450832M *02181900M *08398003M *97818103M 78.00 -.02189433.00190769.07407106.94591557.99999998 -.14650139J -.02914051J -.04274017J *21838207J.0000000,14812838M.02920288M.08551751M *97079709M 79.00 -.01893011.01135817.07529041.93228170 1.00000010 -.14983300J -.03794044J -.04290250J.23067602J.00000008,15102409M.03960411M *08665605M *96039605M 80.00 -.01564852.02510332.07614137 *91440382.99999999 -.15216700J -.04776810J -.04265978J.24259490J *00000002.15296951M.05396265M.08727752M.94603733M 81.00 -.01207529.04447382.07649300.89110851 1.00000000 -.15320723J -.05851022J -.04193397J.25365143J.00000001.15368235M.07349399M.08723324M.92650602M 82.00 -.00826040.07117843 *07617328.86090874 1.00000000 -.15258629J -.06991724J -.04063836J *26314194J.00000005.15280971M.09977369M.08633566M.90022638M 83.00 -.00429017.10741196.07495655.82192162.99999996 -.14984671J -.08152996J -.03867823J.27005487J -.00000003.14990810M.13484978M.08434744M.86515014M 84.00 -.00030395.15599391.07254634.77176366.99999996 -,14441826J -.09257105J -.03595366J.27294297J *00000000.14441857M.18139321M.08096689M.81860674M 85.00.00348105.22054685.06855321.70741896 1.00000000 -.13558826J -.10178339J -.03236493J.26973664J.00000006.13563293M.24290074M.07580918M.75709935M 86.00.00673403.30572420.06246487.62507698 1.00000000 -.12246522J -.10718995J -.02782215J.25747736J.00000004.12265022M.32397063M.06838078M.67602945M 87.00.00895664.41749858.05360663.51993814.99999999 -.10393147J -.10573370J -.02226231J.23192748J.00000000.10431668M.43067931M.05804551M.56932066M 88.00.00940455.56352184.04108867.38598491.99999997 -.07858567J -.09273753J -.015677873.18700107J.00000000.07914640M.57110166M.04397812M.42889829M 89.00.00696900.75356084.02373664.21573354 1.00000000 -,04467246J -.06108842J -.00816455J.11392544J.00000001.04521278M *75603288M.02510155M *24396714M 90.00 -.00000000 1.000010I -.00000006 -.00000103 1.00000000.00000010 39J00023J.000000003 -.00000039J -.0000006 OOOOOO1OM 1.OOQOu90M.00000006M OO0000111M 72

Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).700.250.250.700 ANGLE RP RS TP TS ENERGY.Ou.00000000 -.34228186 *00000000 1.34228180 *99999989 2.0u.02704648 -.34010124.01725680 1.34205030.99999988 4.00.05382065 -.33357851 *03453965 1.34135390.99999996 6.00.08005102 -.32277259.05187462 1.34018590.99999989 8.0u.10546773 -.30778122.06928767 1.33853590.99999993 10.00.12980346 -.28874186.08680457 1.33638860 1.00000000 12.00.15279434 -*26583180.10445059 1.33372390 *99999975 14.00.17418114 -.23926916.12224995 1.33051760.99999977 16.00.19371085 -.20931358.14022471 1.32674000.99999977 18.00.21113889 -.17626775.15839281 1.32235710.99999982 20.00.22623332 -.14047974.17676404 1.31733120.99999988 22.00.23878221 -.10234610.19533240 1.31162330.99999988 24.00.24860961 -.06231791.21405967 1.30519960.99999993 26.00.25561126 -.02091038.23283892 1.29804660.99999988 26.25.25628784 -.01566624.23517958 1.29710250 1.00000000 26.50.25692096 -.01041090.23751649 1.29614770 1.00000000 26.75.25751126 -.00514581.23984886 1.29518250 1.00000000 27.00.25805933.00012762.24217568 1.29420720 1.00000000 27.25.25856580.00540809.24449587 1.29322200.99999985 27.50.25903158.01069416.24680802 1.29222770.99999999 27.75.25945768.01598442.24911088 1.29122450 1.00000000 73

Institute of Science and Technology The University of Michigan 28.00 *25984524.02127737.25140277 1.29021290.99999981 30.00 *26179978 *06351374.26905546 1.28193510.99999990 32.00.26340924.10477261.28366499 1.27411950 1000000000 34.00.27456691.14273880.28519513 1.27144570.99999980 34.25.27884325 *14686879.28225558 1.27252290.99999999 34.75.29431624.15390289.26928106 1.27799130.99999985 35.00.31055150.15597377.25417389 1.28476970.99999985 35.25.36043752.15228454 *20496476 1.30746400.99999991 IMAGINARY 35.50.35160571 *15920790.21580446 1.30256020 1.00000010 -.08872244J.01509685J.08978539J -.04193434J.00000000.36262687M *15992207M.23373699M 1.30323500M 35.75.32123160 *16952030.24813992 1.28743100.99999993 -.11855952J.01939970J.11919084J -.05620539J -.0000000000.34241217M.17062672M.27528144M 1.28865720M 36.00.29276898.17911049.27812276 1.27313730 1.00000000 -.13548989J.02127643J.13531673J -.06442387J -.00000000.32260065M.18036977M.30929417M 1.27476620M 36.25.26615885.18801935.30585467 1.25965910.99999982 -.14525126J.02184193J.14411418J -.06927105J.00000001.30321355M.18928377M.33810644M 1.26156220M 36.50.24133097.19628861.33144623 1.24697140.99999985 -.15022177J.02157926J.14806965J -.07185398J -.00000000.28426610M.19747121M.36301683M 1.24903980M 36.75.21820849.20395972.35501216 1.23504520 1.00CO0010 -.15171771J.02076432J.14856624J -.07278379J -.00000000.26576908M.20501396M.38484483M 1.23718790M 37.00.19670869.21107374.37667025 1.22384770.99999993 -.15058209J.01957724J.14649140J -.07245145J -.00000000.24772822M.21197969M.40415369M 1.22599030M 38.00.12522786.23472442.44653838 1.18565760.99999988 -.12948538J.01320501J.12272267J -.06303072J.00000000.18013461M.23509556M.46309542M 1.18733170M 40.00.U3522947.26550974.52708294 1.13391980 1.00000000 -.05522196J.00237394J.04970292J -.02750565J.00000000.06550252M.26552035M.52942120M 1.13425330M 74

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Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).800.250.250.700 ANGLE RP RS TP TS ENERGY.00.00000000 -.28205132.00000000 1.28205130 1.00000000 2.00.02210576 -.28030897.01140494 1.28191640.99999992 4.00.04400239 -.27509592.02283879 1.28151070 *99999982 6.00.06548110 -.26645483.03433071 1.28083070.99999997 8.00 *08633382 -.25445656.04591052 1.27987030.99999992 10.00.10635353 -.23920071.05760883 1.27862120.99999993 12.00.12533461 -.22081613.06945732 1.27707230.99999995 14.00.14307326 -.19946148.08148888 1.27520990.99999989 16.00.15936813 -.17532585.09373727 1.27301780.99999971 18.00.17402125 -.14863039.10623648 1.27047750.99999984 20.00.18684019 -.11963017.11901879 1.26756820.99999983 22.00.19764243 -.08861735.13211009 1.26426860.99999981 24.00.20626552 -.05592598.14551876 1.26056060.99999994 26.00.21259265 -.02194065.15920890 1.25643670 1.00000000 26.25.21321982 -.01762309.16093464 1.25589250.99999999 26.50.21381084 -.01329314.16266218 1.25534230.99999988 26.75.21436607 -.00895187.16439105 1.25478620.99999991 27.00.21488579 -.00460025.16612057 1.25422440 1.00000000 27.25.21537053 -.00023945.16785007 1.25365680 1.00000000 27.50.21582067.00412958.16957854 1.25308380.99999990 27.75.21623701.00850570.17130507 1.25250590 1.00000010 78

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Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).800 20 250 250 900 ANGLE RP RS TP TS ENERGY.00.00000000 -*16279071.00000000 1.16279070 1*00000000 2.00.01288632 -.16165073.00967152 1.16264270 *99999981 4.,00 02561357 -.15824033 *01937821 1.16219750.99999978 6.00.03802217 -.15258963.02915609 1.16145030 1.00000000 8.00.04995146 -.14474844 *03904298 1.16039260.99999988 10.00.06123897 -.13478697.04907967 1.15901270 *99999987 12.00.07171929 -.12279594.05931104 1.15729480 *99999988 14.00.08122274 -.10888722.06978782 1.15521830.99999982 16.00.08957323 -.09319465.08056890 1.15275730.99999984 18.00.09658498 -.07587495.09172424 1.14987930.99999982 20.00.10205797 -.05710913.10333937 1.14654380 *99999995 22.00.10577055 -.03710500.11552196 1.14269940.99999985 24.00.10746821 -.01610059.12841203 1.13828100.9999978 25.00.10746847 -.00530706.13517879 1.13583100 *99999986 25.25.10737291 -.00258453.13690871 1.13519130.99999984 25.50.10723763.00014636.13865489 1.13454040.999999'97 25.75.10706180.00288509.14041788 1.13387800 1.00000000 26.00.10684463.00563099.14219831 1.13320360.99999985 26.25.10658528.00838335.14399672 1.13251740.99999998 26.50.1C628289.01114152.14581375 1.13181880.99999998 26.75.10593649.01390485.14765004 1.13110770.99999993 113

Institute of Science and Technology The University of Michigan 27.00.10554519.01667256.14950631 1.13038370.99999991 28.uU.10351023 *02777319.15714599 1.12735320.99999991 30.00.09693763.04995162.17364365 1.12057100 *99999997 32.00.08637981.07170711.19226999 1.11262940.99999998 34.00 *07107763 *09242619.21355981 1.10328420.99999983 34.25.06892143.09489880 *21630508 1.10203910 *99999980 34.50.06683036.09733483 *21894942 1.10080880.99999986 34.75 *06498174.09972682.22131779 1.09964120.99999985 35.00.06391730.10205595.22287747 1.09868310 1.00000010 35.25 *06816605 *10417615.21917319 1.09915960.99999997 IMAGINARY 35.50.06048970.10667180.22719071 1.09641670 1.0000000 -.01484452J.00044537J *01457848J -.00402330J -.00000000.06228453M.10667272M.22765796M 1.09642400M 35.75.04931106.10917226.23856255 1.09270730.99999987 -.01768801J.00045410J.01730913J -.00481325J.00000000.05238747M.10917320M.23918966M 1.09271780M 36.00.03891471.11153805.24907492 1.08919130 1.00000000 -,01749523J.00037217J.01705957J -.00477960J -*00000000.04266659M.11153867M.24965845M 1.08920170M 36.25.02926565.11377743.25877083 1.08586230 1.0000000 -.01551219J.00026064J.01507217J -.00425426J -.00000000.03312259M.11377772M.25920939M 1.08587050M 36.50.02032836.11589834.26769325 1.08271340.99999994 -.01229080J.00015069J.01189981J -.00338360J.00000000.02375513M.11589843M.26795761M 1.08271860M 36.75.01206757.11790828.27588428 1.07973820 1.00000000 -.00815233J.uOv6234J.00786505J -.00225265J.00000000.01456320M.11790829M.27599636M 1.07974050M 37.0u.00444806.11981450.28338560 1.07692940 1.00000000 -.00331040J.00000980J G00318246J -.00091806J -.00000000.00554473M.11981449M.28340346M 1.07692970M 37.25 -.00256445.12162373.29023733 1.07428020.99999991.00208116J.00000373J -.00199367J.00057922J -.00000000.00330267M.12162373M.29024417M 1.07428030M 114

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Institute of Science and Technology The University of Michigan 75.75 -.05452653 -.02848114.18225459.64355206 1.00000000 *23980402J *40254303J -.13304372J.19763910J.00000008.24592500M *40354932M.22564876M.67321650M 76.u0 -.05560607 -.03799794.18125522.63662813 1*00000000 *23790563J *40459312J -.13120391J *19913568J *00000008 *24431767M *40637351M *22375862M *66704601M 78.00 -.06337844 -.12293811.17189596.57671221.99999980 ~22018151J.41660058J -.11530370J.20901341J.00000000.22912163M.43436138M.20698590M.61341957M 80.00 -.06894438 -.22494399.15944632.50771433 1.00000000.19750807J.41793161J -.09730978J.21357657J.00000007.20919552M.47462260M.18679486M.55080739M 82.00 -.07105457 -.34579747.14274326.42817762 1.00000000.16929011J.40328257J -.07739472J.20982106J.00000007.18359709M.53123697M.16237481M.47682380M 84.00 -.06795894 -.48651704.12030178.33691296 *99999998.135u7008J *36531398J -.05607663J.19347096J.00000012.15120299M.60840211M.13272944M.38851171M 86.00 -.05726595 -.64633522.09031921.23356135.99999998.09475820J.29415971J -.03446667J *15858984J -.00000001.11071813M.71012615M.09667218M.28231479M 88.00 -.03585632 -.82096337.05080857.11960893 1.00000000.04903842J.17723732J -.01462640J.09730341J.00000003.06074901M.83987731M.05287195M.15418900M 90.00.00000007 -1.0000003 -.0C o00o11 -.00000025 99999990 -.00000008J -.00000i38J OOOOJ -0000001J - 000021 -00000006.00OO0011M 1.00i0002wM.00000011M *00000033M 118

Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).900.250.250.900 ANGLE RP RS TP TS ENERGY.00.00000000 -.10497241 *00000000 1.10497240 1.00000000 2.00.u0820674 -.10427949'.00475436 1.10490650.99999982 4.00.01632281 -.10220567.00953221 1.10470850.99999980 6.00.02425705 -.09876653.01435774 1.10437630.99999992 8.00.03191734 -.09398783.01925663 1.10390640.99999977 10.06.03920989 -.08790574.02425700 1.10329400.99999979 12.00.04603840 -.08056710.02939044 1.10253250.99999964 14.00.05230266 -.07202952.03469353 1.10161380.99999991 16.00.05789682 -.06236188.04020996 1.10052710.99999979 18.00.u6270643 -.05164463.04599336 1.09925970.99999990 20.00.06660412 -.03997075.05211166 1.09779560 *99999985 22.00.06944248 -.02744672.05865424 1.09611510.99999988 24.00.07104259 -.01419519.06574309 1.09419360.99999980 25.,0.07130882 -.00733980 *06954411 1.09313290.99999982 25.25.07131407 -.00560524.07052558 1.09285660.99999991 25.50.07129360 -.00386308.07152053 1.09257560.99999988 25.75.07124677 -.00211367.07252948 1.09228990 *99999987 26.00.07117281 -.00035722.07355307 1.09199940.99999985 26.25.07107106.00140582.07459186 1.09170410 1.00000000 26.50.07094070.00317516.07564651 1.09140370.99999997 26.75.07078094.00495038.07671776 1.09109820.99999998 119

Institute of Science and Technology The University of Michigan 27.00.07059098.00673112.07780627 1.09078750.99999995 28.00.06950965.01390154.08234999 1.08949040.99999978 30.00.06555583.02838025.09256970 1.08660730 1.00000000 32.00.05845018.04282038.10500169 1.08325670.99999992 34.00.04654937.05684407.12118831 1.07928140.99999978 34.25.04462473.05853849.12356734 1.07873360.99999987 34.50.04262952.06021337.12599683 1.07817910 1.00000010 34.75.04064859.06186515.12839053 1.07762880.99999985 35.00.03899690.06348633.13043050 1.07712290 1.00000000 35.25.04077742.06502635.12898936 1.07704720.99999985 IMAGINARY 35.50.03302958.06669494.13713360 1.07579360 1.00000000 -.01004511J.00013683J.01010977J -.00124708J.0000000.03452328M.06669508M.13750574M 1.07579430M 35.75.02304610.06831906.14747808 1.07426930.99999998 -.01040195J.00010578J.01044665J -.00129059J -.00000000.02528484M.06831914M.14784761M 1.07427000M 36.00.01399160.06985061.15683761 1.07286980 1.00000010 -.00804897J.00005326J.00806645J -.00099753J -.00000000.01614158M.06985063M.15704490M 1.07287020M 36.25.00582903.07129564.16525584 1.07159280.99999990 -.00402743J.00001192J.00402767J -.00049829J.00000000.00708504M.07129564M.16530491M 1.07159280M 36.50 -.00147718.07265988.17277461 1.07043670.99999984.00118839J.00000095J -.00118597J.00014669J -.00000000.00189587M.07265988M.17277867M 1.07043660M 36.75 -.00796006.07394863.17943289 1.06940010.99999984.00732119J.00003438J -.00729112J.00090100J -.00000000.01081492M.07394864M.17958096M 1.06940040M 37.00 -.01364922.07516674.18526614 1.06848230.99999990.01419001J.00012366J -.01410256J.00173968J -.OU00000.01968903M.07516684M.18580211M 1.06848360M 38.00 -.02887914.07941395.20086964 1.06602390.99999996.04709663J.00124206J -.04643173J.00562379J -.00000000.05524579M.07942366M.20616623M 1.06603870M 120

Institute of Science and Technology The University of Michigan 38.25 -.03083452.08033449 *20289621 1.06573510.99999998.05647812J.00176744J -.05557341J *00667310J -00C000OO,06434707M 908035393M *21036937M 1.06575590M 38.50 -.03201103.08120194.20414804 1.06559720.99999999.06634408J *00242108J -.06515850J *00773755J.00000000.07366303M ~08123802M.21429431M 1.06562520M 38.75 -.03234174.08201583.20456683 1,06563200 1,00060000.07677647J.00322730J -,07526712J.00881032J.00000000.08331035M,08207930M,21797414M 1,06566840M 39,00 -.03169867.08277342.20403623 1,06587560.99999991.08793476J.00422316J -,08605601J.00988436J -,00000000.09347367M.08288109M.22144168M 1.06592140M 39.25 -.02982835.08346775.20232102 1.06639400 1.0000000.10013251J.00547249J -.09783416J.01095118J -.00000000.10448085M.08364695M.22473388M 1.06645020M 39.50 -.02615324 *08408115.19887849 1.06732820 1.00000010.11407245J.00710763J -.11129516J.01199745J,00000000.11703211M.08438103M.22790188M 1.06739560M 39,75 -.01876460.08455571.19190101 1.06912210.99999999.13204070J.00953822J -.12869874J.01298827J -.00000000.13336737M.08509199M.23106138M 1.06920090M IMAGINARY 40.00.01451523.08791937.15959651 1.07244950.99999984.14307211J.01405417J -.13975047J.01040975J -.00000000.14380654M.08903558M.21213495M 1.07249990M 40.25.02620055.09161009.14803350 1*07153510.99999999.13262042J.01469408J -.12948105J.00834479J -,00000000.13518374M.09278106M.19667043M 1.07156750M 40.50.03248125.09442039.14183761 1.07067980.99999993.12696492J.01523980J -.12382105J.00724235J -,0000000.13105389M.09564236M.18828053M 1.0707042CM 40.75.03679942,09691697.13758670 1.06983820.99999998.12311615J.01576118J -.11990394J.00648531J -*00000000.12849818M.09819019M.18250220M 1.06985780M 41.00.04004582,09924281.13439367 1.06899890 1.O000000.120284013.01627426J -.11696938J.00591736J,00000000.12677504M.10056832M.17816704M 1.06901520M 41.25 *04260778.10145886.13187224 1.06815660.99999999.118118593,01678542J -.11467956J.00547168J,00000000.12556840M.10283797M.17476180M 1.06817050M 121

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Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).800.250 *250 1.000 ANGLE RP RS TP TS ENERGY.00.00000000 -.11111115.00000000 1.11111110 1.00000000 2.00.00893402 -.11022865 *00896322 1.11095870.99999978 4.00.01772983 -.10758932.01796382 1.11050020 *99999994 6.00.02624838 -.10321830.02704024 1.10973010.99999991 8.00.03434876 -.09715706.03623318 1.10863960.99999982 10.00 *04188717 -.08946453.04558701 1.10721590 1000000000 12.00.04871513 -.08021669.05515137 1.10544130.99999977 14.00.05467748 -.06950781 *06498352 1.10329340.99999976 16.00.05960907 -.05745078.07515138 1.10074320.99999983 18.00.06332992 -.04417832.08573795 1.09775370 *99999985 20.00.06563804 -.02984504.09684813 1.09427810.9999996 22.00.06629744 -.01462950.10861921 1.09025550 *99999989 22.25 *06625033 -.01267553.11014567 1.08971050.99999993 22.50.06617235 -.01071138.11168578 1.08915540.99999976 22.75.06606290 -.00873751.11323989 1.08859040.99999992 23.00.06592128 -.00675441.11480852 1.08801490.99999980 23.25.06574679 -.00476249.11639220 1.08742890.99999979 23.50.06553869 -.00276228.11799143 1.08683220.99999985 23.75.06529617 -.00075419.11960676 1.08622450.99999990 24.00.06501851.00126119.12123876 1.08560560.99999996 24.25.06470481.00328338.12288806 1.08497520.99999999 130

Institute of Science and Technology The University of Michigan 24.50.06435422.00531191.12455531 1.08433310.99999993 24.75.06396581.00734631.12624117 1.08367900.99999994 25.00.06353867 *00938593.12794638 1.08301260.99999994 26.00.06142205.01758577.13497641 1.08021830.99999982 28.00.05496954.03405786.15024656 1.07393440.99999986 30.0U.04480727.05032620.16774914 1.06650280 1.00000010 32.00.02933878.06593209.18885892 1.05746480.99999996 34.00.00444460.08018624.21726846 1.04568250.99999981 34.25.00009274.08181646.22186266 1.04386180.99999995 34.50 -.00475863.08339946.22689697 1.04190470.99999998 34.75 -.01030490.08492760.23255491 1.03976030.99999972 35.00 -.01698474.08638741.23925063 1.03731570 1.00000000 35.25 -.02721231.08773101.24927712 1.03395290.99999985 IMAGINARY 35.50 -.03481757.08902738.25673811 1.03123510.99999994.00823476J.00014696J -.00783035J.00210298J -.00000000.03577813M.08902750M.25685749M 1.03123720M 35.75 -.04028409.09029341.26211437 1.02904820 1.0000000.01390355J.00030049J -.01318212J.00356780J.00000000.04261592M.09029391M.26244563M 1.02905430M 36.00 -.04529605.09150896.26701616 1.02696620 1.0000000.01956201J.00049769J -.01849283J.00504368J.00000000.04933969M.09151031M.26765577M 1.02697850M 38.00 -.07166614.09975245.29207849 1.01362190 1.00000010.06869892J.00401076J -.06344911J.01834954J.0000000.09927526M.09983304M.29889067M 1.01378790M 40.00 -.08024845.10609083.29918561 1.00496050 1.00000000.11887081J.01138127J -.10729743J.03271521J.00000000.14342274M.10669956M.31784392M 1.00549280M 42.00 -.07751727.11109568.29533907.99990085 1.00000000.16655417J.02304089J -.14703111J.04686479J -.00000000.18370960M.11345982M.32991409M 1.00099850M 44.00 -.06615813.11493082.28377315.99861068 1.00000000.21314175J.04011904J -.18427764J.06039896J.00000000.22317326M.12173179M.33835698M 1.00043550M 131

Institute of Science and Technology The University of Michigan 46.00 -.03687575 *11751773.25805739 100791760 1.0000000.27320566J.07041845J -.23255799J *07297174J.00000000 *27568306M o13700063M.34738570M 1.01055560M IMAGINARY 46.25 -.01143714.12313925.23652349 1.01553960 1000000010.28448428J.08132795J -.24311287J.06905720J -000000001.28471409M *14757205M.33918611M 1.01788480M 46.50.00016946.13039515 *22548878 1.01356440 1.00000010 *27363205J.08239734J -.23383940J.06389317J.00000000.27363210M *15424726M.32484773M 1.01557620M 46.75.00629248.13488620.21948282 1.01172080 1.00000000.26773199J.08356762J -.22850148J.06138569J.00000000.26780592M.15867524M.31683691M 1.01358130M 47.00.01062463.13848331.21511715 1.00990970 1.00000010.26349253J.08479241J -,22449894J.05973436J.00000001.26370664M.16238035M.31092629M 1.01167470M 47.25.01397001.14158702.21165195 1.00810910 1.00000000.260187213.08605920J -.22125335J.05855267J.00000000.26056197M.16568967M.30618555M 1.00980810M 47.50.01666896.14436419.20877339 1.00630970 1.00000010.25750437J.08736173J -.21851503J.05767879J.00000001 *25804332M.16873971M.30221705M 1.00796130M 47.75.01890366.14690288.20631315 1.00450630 1.00000000.25527501J.08869624J -.21614771J.05702700J -.00000000.25597398M.17160267M.29880587M 1.00612370M 48.00.02078517.14925594.20416855 1.00269600 1.00000020.25339470J.09006017J -.21406677J.05654553J.00000001.25424574M.17432202M.29581984M 1.00428910M 50.00.02882447.16401314.19308888.98779209.99999994.24539763J.10187603J -.20320838J.056210023 -.00000000.24708469M.19307779M.28031582M.98939010M 52.00.03079175.17424390.18688377.97192698.99999999.24342265J.11509514J -.19725233J.05926083J.00000000 24536242M.20882487M.27172417M.97373193M 54.00.02985535.18100355.18263456.95494601 *99999988.24397316J.12959841J -.19327488J.06431906J -.00000002.24579309M.22261633M.26591457M *95710961M 56.00.02711834.18437711.17935171.93672636 1.00000000.24565312J.14533033J -.19012058J.07091464J -.00000001.24714542M.23476759M.26136731M.93940680M 132

Institute of Science and Technology The University of Michigan 58.00.02310430.18415299.17658559.91712700.99999992 *24769356J.16224039J -.18717839J.07881501J -.00000003 *24876878M *24542670M *25732901M.92050732M 60.00.01811054.17996818 *17409359.89597117.99999990.24958035J.18025808J -.18406675J.08786645J -.00000002.25023657M *25471851M *25335576M.90026932M 62.00 *01233155 *17134712.17172156.87303243.99999990 *25091736J.19927496J -.18051572J.09793665J -.00000002.25122020M *26281237M.24914698M.87850850M 64.00.00591340.15770804.16935102.84802196 1.00000010 *25136406J.21912626J -.17631337J.10888542J.00000005.25143360M.26997804M.24447120M.85498378M 66.00 -.00101690.13835348.16686945.82057412 1.0000000.25060118J.23956698J -.17127705J.12054313J -.00000001.25060324M.27664783M.23912599M.82938081M 68.00 -.00833210 *11245391.16415071.79023028 1.00000000.24830932J.26024186J -.16523680J.13268930J.00000006.24844907M.28349904M *23291340M.80129292M 70.00 -.01588803.07902465.16103741.75641927 1.00000000.24415304J.28064147J -.15802544J.14502555J -.00000000.24466944M.29155536M.22562155M.77019641M 72,00 -.02350624.03690003.15732339.71843611 1,00000010.23776734J.30004196J -.14947262J.15713867J -.00000007.23892645M.30230248M.21700855M.73542028M 74.00 -.03095256 -.01529357.15273248.67541759.99999990.22874587J.31741906J -.13940360J.16844813J.00000001.23083052M.31778727M.20678630M.69610609M 76.00 -.03790785 -.07915984.14689209.62631951 1.00000020.21662979J *33132365J -.12764339J.17812874J.00000002.21992151M.34064885M.19460246M.65115740M 78.00 -.04392821 -.15653802.13929897.56989874.99999980.20090093J.33970759J -.11402928J.18500075J -.00000003.20564744M.37403930M.18001911M.59917429M 80.00 -.04838727 -.24946908.12927583.50471606 1.00000000.18098106J.33967404J -.09843816J.18736788J -.00000003.18733785M.42144189M.16248788M.53837256M 82,00 -.05039607 -.36008401.11591641.42917894.99999988.156247433.32713222J -.08083715J.18278887J.00000006.16417375M.48649355M.14131970M.46648293M 84.00 -.04869240 -.49033035.09802439.34167869 1.00000010.12608087J.29633425J -.06137523J.16775967J.00000009.13515670M.57292043M.11565336M.38064107M 133

Institute of Science and Technology The University of Michigan 86.00 -.04149805 -.64141284.07405659 *24089912 *99999991 *08997530J *23929853J -.04053800J *13729957J -*0000002 *09908402M *68459784M *08442576M.27727884M 88.00 -.02635585 -.81272743.04210592.12644559.99999999 *04775914J *14520016J -.01939955J.08447366J.00000004 *05454875M.82559612M *04636001M *15206671M 90.00.00000008 -1.00Q00030 -.0000010 -.00000021.99999990 -*00000012J -*00000042J *00000004J -.00000025J.00000018 ~00000015M 1.0000002 00.OOOOO11M.00000033M 134

Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC) ~900 *250 *250 1.000 ANGLE RP RS TP TS ENERGY.00.00000000 -.05263160.00000000 1.05263160 1.00000000 2.00.00423115 -.05219830 *00424697 1.05256330.99999981 4.00.00839224 -.05090190.00851910 1.05235810.99999989 6.00.01241244 -.04875339.01284247 1.05201360.99999994 8.00.01621926 -.04577094.01724503 1.05152580 *99999992 10.00.01973755 -.04198024.02175786 1,05088920.99999992 12.00.02288804 -.03741459.02641656 1.05009620 *99999981 14.00.02558530 -.03211506.03126339 1.04913720.99999974 16.00.02773493 -.02613119.03635015 1.04799970.99999982 18.00,02922911 -.01952122 *04174248 1.04666780,99999973 20.00.02993949 -.01235319.04752666 1.04512160.99999991 22.00.02970548 -.00470624.05382092 1.04333500.99999976 22.25.02960000 -.00372119.05465124 1.04309330.99999990 22.50.02947605 -.00273023.05549248 1.04284710.99999986.22.75.02933312 -.00173364.05634507 1.04259660.99999999 23.00.02917064 -.00073158.05720945 1.04234140.99999976 23.25.02898810.00027573.05808611 1.04208180 1.00000000 23.50.02878486.00128802.05897553 1.04181730.99999979 23.75.02856032.00230516.05987825 1.04154820 1.00000000 24.00.02831383.00332686.06079481 1.04127400.99999980 24.25.02804468.00435285.06172586 1.04099490.99999987 135

Institute of Science and Technology The University of Michigan 24.50.02775216 *00538300.06267198 1.04071070.99999991 24.75 *02743549.00641701 *06363389 1.04042130.99999999 25.00.02709382.00745461.06461228 1.04012640.99999984 26,00.02545925.01163582.06870681 1,03889100.99999996 28.00.02066249.02008525 *07798224 1.03611570 1,00000000 30.00 *01307209,02849810.08940270 1.03283210.99999990 31.00.00773592 *03261503.09637912 1.03093640.99999985 31.25 *00618378.03362795.09830951 1.03042890.99999978 31.50.00452822 *03463264.10032985 1.02990610.99999998 31.75.00275860.03562821,10245024 1,02936650.99999989 32.00.00086264.03661345.10468238 1.02880880.99999983 32.25 -.00117455.03758715.10704050 1,02823120.99999987 32.50 -.00337077.03854789.10954161 1.02763160.99999998 32.75 -.00574801.03949412.11220681 1.02700720.99999988 33.00 -.00833345.04042381.11506212 1.02635500.99999995 33.25 -.01116213.04133487.11814124 1.02567070.99999987 33,50 -.01427952.04222444.12148784 1.02494900.99999983 33.75 -.01774733.04308900.12516137 1.02418260.99999997 34.00 -.02165294.04392414.12924603 1.02336100.99999992 34.25 -.02612690.04472357.13386787 1.02246880.99999991 34.50 -.03138273.04547793.13923332 1.02148060 *99999996 34.75 -.03782040.04617164.14572959 1.02034880.99999993 35.00 -.04641078.04677050.15429842 1.01895780 1.00000000 35.25 -.06325628.04709070.17087181 1.01658120.99999982 IMAGINARY 35.50 -.07000596.04761274.17757440 1.01539810 1.00000000.02052306J.00061100J -,01995174J.00244437J.00000000.07295225M.04761666M.17869174M 1.01540100M 136

Institute of Science and Technology The University of Michigan 35.75 -.07154727.04825375.17919423 1.01483590 1.00000000 *03107491J.00100677J -.03016539J.00371023J.00000000 *07800425M.04826425M *18171549M 1.01484260M 36.00 -.07267640 *04888516 *18040276 1.01432620 1.00000000.04016097J *00140957J -.03892825J *00480524J.00000000.08303471M.04890548M.18455504M 1.01433750M 38.00 -.06733500.05381442.17594068 1.01225530.99999986.10390607J *00623878J -.09956002J.01241495J.00000000,12381629M.05417485M.20215667M 1.0123314CM 38.25 -.06470883.05445157.17349090 1.01229570 1.00000000.11190680J.C0713302J -.10707661J.01331858J.0-0000000.12926857M.05491679M.20387371M 1.01238320M 38.50 -.06151180.05510663 *17049844 1.01242920 1.0000U000.12008685J.00812252J -.11474570J.01421490J.00000000.13492425M.C5570203M.20551470M 1.01252890M 38.75 -.05763129.05578765.16685893 1.01267530 1.00000010.12853816J.C0922695J -.12265560J.01510353J.00000000.14086668M *05654555M.20709007M 1.01278790M 39.00 -.05287885.05650731.16239665 1.01306520.9999997.13740416J.01047708J -.13094384J.01598358J -.0000000.14722797M.05747039M.20861198M 1.01319120M 39.25 -.04690851.05728790.15678779 1.01365510.99999993.14693704J.01192675J -.13985226J.01685347J -.00000000.15424299M.05851625M.21009775M 1.01379510M 39.50 -.03896468.05817686.14932290 1.01456360 1.00000000.15767046J.01368863J -.14989247J.01770970J -.00000000.16241373M *05976559M.21157760M 1.01471810M 39.75 -.02660140.05932564.13769891 1.01616380.99999998.17129044J.01611330J -.16268236J.01854104J -.0000000.17334373M.C6147496M.21313502M 1.01633290M IMAGINARY 40C.C.00836881.06374748.10454279 1.01913120 *99999995.17136982J.01870083J -.16275981J.01640469J -.00000000.17157404M.06643389M.19344237M 1.01926320M 40.25.01676617.06642060.09655506 1*01845560 *99999998.15700153J.01808277J -.14894564J.01460651J -.00000000.15789421M.06883809M.17750403M 1.01856030M 4C.5u.02127678.06832914.09230688 1.01779770 1.0u000000.14881097J.01785364J -.14099368J.01365252J.00000000.15032433M.07062311M.16852233M 1.01788920M 137

Institute of Science and Technology The University of Michigan 40.75.*2438351 *06996355 *08940636 1.01714080.99999995.14296770J *01777535J -.13527489J *01300732J *00000001.14503213M.07218630M.16215052M 1.01722390M 41.u.0u2672637.C7144791.08723624 1.01648080 1*0000000.13845458J.01778433J -.13082362J.01253311J.00000000 *141U1053M.07362803M.15724179M 1.01655800M 41.25.02858280.07283538 *08552862 1.01581550 1.00000010.13481892J.01785230J -.12720937J.01217019J.00000001.13781551M.07499131M *15328851M 1,01588830M 41.50.03010120.07415396 *08414012 1.01514380 1.00000000 ~13181201J.01796366J -.12419527J.01188646J.00000000.13520535M.07629877M.15001341M 1.01521330M 41.75.03137098.07542039.08298441 1.01446520.99999982.12928018J.01810881J -.12163477J.01166252J.00000000.133(J3196M.07756394M.14724615M 1.01453220M 42.Ou.03245033.07664525.08200522 1.01377930 1.00000000.12712090J.01828132J -.11943003J.01148567J.00000000.13119735M.C7879531M.14487369M 1.01384430M 44.00.03738723.08550234.07747174 1.00799400.99999990.11743084J.02028610J -.10902401J.01107017J -.00000000.12323882M.08787591M.13374642M 1.00805470M 46.Ou.03932947.09323549.07534694 1.00162380 1.00000010.11414872J.022977u2J -.10469169J.01163234J.0000000.12073415M.C9602500M.12898647M 1.00169130M 48.uu.03997650.09999238.07399988.99460451.99999997.11359137J.02615273J -.10289576J.01279473J.0000(000.12042059M.10335589M.12674194M.99468679M 50.u0.u3986437.10569256.07293015.98686987 *99999994.11444592J.02976029J -.10237808J.01444925J -.00000000.12119008M.i0980251M.12569836M.98697564M 52.00.03922547.11018140.07193440.97834112 1.00000000.11608397J.03378859J -.10254288J.01656086J -.00000000.12253214M.11524586M.12525813M.97848127M 54.00.03818114.11325970.07091835.96892174 1.00000000.11814472J.03824166J -.10305581J.01912067J -.00000001.12416108M.11954155M.12509961M *96911038M 56.00.03680375.11468818.06983615.95849178 1.00000000.12038987J.04312872J -.10370399J.02212956J -.00000000.12588978M.12252944M.12502642M.95874720M 58.00.03514112.11418408.06866588.94690051 1.00000000.122642703J 04845925J -.10433715J.02559084J -.00000001.12757793M.12404153M.12490493M.94724625M 138

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Institute of Science and Technology The University of Michigan 88.0o -.00199955 -.75320100.01628466.19013845 *99999996.03353628J.06156227J -.02364344J ~04363336J -0000000000 *03359584M *75571268M.02870892M *19508075M 90.00.00000000 -1.00i0Q50 -.QQO0003 -.Q0000043.99999990 -.00000005J — 00C00011O J o0000003J -o00000008J -.00000006,00OC(00U5M,1.OOGwOW40M.*W00QQ0 5M.00000044M 140

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Institute of Science and Technology The University of Michigan 75.00 -.08756715 -.02088128.23902366.61473079.99999990.19197333J.65130327J -.08972261J *18600747J -*00000004,21100181M *65163791M *25530855M *64225595M 80.00 -.09935129 -.32539183.19250365 *43559291 1.00000000 *14029467J *63982670J -.04122773J.21770420J.00000001.17191065M.71781477M.19686894M.48696641M 85.00 -.07662467 -.69558618.11362828.21610699.99999997 *06810717J *45185311J -.00069294J.17527566J -.00000001.10251794M.82946450M.11363039M.27825130M 90.0U.00000009 -1.00u0010 -.00000008 -.00000007.99999990 -.00000005J -*0000051J -.00000003J -.00000024J.00000012 0 O.OCOuOulM 100OOOOOC9M.0000009M 0026M 144

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Institute of Science and Technology The University of Michigan 60.00.04128692.37513971 *12886971 1.03120720.99999986 *11950435J.14032924J -.10058582J -.01387852J.00000001 *12643535M *40052726M.16347754M 1.03130050M 65.00.02645599.37954426.12124094.97351611 1.00000000,13826004J *19527313J -.10532511J.02415076J.00000002 *14076845M.42683186M.16060119M.97381562M 70.00.00962314.34601210.11435879.90463330 1.00000000.15007827J.26566994J -.10396980J.07345638J -.00000006 *15038647M.43623947M.15455630M.90761073M 75.00 -.00908585.25196347.10771482.81233852.9999990.15129768J.34876836J -.09504279J.13216611J -.00000014 *15157024M.43026150M.14365101M.82301989M 80.00 -.02800072.05190323.09810262.66962260 *99999990.13536977J *42692037J -.07537433J.19171174J.00000003.13823536M.43006387M.12371505M.69652553M 85.00 -.03828978 -.34240770 *07395128.41990692 1.00000000.0896226CJ.42010557J -.04046757J.21045053J *0000004 *09745931M.54197022M.08429956M.46969270M 90.00.0000006 -1.00*0i50 -*.0000009 -.0000039.99999990 -.0000007J -.000O 0064J.OO0000013 - e00000034J -.00O00007.U00OO010M 1.00GWOO40M QQ000009M.00000052M 150

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Institute of Science and Technology The University of Michigan 60.00.00603130.31361455.26252671.93778517.99999990.20788404J.34256374J -.16416327J.03261259J -.00000006 *20797151M.46443944M.30962857M *93835207M 65.00 -.02151439.26093814.25098832.84685660 1.00000000.21642736J.43585106J -.14844791J.08484059J -.00000002.21749407M.50799100M.29160233M.85109577M 70.00 -.04999780.14739402.23633084.73991739 1.00000010.21063167J.52746569J -.12253882J.14203568J -.00000006.21648436M.54767238M.26621049M.75342675M 75.0u -.07473488 -.04405266.21342789.60654163 1.00000000.18592597J.59315681J -.08678581J.19361528J -.00000015.20038405M.59479040M.23039800M.63669429M 80.00 -.08632422 -.32591146.17336039.43447471.99999990.13853633J.58457223J -.04425505J.21803731J -.00000008.16323046M.66928541M.17891991M.48611575M 85.00 -.06815540 -.67989888.10413408.22040698.99999997.07032241J.41857040J -.00625208J.17361629J.00000005 *09793059M.79841322M.1C432159M.28057414M 90.00.00000009 -1.00000010 -.G00000C8 -.0000008.99999980 -.0000005J -00U00O50J -.00000002J -.00000025J.00000015.00000010M 1.00000W;UM.0000C008M.00000026M 152

Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC) *800 *400 *400.800 ANGLE RP RS TP TS ENERGY.00.00000000 -.21951222.00000000 1.21951220 1.00000000 5.00.03224196 -.21123648.01546860 1.21911940 1.00000000 10.00.06298993 -.18690684 *03084144 1.21797210.99999999 15.00.09121561 -.14809559 *04548876 1.21623100 *99999991 20.00.11879412 -.09797072.05527220 1.21467530.99999998 IMAGINARY 25.00.17451295 -.04444799'.02391697 1.21882820.99999995 -.08089191J.01338198J.10116963J -.01283892J.00000000.19234934M.04641876M.10395823M 1.21889580M 30.00.00624898.02717008.25487825 1.20006460.99999993 -~02463058J.00064571J.02892080J -.00260650J.0UOU00.02541C93M.02717775M.25651380M 1.20006730M IMAGINARY 35.00.06964575.08822711.19282887 1.19466080 1.00000000.04666181J.G3030005J -.05836166J -.02797838J -.00000000.08383230M.09328514M.20146725M 1.19498830M 40.00.07419312.15937673.18852339 1.16391720.99999996.06954398J.05311780J -.08112707J -.03892165J.O0000000.10169063M.16799536M.20523808M 1.16456770M 45.00.06929598.22424927.18604615 1.12337150 1.00000000.09440794J.08120059J -.10080324J -.04071590J -.00000001.11711017M.23849794M.21159977M 1.12410900M 50.00.05937166.27717020.18195465 1.07461300.99999984.11967794J.11754118J -.11592961J -.03165500J -.00000002.13359567M.30106352M.21574792M 1.07507910M 55.0U.04581439.31214470.17650530 1.C1911880 1.00000010.14339076J 16464550J - 12547916J -.01077935J -.00000006.15053195M.35290572M.21656209M 1.01917570M 153

Institute of Science and Technology The University of Michigan 60.00.02920867.32224972.17047980.95706566.99999985.16325752J.22417865J -.12879913J.02170651J -.00000003.16584982M.39255692M *21366463M.95731178M 65.0U.00991056.29823672.16427249.88620006 1.00000000.17664972J.29601832J -.12532820J *06457975J -*00000004.17692750M.42020468M *20662189M.88854999M 70.0O -.01145967.22626266.15729339.80052115 1.00000000.18034018J.37633743J -.11423627J.11529401J -.000000001.18070391M.43911803M.19439942M.80878106M 75.00 -.03316341.08465571.14709988.68829618 1.00000000.16995164J.45274937J -.09420269J.16798063J.00000002.17315707M.46059589M.17467833M.70849779M 80.00 -.05027669 -.15872480.12756355.52949959 1.00000010.13930325J.49128252J -.06393512J.20677068J.00000012.14809841M.51628680M.14268902M.56843990M 85.00 -.04946121 -.53618317.08546582.29805133.99999991.08140899J.40401680J -.02583494J.18708438J -.00000006.09525668M.67135829M.08928522M.35190220M 90.Uu.00000007 -1.00w0i20 -.0000008 -.0000021.99999980 -.00000007J -.00000054J.*000OOOOJ -.00000027J.00000006.0000001.M 1.000CO10NM.o00000008M.00000034M 154

Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV wAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).900.400.400.800 ANGLE RP RS TP TS ENERGY.00.00000000 -.16279071.00000000 1.16279070 1.00000000 5.00 *02446514 -.15696742.00630065 1.16258030 *99999987 10.00.04817560 -.13979564 *01231586 1.16196340.99999977 15.00.07086433 -.11222193.01721197 1.16100780.99999971 20.00.09528768 -.07620426.01662404 1.15998810.99999981 IMAGINARY 25.00.14459585 -.03577793 -.01721220 1.15953330.99999996 -.10194314J.01132109J.12205371J -.00224573J. 00000000.17691908M.03752636M *12326138M 1.15953540M IMAGINARY 30.00.05661855 *01731144.10505926 1.16029910.99999996 -.01144731J.00861154J.01161232J -.00971741J.00000000.05776419M.01933506M.10569907M 1.16033970M 35.00.06405045.07149670.10578683 1.14931530 100000000.01048537J.01570487J -.01413557J -.01868988J -.00000000.06490303M.07320123M.10672706M 1.14946720M 40.00.06441054.12689962.10817536 1.13223650.99999993.02925203J.02456269J -.03363811J -.02504140J -.06000000.07074178M.12925493M.11328473M 1.13251330M 45.00.06132609.17978824.10851104 1.10888100 1.00000000.04814140J.03626144J -.05056461J -.02732799J.00000000.07796463M.18340856M.11971393M 1.10921760M 50.00.05581103.22638569.10656655 1.07954620.99999990.06719554J *05217898J -.06502753J -.02384232J -.00000000.08735051M.23232117M.12483993M 1.07980940M 55.00.04842061.26264113.10281054 1.04457180.99999993.08563926J.07396039J -.07662698J -.01326680J.00000000.09838007M.27285619M.12822519M 1.04465600M 155

Institute of Science and Technology The University of Michigan 60.00.03947074.28378005.09792215 1.00366110.99999994.1023066UJ.10329175J -.08492143J.00518463J -.00000000 *10965664M.30199387M *12961635M 1.00367440M 65.00.02910869.28323162.09253873 *95492630.99999995.11573474J.14158044J -.08943812J.03180418J -.00000004.11933920M.31664675M.12869574M.95545577M 70.00.01740162.25040290.08702350.89334626 1.00000000.12403608J.18933189J -.08946954J.06634402J -.0000007.12525080M.31392383M.12481141M.89580637M 75.00.00452995 *16601698.08106748.80771815.99999990.12442266J.24423565J -.08367431J.10723093J -.00000007.12450509M.29531794M.11650462M.81480493M 80.00 -.00857148 -.00812967.07259464.67375646 1.0000000.11199657J.29407502J -.06941957J.14768670J -.00000005.11232409M.29418736M.10044430M.68975294M 85.00 -.01742054 -.35110948.05411804.43825470 1.00000000.07687303J.28739217J -.04213478J.15805431J.00000009.07882219M.45373133M.06858646M.46588447M 90.00.00000005 -1.00000 60 -.U0000007 -.00000040.99999990 -.00000010J -.00000O59J *.0000004J -.0000036J.00000025 00OOO0001M 1.00U0G 50M.60000008M.00000054M 156

Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV wAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).700.400.400.900 ANGLE RP RS TP TS ENERGY.00.00000000 -*22699386.00000000 1.22699380.99999990 5.00 *03251856 -.21777604.02542239 1.22616740 1.00000000 10.00.06291080 -.19074508.05103316 1.22368260 1.00000000 15.00.08936431 -.14784006.07667159 1.21959110.99999981 20.00.11215639 -.09273999.09969329 1.21458880.99999977 IMAGINARY 25.00.15185699 -.03330904.09382345 1.21612020.99999998 -.05934342J.00961457J.07271873J -.01826887J.00000000.16304044M.03466889M.11870490M 1.21625730M 30.00.02437738.04202754.27264489 1.16704470.99999992 -.03932140J.00214042J.04429848J -.01284688J -.0000OO00.04626477M.04208201M.27622018M 1.16711530M 35.00 -.01355497.07125935.32973949 1.16396610.99999991.08858373J *01184968J -.09292512J.02550711J.0000000.08961481M.07223787M.34258312M 1.16424550M IMAGINARY 40.00.05449787.14275225.25926579 1.15138390 1.00000000.12642382J.07677923J -.13536577J -.01002777J -.00000000.13766989M.16209026M.29247673M 1.15142750M 45.00.05523049.20619813.24888492 1.10336470 1.00000010.14596274J.12202621J -*14637662J -.01259385J -.0000000.15606257M.23959980M.28873832M 1.10343650M 50.00.04484480.25220388.24228412 1.04619140.99999987.16798653J.17584591J -.15443808J -.00079602J -.U0000004.17386928M.30745500M.28731988M 1.04619160M 55.00.02824660.27464472.23570581.98109771.99999990.18810513J.24059596J -.15648570J.02397392J -.00000006.19021411M.36512481M.28292225M.98139057M 157

Institute of Science and Technology The University of Michigan 60.00.00725557.26551745.22855342 *90785661.99999990 *20292339J *31615747J -.15120049J.06018556J -.00000006.20305305M.41286203M *27404060M.90984939M 65.00 -.01673276.21465274.22009662.82379133.99999990.20902193J.39901264J -.13782305J.10507310J -. 00000005.20969061M.45308595M.25968772M.83046523M 70.00 -.04165643.10885315.20834239.72303703 1.00000000.20263135J *47963090J -.11578958J.15374597J.00000002 *20686885M.49182801M.23835640M.73920252M 75.00 -.06353152 -.06791762.18907365.59615596 1.00000000.17954270J.53719974J -.08501207J.19676072J -.00000020.19045166M.54147609M.20730628M.62778715M 80.00 -.07443969 -.32946623.15475241.43152714.99999990.13586316J.53001807J -.04748839J.21467602J -.00000007.15491954M.62407303M.16187481M.48197661M 85.00 -.05993368 -.66719039.09445215.22377904.99999999.07157058J.38361940J -.01169000J.16915630J.00000000.09335092M.76961474M.09517281M.28051900M 90.00.00000006 -1.00i00020 -.00000008 -.00000017 1.00000000 -00000004J -.0000004J - 00000 -OCOOOOOOJ -.00000019J -.00000001.000008M 1.C00OOl1WM.OQ000OO8M.00000025M 158

Institute of Science and Technology The University of Michigan AMPLITUDL RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).800.40u.400.900 ANGLE RP RS TP TS ENERGY.00.00000000 -.16279071.00000000 1.16279070 1.00000000 5.0u.02355333 -.15606725.01576040 1.16221650.9999990 10.00.04550391 -.13630217.03184981 1.16048410.99999983 15.0G.06435720 -.10475542.04849127 1.15759210.99999975 20.OU.07968263 -.06378828.06469978 1.15378250.99999987 IMAGINARY 25.00.10022759 -.01767233.06930034 1.15126710.99999980 -.04830900J *00447750J.05610901J -.00807579J.00000000.11126243M.01823072M.08916703M 1.15129540M 30.00 -.00639094.02718661.20953786 1.13468720.99999976 ~02518830J.00067529J -.02770780J.00340031J -000000000.02598644M.02719499M.21136186M'1.13469220M IMAGINARY 35.00.05725072.08145303.15018129 1.12735630.99999990.06656279J.02675253J -.07270055J -.01137789J.00000000.08779664M.08573386M.16685260M 1.12741360M 40.00.06221153.13764139.14804146 1.10188050.99999987.08192899J.04624977J -.08487133J -.015549503.00000000 *10287193M.14520397M.17064412M 1.10199010M 45.00.05940312.18823515.14763625 1.06893270 1.00000010.10048118J.07U79551J -.09740509J -.01332727J -.0O00O001.11672702M.20110812M.17687344M 1.06901570M 50.00.05229478.22886285.14608660 1.02896620.99999991.11974672J.10226717J -.10776495J -.00355708J -.00000000.13066759M.25067265M.18153396M 1.02897230M 55.0u.04199574.25439265.14330514.98227497.99999995.13788479J.14219448J -.11465994J.01463493J -.00000000.14413832M.29143591M.18353001M.98238398M 159

Institute of Science and Technology The University of Michigan 60.00.02904587 *25861433.13967490.92821391.99999985.15297761J.19150641J -.11721099J *04139125J -.00000003.15571066M *32180128M *18233895M.92913631M 65.00.01383673 *23319886.13538767.86427910 1.00000000.16284476J.24979824J -.11463869J.07600861J.00000001 *16343154M.34173214M.17740307M.86761492M 70.00 -.00305767.16586770.12996894.78487171 1.00000000.16479282J.313801273 -.10598682J.11649640J.00000009.16482118M *35494130M.16770548M.79347023M 75.00 -.02029688.03752502.12158190.67937875.99999990.15515226J.37364348J -.08990962J.15787292J -.00000010.15647423M.37552306M.15121474M.69748070M 80.00 -.03434553 -.18115647.10559232.52937788.99999990.12859437J.40300454J -.06485212J.18684267J.00000009.13310194M.44184875M *12391745M.56138322M 85.00 -.03566468 -.52726230.07160726.30771064.99999993.07799136J.33340780J -.03108145J.16651030J.00000000.08575909M.62383194M.07806188M.34987356M 90.00.00000006 -1.0000U030 -.00000007 -.Q0000024.99999990 -.00000007J -.00000047J.OO000001J -.00000026J.0000008.00000009M 1.000Q00(2M.OQ000008M.00000035M 160

Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).900.400 *400.900 ANGLE RP RS TP TS ENERGY.00.00000000 -.10497241.00000000 1.10497240 1.00000000 5.00.01552639 -.10079566.00701925 1.10467370.99999985 10.00,03018967 -.08847485.01418650 1.10377320.99999992 15.00.04321640 -.06865884.02156589 1.10226960.99999979 20.00.05464329 -.04255597.02834887 1.10025850.99999989 IMAGINARY 25.00.06412643 -.01198695.03438120 1.09812240 1.00000000 -.04713458J.00229091J.05231800J -.00229916J.00000000.07958560M.01220390M.06260384M 1.09812470M IMAGINARY 30.00.04094126.02157581.07203950 1.09390660 1.00000000.01519647J.00481334J -.01678831J -.00454848J -.00000000.04367058M.02210620M.07396983M 1.09391590M 35.00.04723345.05937152.07281430 1.08464430 1.O0000000.02636737J.01002337J -.02803433J -.00772245J.00000000.05409470M.06021167M.07802465M 1.08467170M 40.00.04854038.09743782.07489876 1.07146090.99999990.03825173J.01668714J -.03889348J -.00940293J.00000000.06180100M.09885641M.08439507M 1.07150210M 45.00.04736712.13329750.07574971 1*05394760 1.00000000.05078166J.02549794J -.04918617J -.00874688J -.00000000.06944365M.13571429M.09031776M 1.05398380M 50.00.04434913.16410681.07509975 1.03175720.99999979.06351514J.03718167J -.05847495J -.00479064J -.00000001.07746624M.16826622M.09518032M 1.03176820M 55.00.03984500.18651217.07310974 1.00434800.99999986.07578298J.05255518J -.06627834J.00329388J -.00000000.08561941M.19377522M.09868056M 1.00435330M 161

Institute of Science and Technology The University of Michigan 60.00.03410481.19624179.07008547.97052579.99999979.08672475J.07242633J -.07211174J *01609409J -*00000000 *09318970M *20918033M *10055882M *97065921M 65.00 *02730767.18721159.06633910.92767496 1.00000000 *09526120J.09738278J -.07543788J.03387857J.00000003.09909796M.21102508M.10045770M *92829336M 70*00.01959654.14969095.06203955 *87037345 *99999990 *09996293J.12730451J -.07552360J.05640088J.00000003 *10186566M *19650399M.09773802M *87219894M 75.00 *01116412 *06649670.05693911.78763592.99999990.09870542J.15997718J -.07116092J.08215408J -.00000005.09933478M.17324695M.09113693M.79190885M 80.00.00253929 -*09528267 *04967957.65688276 1.00000000.08784209J.18658264J -.06015740J.10559114J *00000005.08787879M.20950386M.07801905M.66531529M 85.00 -.00424584 -.40319214.03570327.42977889.99999994.06018008J.17518249J -.03848863J.10624394J -.00000001.06032967M.43960527M.05249855M.44271622M 90.00.00000002 -1.0000060 -.*0000005 -.00000043.99999990 -.00000009J -.0000039J *0000005J -.Q0000025J.00000027.00000009M 1.0O~O5QM.00000007M.00000050M 162

Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).700.400.400 1.000 ANGLE RP RS TP TS ENERGY.00.00000000 -.17647C61.00000000 1.17647060 1.00000000 5.00.02477649 -.16861419.02523767 1.17541770.99999991 10.00.04731995 -.14559500.05102037 1.17220130.99999993 15.00.06541089 -.10911177.07788664 1.16665990.99999974 20.00.07743291 -.06225034.10567137 1.15872880 *99999981 IMAGINARY 25.00.08834408 -.01020717.12696261 1.15051160.99999998 -.03567341J.00328317J.04092976J -.01072540J *00000000.09527470M.01072220M.13339696M 1.15056150M 30.00 -.00288992 *04162429.24994261 1.11098990.99999996.00466665J.00003012J -.00497441J.00152089J -.00000000.00548901M.04162430M.24999210M 1.11099090M 35.00 -.01909714.06481165.27951217 1.10729540 1.0000000.11710545J.02077303J -.11696094J.03546918J -.00000001.11865237M.06805930M.30299655M 1.10786330M IMAGINARY 40.00.04605926.13069307.21656807 1.09415540.99999992.14012867J.07653957J -.13823838J.01079501J.00000000.14750423M.15145621M.25692718M 1.09420860M 45.00.04756153.18291111.20974026 1.05240750 *99999998.15397925J.11708806J -.14261191J.01265768J -.00000002.16115740M.21717754M.25363188M 1.05248350M 50.00.03920721.21937419.20617559 1.00246970 *99999993.17106400J.16590565J -.14669959J.02565736J -.00000005.17549956M.27504494M.25303980M 1.00279790M 55.00.02524158.23486557.20247604.94461871.99999988.18682782J.22427136J -.14690848J.04869367J -.00000008.18852525M.32474523M.25015724M.94587291M 163

Institute of Science and Technology The University of Michigan 60.00 *00728931.22213604 *19792196.87802742.99999990.19812391J.29161007J -.14162851J.08068870J -.00000012 *19825795M *36657993M.24337571M.88172717M 65.00 -.01336841.17186870 *19178760.79993351 1.00000000 *20188533J.36456868J -.12984073J *11945608J -.00000001.20232745M.40304983M *23160548M *80880366M 70.00 -.03490529.07195588 *18238470 *70489480 1.00000000 *19473456J *43475548J -.11074999J *16077152J -.00000000 *19783813M *44066991M *21337698M.72299665M 75.00 -.05393042 -.09259393.16621274.58426682.99999990.17283074J *48424584J -*08394854J.19619917J -.00000014.18104959M *49301892M *18620964M.61632931M 80.00 -.06379988 -.33626315.13691818 *42701546 1.00000010.13231491J *47720729J -.05057947J *20831435J -.0000009.14689335M.58378053M.14596187M *47511794M 85.00 -.05213354 -.65807677.08472644.22604858.99999997.07181367J.34791161J -.01671255J.16235641J.00000003.08874182M.74438399M.08635901M.27831199M 90.00.00000005 -1.00 Q0020 -.00000008 -.00000018 1.00000000 -.00000053 -,00000036J -000000 -000000 -00017J -.00000003.00000007M 1.000OOO0OM *00000008M *00000025M 164

Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV WAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).800.400.400 1.000 ANGLE RP RS TP TS ENERGY.00.00000000 -.11111115.00000000 1.11111110 1.00000000 5.00 *01555524 -.10584780 *01594016 1.11038530.99999988 10.00.02940146 -.09039648.03255908 1.10816070.99999983 15.00.03960422 -.06580720.05078307 1.10428540.99999983 20.00.04355908 -.03400383.07224011 1.09847400.99999987 IMAGINARY 25.00.03193826.00171902.10570054 1.08950780.99999979 -.01590275J *00046041J *01725735J -.00274989J -.00000000.03567842M.00177961M.10710004M 1.08951120M 30.00 -.01787278.02968556.17269568 1.07759690 1.00000000.06967106J *00517349J -.07223594J *01098991J -*00000000.07192700M *03013300M.18719462M 1.07765290M IMAGINARY 35.00.04574609.07671622.11575122 1.06997710 1.00000010.08418459J.02618494J -.08482482J.00167280J.00000000.09581101M.08106189M.14350468M 1.06997830M 40.00.05062334.11944590.11485600 1.04812040.99999992.09251265J.04228731J -.08888986J.00151760J.00000000.10545764M.12671045M.14523535M 1.04812150M 45.00.04924478.15696868.11547894 1.02037150 1.00000000.10532955J.06304850J -.09584638J.00611850J.00000000.11627279M.16915756M.15007303M 1.02038980M 50.00.04432713.18585093.11529854.98654696.99999995.11924339J.08949453J -.10226825J.01607937J.00000001.12721587M.20627612M.15411861M.98667798M 55.00.03673616.20169310.11407888.94621185.99999999.13240813J.12246310J -.10668881J.03200939J -.00000003.13740982M.23596041M.15619376M.94675311M 165

Institute of Science and Technology The University of Michigan 60.00.02693314 *19895682 *11195863.89813656.99999991.14315000J.16232835J -.10813752J *05406575J -.00000007 *14566165M.25677676M.15565493M.89976240M 65.00.01529236.17014391.10897626 *83955596 1.00000000.1496339CJ *20841663J -l10575561J *08172504J -.00000002 *15041329M *26904728M.15185543M *84352426M 70.C00 00232740.10429593.10471195.76507535 1.00000010.14960602J.25779435J -.09855494J *11328785J -.00000005.14962411M *27809273M.14379732M *77341736M 75.00 -.01091497 -*01548313.09775634.66491547.99999990.14000130J.30241704J -.08521969J.14442510J -.00000007.14042613M.30281313M.12968693M.68041986M 80.00 -.02190245 -.21556898.08463824.52215917 1.00000000.11631810J.32188284J -.06409291J.16400999J -.000000003.11836222M.38739971M.10616748M.54731112M 85.00 -.024051C7 -.53375810.05751101.31000771 1.00000000.07197451J.26440453J -.03411796J.14234660J -.00000007.07588665M.59565716M.06686966M.34112656M 90.00.00G00003 -1.00000w30 -000000Q06 -Q00000028.99999980 -.00000006J -000OOC35J.00000002J -.00000020J.0000000.00000007M 1.00000020M.00000006M.00000034M 166

Institute of Science and Technology The University of Michigan AMPLITUDE RATIOS FOR AN INCIDENT SV wAVE VELOCITY POISSONS POISSONS DENSITY RATIO RATIO RATIO RATIO (TRANS/INC) (TRANS) (INC) (TRANS/INC).900 *400 *400 1.000 ANGLE RP RS TP TS ENERGY.00.00000000 -.05263160.00000000 1.05263160 1.00000000 5.00.00734501 -.04998781 *00757655 1.05225810.99999982 10.00.01371702 -.04220386 *01565482 1.05111350.99999980 15.00.01786230 -002973793 *02503260 1.04911690.99999982 20.00.01725995 -.01344018.03781846 1.04608990 1.00000000 IMAGINARY 25.00 -.00834052.00472418.07434848 1.04089470 1.00000000 ~00633027J.00003965J -.00655888J.00043940J.00000000.01047075M.00472434M.07463723M 1.04089470M IMAGINARY 30.00.02700C21.02612170.04553912 1.03766910 1.00000000 *03916675J.00441776J -.03971409J.00041176J -.00000000.04757148M.02649264M *06042368M 1.03766910M 35.00.03169701.04917382.04618965 1.02960250.99999992 0.4013073J.00771679J -.U3964024J -.00007329J -u00000000.05113879M.04977563M.06086733M 1.02960240M 40.00.03317369.07163743.04772362 1.01881840.99999987.04562606J.01224626J -.04377548J.00052106J.0000000.05641127M.07267663M.06475984M 1.01881840M 45.00.03303453.09182208.04854094 1.00479880.99999997.05248176J.01825252J -.04880669J.00247936J.0000000.062U1303M.09361863M.06883543M 1.00480180M 50.00.03164705.10754023.04842656.98686259.99999993.05973761J.02604927J -.05378489J.00623728J.00000000.06760265M.11065019M.07237366M.98688229M 55.00.02921421.11599109.04741081.96395637.99999991.06672272J.03597214J -.05814610J.01220083J -.00000000.07283812M.12144104M.07502502M.96403357M 167

Institute of Science and Technology The University of Michigan 60.0U.02589354.11335802 *04560711.93427569 *99999984.07276172J.04831296J -.061411173 *02066877J.00000000 *07723175M *12322411M *07649406M *93450428M 65.00.02182026 *09399904.04313887.89458542.99999998 *07705473J *06317666J -.06306401J.03173653J *00000002.C8008467M.11325683M.07640701M *89514818M 70.00.01711881.04886325.04005367.83895831.99999990.07854042J.08013564J -.06242422J.04508127J -.0000000.08038440M.09385808M *07416927M *84016865M 75.00.01193073 -.03765503.03615914.75631606.99999990.07563965J.09731235J -.05844013J.05935599J -.00000001.07657479M.10434363M.06872214M.75864162M 80.00.00651091 -.19418580.03063313.62536257 *99999989.06571756J.10875115J -.04931446J.07035887J *00000004.06603930M.22256445M.05805432M.62930812M 85.00.00159756 -.47644020.02099072.40343363 1000000000.04387804J.09621426J -.03180777J.06509384J -.00000001.04390711M.48605806M.03810964M.40865130M u.u00.00000000 -1.00000Q40 -.00000002 -.00000043.99999970 -.00000004J -.00000012J.00000002J -.00000008J -.00000003.00000004M 1 0000M 00000030M OOOO03M.00000044M 168

Institute of Science and Technology The University of Michigan DISTRIBUTION LIST Advanced Research Projects Agency Air Force Office of Aerospace Research Air Force Systems Command Nuclear Test Detection Office Headquarters Andrews Air Force Base The Pentagon Washington 25, D. C. (2) Washington 25, D. C. (15) Washington 25, D. C. (4) Washington 25, D. C. (4) ATTN: Major Philip J. Crossman (RROS) Air Force Systems Command Advanced Research Projects Agency Andrews Air Force Base Air Force Aerospace Research Washigton 25, D. C. The Pentagon Washington 25, D. C. Washington 25, D. C. ~Washington 25,D.C.Washington 25, D. C. (2) ATTN: Major J. C. Stokes, USAF ATTN: Dr. Charles C. Bates ATTN: Lt. Col. James A. Fava (RROS) HQ USAF (AFTAC) Advanced Research Projects Agency Air Force Ca dge Research Laoratories VELA Seismological Center The Pentagon Electronic Systems Division Washington 25, D. C. (15) Washington 25, D. C. L. G. Hanscom Field ATTN: TD-1, Lt. Col. Ridenour ATTN: Mr. Russell Beard Bedford, Massachusetts University of Alaska ATTN: Project Officer University of Alaska Advanced Research Projects Agency Sys tem 477-L (ESH) Geophysical Institute The Pentagon S L ( ) College, Alaska Washington 25, D. C. Air Force Cambridge Research Laboratories ATTN: Dr. Edward Berg ATTN: Mr. R. Black Headquarters L. G. Hanscom Field Alberta, University of Advanced Research Projects Agency Bedford, Massachusetts (5) Calgary Campus The Pentagon Calgary, Alberta, Canada Washington 25, D. C. ATTN: Major Robert A. Gray USAF ATTN: Prof. K. Vozoff ATTN: Mr. William Bolton VIA: Office of the Secretary of Defense Air Force, Department of the Advanced Research Projects Agency Airecor ate of eearh an ehnoo Advanced Research Projects Agency Advaned ResearchProjetoAgDirectorate of Research and Technologyhe Pentagon The Pentagon DCS/DThe Pentagon Washington 25, D. C. Washington 25, D. C. Washington 25, D. C. ATTN: Mr. D. Clements ATTN: Major E. C. Lowry ATTN: J. R. Loftis, Jr. Advanced Research Projects Agency Air Force Office of AerospaceAllied Research Associates, Inc. The Pentagon European Office 43 Leon Street Washington 25, D. C. The Shell Building Boston, Massachusetts ATTN: Mr. Robert Frosch 47 Rue Cahtersteen American Geological Institute Bruss els, Belgium 2101 Constitution Ave., N. W. Advanced Research Projects Agency VIA: Office of the Secretary of Defense Washington, D. C. The Pentagon Advanced Research Projects Agency Washington 25, D. C. The Pentagon ATTN: Lt. Col. Robert Harris Washington 25, D. C. ALPENS ATTN: J. R. Loftis, Jr. 10 Rue Claude Bernard Advanced Research Projects Agency Paris V, France The Pentagon Washington 25, D. C. Air Force, Department of ATTN: Prof. Y. Rocard Washington T25,~ D. C. Office of the Assistant Secretary of the Air Force ATTN: Dr. Robert L. Sproull (Research and Development) VIA: Office of the Secretary Washington 25, D. C. Advanced Research Projects Agency Advanced Research Projects Agency ATTN: Mr. Franklin J Ross The Pentagon The Pentagon Washington 25, D. C. Washington 25, D. C. (10) Air Force, Department of the ATTN: J. R. Loftis, Jr. ATTN: TIO Office of the Deputy Chief of Staff Development American Museum of Natural History Aerospace Corporation Washington 25, D. C. Central Park West at 79th Street P. 0. Box 95085 New York 24, New York Los Angeles 45, California (2) ATTN: Lt. Col. G. T. Grottle AFDSD/MS ATTN: Mr. George H. Goodwin, Jr., Librarian ATTN: Mr. Carlton M. Beyer Air Force Office of Aerospace Research American University Aerospace Corporation Commander Department of Earth Science 2400 East El Segundo Boulevard Tempo D Washington, D. C., 20016 El Segundo, California El Segundo, California 6th and Constitution Ave., S. W. ATTN: Professor Paul Bauer ATTN: Dr. Byron P. Leonard Washington 25, D. C. (4)' Arctic Institute of North America AGI Technical Publications Air Force Office of Scientific Research 3458 Re th Street 2101 Constitution Ave., N. W. Executive Director M ta Washington 25, D. C. Washington 25, D. C.ntreal 25, Canada ATTN: Mr. John C. Reed ATTN: Mr. Martin Russell ATTN: SRYG Execue Diretor Executive Director Air Force, U. S., Headquarters Air Force Office of Scientific Research VIA: Office of the Secretary of Defense Aeronautical Chart & Information Center Washington 25, D. C. (4) Advanced Research Projects Agency Second and Arsenal ATTNThe Pentagon St. Louis 18, Missouri Lt. Col. William J. Best Washington 25, D. C. Lt. Col. William J. BestJ ATTN: ACDEG-4 USAF ATTN: J. R. Loftis, Jr. 169

Institute of Science and Technology The University of Michigan Armour Research Foundation Atomic Energy Establishment Observatoire de Geophysique Illinois Institute of Technology Apollo Pier Road College Jean-de-Brebeuf Technology Center Bombay 1, India 3200 Chemin Ste-Catherine Chicago 16, Illinois ATTN: Dr. H. M. yer Montreal 26, Canada ATTN: Mr. Andrew Unger VIA: Office of the Secretary Prof. M. Buist, S. J. Advanced Research Projects Agency Director Arms Control and Disarmament Agency The Pentagon VIA: Office of the Secretary of Defense Science and Technology Bureau Washington 25, D.C. Advanced Research Projects Agency Room 5486, State Department The Pentagon Washington 25, D. C. ATTN: J. R. Loftis Washington 25, D. C. ATTN: Dr. H. R. Meyers Roland F. BATTN: J. R. Loftis, Jr. Roland F. Beers, Inc. Army. P.O. Box 23 Signal Research and Development Laboratory, U. S. Alexandria, Virginia Professo r Dr. HansBCloss ~~~~~~~~~~~~~Fort Monmouth, New Jersey'Bundesanstalt fur Bodenforschung Fort Monmouth, New Jersey ATTN: Roland F. Beers Wiesenstrasse 1, Hannover 3 ATTN: Commanding Officer West Germany Army, Department of the Bell Telephone Laboratories VIA: Science Attache Army, Department of the Mr ilewy VIA: Sin A Office of the Chief Murray H, New Jersey U. S. Embassy Research and Development ATTN: Dr. Bruce P. Bogert Bonn, Germany OCS OCS^^~~~~~~~~~~~~~~~~~~~~~ ~VIA: Office of the Secretary of Defense Washington 25, D. C. Bell Telephone Laboratories Advanced Research Projects Agency ATTN: Brig. Gen. David C. Lewis Room 1A-218 The Pentagon Murray Hill, New Jersey Washington 25, D. C. Army Engineer Research and Development ATTN: Dr. John W. Tukey ATTN J. R Loftis Jr. Laboratories, U. S. Fort Belvoir, Virginia Bell Telephone Laboratories Bureau of Mines, U. S. ATTN: Mine Detection Branch Whippany, New Jersey Applied Physics Research Laboratory ATTN: Dr. R. A. Walker College Park, Maryland Army Research Office Army Research Office ATTN: Dr. Leonard Obert CM Duke Station Bell Telephone Laboratories Durham, North Carolina Western Electric Company Bureau of Ships, U. S. Atlantic Refining Company Whippany, New Jersey Department of the Navy 4500 West Mockingbird Lane ATTN: C. F. Weibush Washington 25, D. C. Dallas, Texas ATTN: Code 689D ATTN: Helen McKenzie Dr. F. G. Blake, Jr. Librarian Bureau of Ships, U. S. c/o Mrs. F. G. Blake Code 689D Atomic Energy Commission, U. S. 226 Lawrence Street Washington 25, D. C. Albuquerque Operations Office New Haven 11, Conn. ATTN: Mr. A. H. Sobel P. 0. Box 5400 Albuquerque, New Mexico Blue Mountains Seismological Observatory California Institute of Technology ATTN: Mr. R. E. Miller The Geotechnical Corporation Seismological Laboratory Baker, Oregon 220 North San Rafael Avenue Atomic Energy Commission, U. S. ATTN: Station Manager Pasadena, California Director ~~~~~~~~~~~~~~~~~Director ~~ATTN: Dr. Hugo Benioff Division of Military Applications Group Captain John Rowlands, RAF Washington 25, D. C. (2) Atomic Coordinating Office C ATTN: Brig. Gen. Austin W. Betts R shefenceStaffs Division of Engineering British Defence Staffs Atomic Energy Commission, U. S. British Embassy Division of Military Applications 3100 Massachusetts Avenue, N. W. ATTN: Dr. George W. Housner Chairman Washington 8, D. C. (5) Washington 25, D. C. California Institute of Technology VIA: Office of the Secretary of Defense, ARPA Seismological Laboratory ATTN: Mr. Don Gale The Pentagon 220 North San Rafael Avenue Washington 25, D. C. Pasadena, California Atomic Energy Commission Division of Peaceful Nuclear Explosions ATTN: J. R. Loftis, Jr. ATTN: Dr. Frank Press Chairman Washington 25, D. C. British Petroleum Company Ltd., Jet Propulsion Laboratories ATTN: Mr. John Kelly Exploration Division California Institute of Technology BP Research Center 4800 Oak Grove Drive Atomic Energy Commission Chertsey Road Pasadena, California General Managers Office Sunbury-on-Thames, Middlesex, England A Germantown, Maryland (2) ATTN: Manager ATTN: Dr. S. G. English VIA: Office of the Secretary of Defense California Institute of Technology Atomic Energy Commission Advanced Research Projects Agency Seismological Laboratory Technical Information Service Extension The Pentagon 220 N. San Rafael Avenue Oakridge, Tennessee (2) Washington 25, D. C. Pasadena, California ATTN: Hugh Voress ATTN: J. R. Loftis, Jr. ATTN: Dr. L. Knopoff 170

Institute of Science and Technology The University of Michigan California Research Corporation Carnegie Institution of Washington Cornell University 200 Bush Street Department of Terrestrial Magnetism Research and Advanced Studies San Francisco, California 5241 Broadbranch Road, N. W. 303 Day Hall ATTN: Mr. R. S. Faull Washington 15, D. C. Ithaca, New York ATTN: Dr. John J. Steinhart ATTN: Dr. Frank A. Long California Research Laboratory Vice President P. 0. Box 446 Century Geophysical Corporation La Habra, California P. O. Box C Cumberland Plateau Seismological Observatory Admiral Station McMinnville, Tennessee ATTN: Dr. P. Edward ByerlyTulsa 15, JOklahoma ATTN: Station Manager California, University of ATTN: R. A. Broding Lawrence Radiation Laboratory Data Analysis and Technique Development Center Livermore, California Century Geophysical Corporation P. O. Box 334 Livermore, California 2) P. 0. Box C Alexandria, Virginia (6) ATTN: Dr. Roland F. Herbst Admiral Station Dr. Charles E. Violet Tulsa 15, Oklahoma ATTN: Mr. F. B. Coker ATTN: Daniel Hearn Defense Atomic Support Agency California, University of Department of Defense Lawrence Radiation Laboratory Century Geophysical Corporation Chief Livermore, California P. 0. Box C Washington 25, D. C. Admiral Station ATTN: Dr. Kenneth M. Watson Tulsa 15 Oklahoma ATTN: Major J. Dickson Tulsa 15, Oklahoma ATTN: J. E. A. T. Woodburn Defense Atomic Support Agency California, University of Field Command Seismograph Station Commerce, Department of Sandia Base Berkeley 4, California Coast & Geodetic Survey, U. S. Albuquerque, New Mexico Geophysics Division ATTN: Prof. P. Byerly Washington 25, D.C. ATTN: Lt. Col. Conrad R. Peterson California, University of ATTN: Dr. Dean S. Carder Defense Atomic Support Agency Lawrence Radiation Laboratory Headquarters Technical Information Division Commerce, Department of Washington 25, D. C. P. 0. Box 808 Coast & Geodetic Survey, U. S. ATTN: John G. Lewis Livermore, California Geophysics Division ATTN: Clovis G. Craig Washington 25, D. C. Defense Atomic Support Agency ATTN: Mr. J. Jordan Weapons Effects and Tests Headquarters California, University of Commerce, Department of Field Command La Jolla Laboratories Coast & Geodetic Survey, U. S. Sandia Base La Jolla, California Geophysics Division Albuquerque, New Mexico ATTN: Dr. Walter Munk Washington 25, D. C. ATTN: FCWT ATTN: Mr. Leonard Murphy VELA UNIFORM Programs Officer California, University of Seismological Laboratory Commerce, Department of Defense, Department of Berkeley 4, California Coast & Geodetic Survey, U. S. Office of the Assistant Secretary of Defense Camp Mercury, Nevada for International Security Affairs ATTN: T. H. Pearce Washington, D. C. ATTN: Cdr. E. C. Cline Cambridge University Commerce, Department of Room 4E829 Department of Geodesy & Geophysics Seismological Data Center Madingley Rise, Madingley Road U. S. Coast and Geodetic Survey Defense, Department of Cambridge, England 25, D. (2) Office of the Assistant to the Secretary of ATTN: Sir Edward Bullard AT.DrtrDefense of Atomic Energy Dr. Maurice Hill ATTN: Director Washington 25, D. C. Commerce, Department of ATTN: Dr. Gerald Johnston VIA: Office of the Secretary of Defense Coast & Geodetic Survey, U. S. Advanced Research Projects Agency Advanced Research Projects Agency Seismological Laboratory Defense Documentation Center WheiPentagon Sandia Base Cameron Station Washington 25, D.C. Albuquerque, New Mexico Alexandria, Virginia (20) ATTN: J. R. Loftis, Jr. ATTN: J. R. Loftis, Jr. ATTN: Technical Director Defense, Department of ~Canadian~ D~~efense~ R ~esearc~h ^Sta ff ~Office of the Director of Defense 2450 Massachusetts Avenue, N W. Commerce, Department of Research & Engineering 2450 Massachusetts Avenue, N. W. Washingn 8, D.C. (5) National Bureau of Standards, U. S. The Pentagon Washington 8, D. C. (5) Washington 25, D. C. Washington 25, D. C. ATTN: Dr. C. E. Hubleiy ATTN: Mr. Harry Matheson ATTN: Director, Office of Atomic Programs VIA: Office of the Secretary of Defense Advanced Research Projects Agency Continental Oil Company Director of Research and Development The Pentagon P. 0. Drawer 293 Office of the Secretary of the Army Washington 25, D. C. Ponca City, Oklahoma Washington 25, D. C. ATTN: Mr. J. R. Loftis, Jr. ATTN: Dr. John M. Crawford ATTN: Lt. Col. William D. Sydnor 171

Institute of Science and Technology The University of Michigan Dresser Electronics European Research Office (9851 DU) Hughes Aircraft Company SIE Division U. S. Department of the Army Communications Division P. 0. Box 22187 Frankfurt/Main, Germany P. 0. Box 90902 Houston 27, Texas (2) APO 757, U. S. Forces (5) Airport Station ATTN: Mrs. Mildred Beaman Los Angeles 45, California ATTN: Mrs. Mildred Beaman VIA: Office of the Secretary of Defense Angeles 4, California Librarian Advanced Research Projects Agency Humble Oil and Research Labs. The Pentagon \The ^- PntagOn r~ Geophysics Department Dresser Electronics Washington 25, D. C. Geophyss D. B SIE Division ATTN: J. R. Loftis, Jr. Houston 1, Texas P. 0. Box 22187 Houston 27, Texas General Atronics Corporation ATTN: Dr. Lynn Howell ATTN: Mr. Howard A. Bond 1200 East Mermaid Lane Hunting Geophysical Services Inc. Vice-Pres., Military Engineering Philadelphia, Pennsylvania 19118 10 Rockefeller Plaza ATTN: Mr. Joseph T. Underwood, III New York 20, N. Y. Dunbar Laboratory General Dynamics Corporation ATTN: Mr. R. H. Stebbins, Gen. Mgr. Electric Boat Division Oxford Street Electric Boat Divsion Illinois, University of Cambridge 28, Massachusetts Groton, Connecticut Department of Mining ATTN: Dr. H. Pollock ATTN: Mr. J. V. Harrington Urbana, Illinois General Electric Company ATTN: Dr. Adrian Scheidegger Dupont Company 735 State Street Interior, Department of Eastern Laboratory Santa Barbara, California Bureau of Mines U. S. Gibbstown, New Jersey ATTN: Mr. Finn Dyolf Bronner Washington 25, D. C. (5) ATTN: Mr. A. B. Andrews Defense Electronics Division ATTN- James Hill Explosives Department Geophysical and Polar Research Center Interior, Department of Edgerton, Germeshausen, and Grier, Inc. 6021 South Highland Road Branch of Crustal Studies Director of Research Madison 6, Wisconsin U. S. Geological Survey 160 Brookline Drive ATTN: Prof. George Woollard 7580 W. 16th Street Boston, Massachusetts Director Lakewood 15, Colorado ATTN: Clyde Dobbie Geophysical Service Inc ATTN: Dr. George Keller P. 0. Box 35084 Interior, Department of Edgerton, Germeshausen, and Grier, Inc. Dallas 35, Texas Branch of Crustal Studies 160 Brookline Drive ATTN D Saunders U. S. Geological Survey Boston, Massachusetts 7580 W. 16th Street ATTN: Dr. Raymond C. O'Rourke Georgia Institute of Technology Lakewood 15, Colorado (5) Engineering Experiment Station ATTN: Louis C. Pakiser Atlanta, Georgia Edgerton, Germeshausen, and Grier, Inc. Interior, Department of 160 Brookline Avenue ATTN: Mr. Frederick Bellinger, Chief Glogical Surve Boston, Massachusetts Materials Sciences Division Denver Federal enter ATTN: F. T. Strabala Georgia Institute of Technology Denver 25, Colorado Engineering Experimental Station ATTN: Dr. H. Roach Electro-Mechanics Company Atlanta, Georgia TP.. Box 802 Be Interior, Department of'~P. O. Box 802 ATTN: Mr. John E. Husted Office of the Science Advisor to the Secretary Austin 64, Texas Research Scientist, Head Washington 25, D. C. ATTN: Dr. Fred H. Morris Geotechnical Corporation ATTN: Dr. Calhoun WMSO Engineer Research and Development Laboratory P. 0. Box 2071 Interior, Department of the Mines Detection Branch Lawton, Oklahoma (2) U. S. Geological Survey Fort Belvoir, Virginia Room 4215, GSA Building TFort BelvoirM. S inia ATTN: Station Director Washington 25, D. C. (2) ATTN: Mr. S. E. Dwornik Geotechnical Corporation ATTN: Dr. William Thurston Engineering-Physics Company 3401 Shilo oad Dr. Wayne Hall P. W. Box 28277 5515 Randolph Street P.. Bx 2827 Interior, Department of Rockville, Maryland Dallas 28, Texas (19) Geological Survey ATTN: Mr. Vincent Cushing ATTN: Dr. W. Heroy, Jr. Branch of Military Geology Washington 25, D. C. (3) Harvard University ATTN: Mrs. Mildred P. White The Superintendent Department of Geology The Observatory Cambridge, Massachusetts Itek Laboratories Eskdalemuir ATTN: Prof. L. Don Leet Lexington 73, Massachusetts Langholm, Dumfriesshire, Scotland ATTN: Mr. Robert Fleming VIA: Office of the Secretary of Defense Hawaii, University of Advanced Research Projects Agency Hawaii Institute of Geophysics Jersey Production Research Company The Pentagon Honolulu 14, Hawaii 1133 North Lewis Avenue Washington 25, D. C. ATTN: Dr. Doak Cox Tulsa 10, Oklahoma ATTN: J. R. Loftis Department of Earth Sciences ATTN: Mr. P. Jacobson 172

Institute of Science and Technology The University of Michigan John Carroll University Massachusetts Institute of Technology National Bureau of Standards Cleveland 18, Ohio Department of Electrical Engineering Boulder Laboratories Cambridge, Massachusetts Boulder, Colorado ATTN: Rev. H. F. Birkenhauer, S. J. ATTN: Prof. J. Ruina ATTN: Mrs. Victoria S. Baker, Librarian John Carroll University Cleveland 18, Ohio Massachusetts Institute of Technology National Engineering Science Company Lincoln Laboratory 1711 South Fair Oaks Avenue ATTN: Dr. Edward Walter Lexington-73, Massachusetts (2) Pasadena, California Jordskelstasjonen ATTN: Dr. Paul Green ATTN: Dr. N. D. Baratynski University of Bergen Bergen, Norway National Engineering Science Company Massachusetts Institute of Technology 1711 South Fair Oaks VIA: Office of the Economic Counselor Lincoln Laboratory Pasadena California U. S. Embassy Lexington 73, Massachusetts Drammesveien, Oslo, Norway ATTN: Librarian ATTN: Dr. J. F. Hook VIA: Office of the Secretary of Defense Advanced Research Projects Agency Massachusetts Institute of Technology National Science Foundation The Pentagon Department of Earth Sciences 1951 Constitution Avenue, N. W. Washington 25, D. C. Cambridge 39, Massachusetts Washington, D. C. ATTN: J. R. Loftis, Jr. ATTN: Prof. S. M. Simpson ATTN: Dr. Roy E. Hanson LaCoste and Romberg National Science Foundation Austin, Texas Melpar, Inc. Office of Antarctic Programs Technical Information Center ti ATTN: Mr. Lucian J. B. LaCoste 3000 Arlington Boulevard 1951 Constitution Avenue, N. W Falls Church,: Virgins Washington 25, D. C. Lamont Geological Observatory ATTN: Information Officer Columbia University ATTN: P. D.VachonOcer Palisades, New York r r Melpar, Inc. Director ATTN: Dr. Maurice Ewing Science Division National Security Agency Applied Dr. Maurice Ewing St Fort George G. Meade, Maryland Lamont Geological Observatory 11 Galen Street Columbia University Watertown 72, Massachusetts ATTN: CS/TDL (Room 2C087) Palisades, New York ATTN: Mrs. Lorraine Nazzaro Miss Jean Creswell ATTN: Dr. K L. Hunkins Librarian U. S. Naval Radiological Defense Laboratory Lamont Geological Observatory Meteorological Office (M. O. 14) San Francisco 24, California Colubia University (2London Road, Bracknell ATTN: Mr. E. R. Bowman Palisades, New York () Berkshire, England Head, Library Branch ATTN: Library ATTN: The Director-General LATTN: Library ATTN: The Director-General Obs yjU. S. Naval Radiological Defense Laboratory Lamont Geological Observatory VIA: Office of the Secretary of Defense San Francisco 24, California Columbia University Advanced Research Projects Agency Palisades, New York The Pentagon ATTN: Mr. Ken Sinclair ATTN: Dr. Jack E. Oliver Washington 25, D. C. Naval Research Laboratory Lebel, Jean ATTN: J. R. Loftis Washington 25, D. C. CLES ATTN: The Librarian 6 Avenue Daniel Leseur Minnesota, University of Paris 7a, France Institute of Technology School of Mines and Metallurgy Navy Department VIA: Office of the Secretary of Defense Minneapolis 14, Minnesota Bureau of Ships Advanced Research Projects Agency Washington 25 D. C. The Pentagon ATTN: Prof. Harold M. Mooney Washington 25, D. C. Geophysics ATTN: Code 362 B ATTN: J. R. Loftis Minneapolis Honeywell Company Navy, Department of the Heiland Division Office of the Deputy Chief of Naval Operations Los Alamos Scientific Laboratory Denver, Colorado (Development) Los Alamos, New Mexico Washington 25, D.C. ATTN: Mr. John Paul ATTN: Dr. Conrad L. Longmire Director of Magnetic Tape Division ATTN: Mr. W. Magnitizky Op-07T Mandrel Industries, Inc. Electro-Technical Labs Division T R CorPOron Electro-Technical Labs Division Dept. D-17 Navy, Director of the 5234 GlenmntDrive Box 208 Office of the Deputy Chief of Naval Operations P. O. Box 363060 Bedford Massachusetts (Development) Houston 36, Texas Op-75 ATTN: Dr. R. N. Ostreim ATTN: Dr John C. Morganstein Washington 25, D. C. Mandrel Industries, Inc. MOHOLE Project Navy, Department of Research Division National Academy of Sciences Office of Naval Research 1025 S. Shepard 2101 Constitution Avenue, N. W. Washington 25, D. C. (5) Houston 19, Texas Washington 25, D. C. ATTN: James W. Winchester ATTN: Dr. Lewis M. Mott-Smith ATTN: Executive Secretary Code 418 173

Institute of Science and Technology The University of Michigan Navy Electronics Laboratory, U. S. PETTY Geophysical Engineering Co. Rice University Director P. 0. Drawer 2061 Houston 1, Texas San Diego 52, California San Antonio 6, Texas ATTN: Prof. J. C. DeBremaecker ATTN: Code 2350 ATTN: J. O. Parr, Jr. Dept. of Geology Navy Electronics Laboratory, U. S. Phillips Petroleum Company Sandia Corporation Point Loma Laboratory Bartelsville, Oklahoma Division 7000 San Diego, California Sandia Base ATTN: Mr. Harold L. Mendenhall Albuquerque, New Mexico ATTN: Charles Johnson District Geophysicist ATTN: Mr. G. A. Fowler Director Planetary Sciences, Inc. Navy Electronics Laboratory 501 Washington Street Sandia Corporation San Diego 52, California P. O. Box 561 Sandia Base ATTN: Mr. T. McMillian Santa Clara, California Albuquerque, New Mexico ATTN: Dr. William Adams ATTN: William R. Perret Navy Oceanographic Office, U. S. The Hydrographer Prengle, Dukler, and Crump, Inc. Saskatchewan, University of Washington 25, D. C. 5417 Crawford Street Saskatoon Navy Radiological Defense Lab UHouston 4, Texas Saskatchewan, Canada Navy Radiological Defense Lab., U. S. Director ATTN: Dr. Clark Goodman ATTN: Dr. James Mawdsley San Francisco 24, California San Francisco 24, California Princeton University VIA: Office of the Secretary of Defense ATTN: Dr. Eugene Cooper Physics Department Advanced Research Projects Agency Princeton, New Jersey The Pentagon Navy Radiological Defense Laboratory Washington 25 D C Hunters Point ATTN: Dr. Val L. Fitch Building 815 ATTN: J. R. Loftis, Jr. San Francisco, California Pure Oil Company ATTN: Dr. L. Gevantman Research Laboratories Seismograph Service Corporation Crystal Lake, Illinois P. O. Box 1590 New Mexico, University of ATTN: Dr. Ira Cram, Jr. Tulsa, Oklahoma Albuquerque, New Mexico Albuquerque, New Mexico Radio Corporation of America ATTN: Dr. James E. Hawkins ATTN: Dr. H. L. Walter David Sarnoff Research Center Director of Research Princeton, New Jersey Seismological Laboratory Uppsala, Sweden North American Aviation (S+ID) ATTN: Dr. D. S. McCoy ATTN: Dr. Markus B&th 12214 Lakewood Boulevard Downey, California Rand Corporation, The VIA: Office of the Secretary of Defense 1700 Main Street Advanced Research Projects Agency ATTN: Mr. Robert Fowler Santa Monica, California The Pentagon Dept. 197-330 ATTN: Dr. Richard Latter Washington 25 D C. ATTN: J. R. Loftis, Jr. Nortronics Raytheon Company Geophysics Research Group Missile and Systems Division Shell Development Lab. 77 A Street Bedford, Massachusetts Development Lab. Needham Heights 94, Massachusetts P.. Box 481 ATTN: Mr. C. C. Abt Houston 1, Texas ATTN: Dr. Paul R. Miles Rensselaer Polytechnic Institute ATTN: Dr. Sidney Kaufman The Ohio State University Research Foundation Troy, New York 1314 Kinnear Road Sinclair Research Inc. Columbus 12, Ohio ATTN: Mr R B P. R. B. Fincox 3006, Whittier Station Director of Research Tulsa Oklahoma ATTN: Dr. Robert C. Stephenson Executive Director Rensselaer Polytechnic Institute ATTN: Mr. John Bemrose Troy, New York Oklahoma, The University of South Carolina, University of Research Institute ATTN: Dr. Samuel Katz Columbia, South Carolina Norman, Oklahoma Research Institute of National Defense ATTN: Professor 0. Scheutte ATTN: Dr. Norman Ricker Stockholm 80, Sweden Head, Dept. of Physics Oregon State University ATTN:S Methodist University Southern Methodist University Department of Oceanography VIA: Office of the Science Attache Department of Geology Corvallis, Oregon U. S. Embassy Dallas Texas ATTN: Dr. P. Dehlinger Stockholm, Sweden ATTN Dr. Eugene T. Herrin ATTN: Dr. Eugene T. Herrin VIA: Office of the Secretary of Defense Oregon State University Advanced Research Projects Agency Southwest Research Institute Department of Oceanography The Pentagon 8500 Culebra Road Corvallis, Oregon Washington 25, D. C. San Antonio 5, Texas ATTN: Dr. Joe Berg ATTN: J. R. Loftis, Jr. Space-General Corporation Pennsylvania State University University of Rhode Island 777 Flower Street University Park, Pennsylvania Kingston, Rhode Island Glendale 1, California ATTN: Dr. B. F. Howell, Jr. ATTN: Professor Kane ATTN: Dr. Glenn Brown 174

Institute of Science and Technology The University of Michigan Space Technology Laboratories, Inc. St. Louis University Toronto, University of One Space Park The Institute of Technology Department of Physics Redondo Beach, California 3621 Olive Street Toronto 5, Canada St. Louis 8, Missouri ATTN: Mr. R. Whitmer S ATTN: Prof. J. T. Wilson ATTN: Dr. R. R. Heinrich VIA: Office of the Secretary of Defense Special Assistant to the President for Science and Technology St. Louis University Advanced Research Projects Agency Science and Technology St. Louis University Office of the Executive Office Building Department of Geophysics The Pentagon The White House 3621 Olive Steet Washington 25, D. C. Washington 25, D. C. St. Louis 8, Missouri ATTN: J. Loftis, ATTN: Mr. Spurgeon M. Keeny, Jr. ATTN: Dr. William Stauder, S. J. Texas Instruments, Inc. Sperry Rand Research Center Strategic Air Command P. 0. Box 35084 Sudbury, Massachusetts (OAWS) Dallas 35, Texas (7) ATTN: Mr. Alan Steeves Headquarters ATTN R. Arnett Librarian Offutt Air Force Base, Nebraska (2) W. F. Sprengnether Instrument Co., Inc. Sydney, University of Uinta Basin Seismological Observatory 4567 Swan Avenue Department of Mathematics Vernal, Utah St. Louis 10, Missouri Sydney, Australia ATTN: Station Manager ATTN: Mr. R. F. Hautly ATTN: Dr. Keith Bullen Stanford Research Institute VIA: Office of the Secretary of Defense United Earth Sciences Division Palo Alto, California Advanced Research Projects Agency P. 0. Box 334 The Pentagon Alexandria, Virginia ATTN: Dr. Allan Peterson Washington 25, D. C. ATTN: E. A. Flinn Stanford Research Institute ATTN: J. R. Loftis, Jr. Menlo Park, California United Earth Sciences Division Technical Operations, Inc. p o 114 ATTN: Dr. Thomas C. Poulterntral Researh ffice. x Central Research Office Alexandria, Virginia Director Poulter Laboratories South Research OffceAlexandria, Virginia Stanford Research Institute Burlington, Massachusetts ATTN: Mr. J. Griffin Menlo Park, California ATTN: Mr. C. Fain ATTN: L. M. Swift United Earth Sciences Division Tenneco Oil and Gas Co. P. 0. Box 334 Stanford Universiy P. 0. Box 18 Alexandria, Virginia Stanford University High Energy Physics Laboratory Houston 1, Texas ATTN: Ted Winston Stanford, California ATTN: Lynn Ervin United ElectroDynamics, Inc. ATTN: Dr. Wolfgang K. H. Panofsky Texaco, Inc. 200AllendaletroDynamics Texaco, Inc. 200 Allendale Road Stanford Research Institute Research and Technical Department Pasadena, California (2) Building 108 P. 0. Box 509 Menlo Park, California Beacon, ew orTTN: Mrs. Dorothy A. Al ATTN: Dr. Robert B. Vaile, Jr. ATTN: Dr. L. C. Roess United Kingdom Atomic Energy Authority Director, Physics Division Graduate Research Center Blacknest, Brimpton, Near Reading Stanford Research Institute P. O. Box 8478 Berkshire, England Menlo Park, California Dallas 5, Texas ATTN: Dr. Eric Carpenter ATTN: Mr. E. C. Wood ATTN: Dr. Anton L. Hales VIA: Office of the Secretary of Defense Advanced Research Projects Agency Manager, Geophysics Dept. Gravity Meter Exploration Co. The Pentagon State, Dept. of 3621 W. Alabama Avenue Washington 25, D. C. Arms Control and Disarmament Agency Houston 27, Texas ATT ATTN: J. R. Loftis, Jr. Washington 25, D. C. (2) ATTN: Dr. Nelson Steenland ATTN: Bureau of International Relations Gulf Research and Development Co. Virginia Polytechnc Institute State, Dept. of Geophysical Research Divisiontment of Geology Arms Control and Disarmament Agency P. 0. Box 2038 Blacksburg, Virginia Washington 25, D. C. Pittsburgh 30, Pennsylvania ATTN: Professor Charles Sears ATTN: Research Reference Staff ATTN: Dr. T. J. O'Donnell Director University of Utah State, Department of the Department of Geophysics Office of International Scientific Affairs Texas, University of Mines Building Washington 25, D. C. Austin 12, Texas Salt Lake City, Utah ATTN: Dr. A. Rollefson ATTN: Prof. W. T. Muehlberger ATTN: Professor Ken Cook Dept. of Geology St. Louis University University of Wisconsin The Institute of Technology Tonto Forest Seismological Observatory Geophysical and Polar Research Center 3621 Olive Street P. 0. Box 337 6021 South Highland Road St. Louis 8, Missouri Payson, Arizona Madison 6, Wisconsin ATTN: Dr. Carl Kisslinger ATTN: Mr. Allen M. Rugg, Jr. ATTN: Director 175

Institute of Science and Technology The University of Michigan University of Witwatersrand Waterways Experiment Station Western Geophysical Corporation Bernard Price Institute of Geophysical Research Jackson, Mississippi 933 N. LaBrea Street Johannesburg, South Africa ATTN: Mr. James Patty Los Angeles 38, California ATTN: Director ATTN: Mr. Carl H. Savit VIA: Office of the Secretary of Defense Advanced Research Projects Agency Waterways Experiment Station, U. S. Weston Observatory The Pentagon Vicksburg, Mississippi Weston 93, Massachusetts Washington 25, D. C. ATTN: Librarian ATTN: Rev. Daniel Linehan, S.J. ATTN: J. R. Loftis, Jr. Xavier University U.S. Geological Survey Weizmann Institute of Science Cincinnatti, Ohio Post Office Box 26 345 Middlefield Road ATTN: Rev. E. A. Bradley, S. J. Rehovoth, Israel Menlo Park, California ATTN: Librarian ATTN: Prof. C. L. Pekeris Assistant Chief Geologist for Engineering Geology VIA: Office of the Secretary of Defense U. S. Geological Survey Advanced Research Projects Agency GSA Building The Pentagon Washington 25, D. C. Washington 25, D. C. ATTN: V. R. Wilmarth ATTN: J. R. Loftis, Jr. 176

+ + + AD Div. 2/10 UNCLASSIFIED AD Div. 2/10 UNCLASSIFIED Inst. of Science and Technology, U. of Mich.,AnnArbor I. Title: VESIAC Inst. of Science and Technology, U. of Mich., Ann Arbor I. Title: VESIAC TABLES OF AMPLITUDE AND ENERGY RATIOS FOR II. Costain, John K., Cook, TABLES OF AMPLITUDE AND ENERGY RATIOS FOR II. Costain, John K., Cook, PLANE SV WAVES, by John K. Costain, Kenneth L. Kenneth L., Algermissen, PLANE SV WAVES, by John K. Costain, Kenneth L. Kenneth L., Algermissen, Cook, and S. T. Algermissen. VESIAC Special Report. S. T. Cook, and S. T. Algermissen. VESIAC Special Report. S. T. Dec. 63. 168 p. incl. illus., tables, 6 refs. HI. Advanced Research Proj- Dec. 63. 168 p. incl. illus., tables, 6 refs. III. Advanced Research Proj(Rept. No. 4410-68-X) ects Agency (Rept. No. 4410-68-X) ects Agency (Contract SD-78) Unclassified report IV. Contract SD-78 (Contract SD-78) Unclassified report IV. Contract SD-78 This report presents tabulations of energy ratios calcu- This report presents tabulations of energy ratios calculated from Knott's energy equation, and amplitude ra- lated from Knott's energy equation, and amplitude ratios calculated from the Zoeppritz equations, for a plane tios calculated from the Zoeppritz equations, for a plane SV wave incident on a plane elastic discontinuity. All SV wave incident on a plane elastic discontinuity. All computations were programmed in FORTRAN for an computations were programmed in FORTRAN for an IBM 1620 digital computer. Incident angles were varied IBM 1620 digital computer. Incident angles were varied from 00 to 90~ in increments of 20 except near the crit- from 0~ to 900 in increments of 20~ except near the critical angles, where the ratios were calculated in incre- ical angles, where the ratios were calculated in incre-.ments of 0.250 generally. Both real and imaginary co- Defense.ments of 0.250 generally. Both real and imaginary co- Defense efficients were considered in the calculations. The Documentation Center efficients were considered in the calculations. The Documentation Center (over) UNCLASSIFIED (over) UNCLASSIFIED + + + AD Div. 2/10 UNCLASSIFIED AD Div. 2/10 UNCLASSIFIED Inst. of Science and Technology, U. of Mich., Ann Arbor I. Title: VESIAC Inst. of Science and Technology, U. of Mich., Ann Arbor I. Title: VESIAC TABLES OF AMPLITUDE AND ENERGY RATIOS FOR II. Costain, John K., Cook, TABLES OF AMPLITUDE AND ENERGY RATIOS FOR II. Costain, John K., Cook, PLANE SV WAVES, by John K. Costain, Kenneth L. Kenneth L., Algermissen, PLANE SV WAVES, by John K. Costain, Kenneth L. Kenneth L., Algermissen, Cook, and S. T. Algermissen. VESIAC Special Report. S. T. Cook, and S. T. Algermissen. VESIAC Special Report. S. T. Dec. 63. 168 p. incl. illus., tables, 6 refs. III. Advanced Research Proj- Dec. 63. 168 p. incl. illus., tables, 6 refs. III. Advanced Research Proj(Rept. No. 4410-68-X) ects Agency (Rept. No. 4410-68-X) ects Agency (Contract SD-78) Unclassified report IV. Contract SD-78 (Contract SD-78) Unclassified report IV. Contract SD-78 This report presents tabulations of energy ratios calcu- This report presents tabulations of energy ratios calculated from Knott's energy equation, and amplitude ra- lated from Knott's energy equation, and amplitude ratios calculated from the Zoeppritz equations, for a plane tios calculated from the Zoeppritz equations, for a plane SV wave incident on a plane elastic discontinuity. All SV wave incident on a plane elastic discontinuity. All computations were programmed in FORTRAN for an computations were programmed in FORTRAN for an IBM 1620 digital computer. Incident angles were varied IBM 1620 digital computer. Incident angles were varied from 0~ to 90~ in increments of 20 except near the crit- from 0~ to 900 in increments of 20 except near the critical angles, where the ratios were calculated in incre- ical angles, where the ratios were calculated in incre-.ments of 0.250 generally. Both real and imaginary co- Defense.ments of 0.250 generally. Both real and imaginary co- Defense efficients were considered in the calculations. The Documentation Center efficients were considered in the calculations. The Documentation Center (over) UNCLASSIFIED (over) UNCLASSIFIED + + +

AD UNCLASSIFIED AD UNCLASSIFIED varying parameters were the velocity ratio and density DESCRIPTORS varying parameters were the velocity ratio and density DESCRIPTORS ratio across each interface, and the angle of incidence. S W ratio across each interface, and the angle of incidence. S W Energy ratios were computed for a Poisson's ratio of Seismology Energy ratios were computed for a Poisson's ratio of Seismiolog 0.25 only, and amplitude ratios were computed for 0.25 only, and amplitude ratios were computed for Poisson's ratios of both 0.25 and 0.40. Compressional Poisson's ratios of both 0.25 and 0.40. Compressional velocity ratios (transmitted/incident) of 0.7, 0.8, and 0.9, velocity ratios (transmitted/incident) of 0.7, 0.8, and 0.9, and density ratios (transmitted/incident) of 0.7, 0.8, 0.9, and density ratios (transmitted/incident) of 0.7, 0.8, 0.9, and 1.0 were used. The data are presented in 36 tables, and 1.0 were used. The data are presented in 36 tables, 12 for energy ratios and 24 for amplitude ratios. 12 for energy ratios and 24 for amplitude ratios. UNCLASSIFIED UNCLASSIFIED AD UNCLASSIFIED AD UNCLASSIFIED varying parameters were the velocity ratio and density DESCRIPTORS varying parameters were the velocity ratio and density DESCRIPTORS ratio ratio across each interface, and the angle of incidence...Seisi Energy ratios were computed for a Poisson's ratio of Seismology Energy ratios were computed for a Poisson's ratio of Seismiolog 0.25 only, and amplitude ratios were computed for 0i25 ol and amplitude ratios were computed for Poisson's ratios of both 0.25 and 0.40. Compressional Poisson's ratios of both 0.25 and 0.40. Compressional velocity ratios (transmitted/incident) of 0.7, 0.8, and 0.9, velocity ratios (transmitted/incident) of 0.7, 0.8, and 0.9, and density ratios (transmitted/incident) of 0.7, 0.8, 0.9, and density ratios (transmitted/incident) of 0.7, 0.8, 0.9, and 1.0 were used. The data are presented in 36 tables, and 1.0 were used. The data are presented in 36 tables, 12 for energy ratios and 24 for amplitude ratios. 12 for energy ratios and 24 for amplitude ratios. UNCLASSIFIED UNCLASSIFIED

+ + + AD Div. 2/10 UNCLASSIFIED AD Div. 2/10 UNCLASSIFIED Inst. of Science and Technology, U. of Mich.,AnnArbor I. Title: VESIAC Inst. of Science andTechnology, U. of Mich.,AnnArbor I. Title: VESIAC TABLES OF AMPLITUDE AND ENERGY RATIOS FOR II. Costain, John K., Cook, TABLES OF AMPLITUDE AND ENERGY RATIOS FOR II. Costain, John K., Cook, PLANE SV WAVES, by John K. Costain, Kenneth L. Kenneth L., Algermissen, PLANE SV WAVES, by John K. Costain, Kenneth L. Kenneth L., Algermissen, Cook, and S. T. Algermissen. VESIAC Special Report. S. T. Cook, and S. T. Algermissen. VESIAC Special Report. S. T. Dec. 63. 168 p. incl. illus., tables, 6 refs. III. Advanced Research Proj- Dec. 63. 168 p. incl. illus., tables, 6 refs. III. Advanced Research Proj(Rept. No. 4410-68-X) ects Agency (Rept. No. 4410-68-X) ects Agency (Contract SD-78) Unclassified report IV. Contract SD-78 (Contract SD-78) Unclassified report IV. Contract SD-78 This report presents tabulations of energy ratios calcu- This report presents tabulations of energy ratios calculated from Knott's energy equation, and amplitude ra- lated from Knott's energy equation, and amplitude ratios calculated from the Zoeppritz equations, for a plane tios calculated from the Zoeppritz equations, for a plane SV wave incident on a plane elastic discontinuity. All SV wave incident on a plane elastic discontinuity. All computations were programmed in FORTRAN for an computations were programmed in FORTRAN for an IBM 1620 digital computer. Incident angles were varied IBM 1620 digital computer. Incident angles were varied from 00 to 90~ in increments of 20 except near the crit- from 0~ to 90~ in increments of 20 except near the critical angles, where the ratios were calculated in incre- ical angles, where the ratios were calculated in incre-.ments of 0.250 generally. Both real and imaginary co- Defense.ments of 0.250 generally. Both real and imaginary co- Defense efficients were considered in the calculations. The Documentation Center efficients were considered in the calculations. The Documentation Center (over) UNCLASSIFIED (over) UNCLASSIFIED + + + AD Div. 2/10 UNCLASSIFIED AD Div. 2/10 UNCLASSIFIED Inst. of Science andTechnology, U. of Mich., AnnArbor I. Title: VESIAC Inst. of Science andTechnology, U. of Mich., AnnArbor I. Title: VESIAC TABLES OF AMPLITUDE AND ENERGY RATIOS FOR II. Costain, John K., Cook TABLES OF AMPLITUDE AND ENERGY RATIOS FOR II. Costain,, PLANE SV WAVES, by John K. Costain, Kenneth L. Kenneth L., Algermissen, PLANE SV WAVES, by John K. Costain, Kenneth L. Kenneth L., Algermissen, Cook, and S. T. Algermissen. VESIAC Special Report. S. T. Cook, and S. T. Algermissen. VESIAC Special Report. S. T. Dec. 63. 168 p. incl. illus., tables, 6 refs. III. Advanced Research Proj- Dec. 63. 168 p. incl. illus., tables, 6 refs. III. Advanced Research Proj(Rept. No. 4410-68-X) ects Agency (Contract SD-78) Unclassified report IV. Contract SD-78 (Contract SD-78) Unclassified report IV. Contract SD-78 This report presents tabulations of energy ratios calcu-This report presents tabulations of energy ratios calculated from Knott's energy equation, and amplitude ra-lated from Knott's energy equation, and amplitude ratios calculated from the Zoeppritz equations, for a plane tios calculated from the Zoeppritz equations, for a plane SV wave incident on a plane elastic discontinuity. All. SV wave incident on a plane elastic discontinuity. All SV wave incident on a plane elastic discontinuity. All computations were programmed in FORTRAN for an computations were programmed in FORTRAN for an IBM 1620 digital computer. Incident angles were varied from 0~ to 900 in increments of 20 except near the crit-from 0O to 90 in increments of 2 ex cept near the critical angles, where the ratios were calculated in incre- ical angles, where the ratios were calculated in incre-.ments of 0.250 generally. Both real and imaginary co- Defense.ments of 0.250 generally. Both real and imaginary co- Defense efficients were considered in the calculations. The Documentation Center efficients were considered in the calculations. The Documentation Center (over) UNCLASSIFIED (over) UNCLASSIFIED + + +

AD UNCLASSIFIED AD UNCLASSIFIED varying parameters were the velocity ratio and density DESCRIPTORS varying parameters were the velocity ratio and density DESCRIPTORS ratio across each interface, and the angle of incidence. Seismic Waves ratio across each interface, and the angle of incidence. Seismic Waves Energy ratios were computed for a Poisson's ratio of Seismology Energy ratios were computed for a Poisson's ratio of Seism 0.25 only, and amplitude ratios were computed for 0.25 only, and amplitude ratios were computed for Poisson's ratios of both 0.25 and 0.40. Compressional Poisson's ratios of both 0.25 and 0.40. Compressional velocity ratios (transmitted/incident) of 0.7, 0.8, and 0.9, velocity ratios (transmitted/incident) of 0.7, 0.8, and 0.9, and density ratios (transmitted/incident) of 0.7, 0.8, 0.9, and density ratios (transmitted/incident) of 0.7, 0.8, 0.9, and 1.0 were used. The data are presented in 36 tables, and 1.0 were used. The data are presented in 36 tables, 12 for energy ratios and 24 for amplitude ratios. 12 for energy ratios and 24 for amplitude ratios. UNCLASSIFIED UNCLASSIFIED AD UNCLASSIFIED AD UNCLASSIFIED O varying parameters were the velocity ratio and density DESCRIPTORS varying parameters were the velocity ratio and density DESCRIPTORS ratio across each interface, and the angle of incidence. Seismic Waves ratio across each interface, and the angle of incidence. Ss Wave Energy ratios were computed for a Poisson's ratio of eism Energy ratios were computed for a Poisson's ratio of Seismog 0.25 only, and amplitude ratios were computed for eismology.25 only, and amplitude ratios were computed forSeismology Poisson's ratios of both 0.25 and 0.40. Compressional Poisson's ratios of both 0.25 and 0.40. Compressional velocity ratios (transmitted/incident) of 0.7, 0.8, and 0.9, velocity ratios (transmitted/incident) of 0.7, 0.8, and 0.9, and density ratios (transmitted/incident) of 0.7, 0.8, 0.9, and density ratios (transmitted/incident) of 0.7, 0.8, 0.9, and 1.0 were used. The data are presented in 36 tables, and 1.0 were used. The data are presented in 36 tables, 12 for energy ratios and 24 for amplitude ratios. 12 for energy ratios and 24 for amplitude ratios. UNCLASSIFIED UNCLASSIFIED