Preface |
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xi | |
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One-Dimensional Viscoelasticity |
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1 | (18) |
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2 | (3) |
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Stored and Dissipated Energy |
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5 | (2) |
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7 | (8) |
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15 | (2) |
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17 | (2) |
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Three-Dimensional Viscoelasticity |
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19 | (13) |
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19 | (1) |
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20 | (3) |
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23 | (2) |
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25 | (1) |
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26 | (4) |
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30 | (2) |
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Viscoelastic P, SI, and SII Waves |
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32 | (66) |
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Solutions of Equation of Motion |
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32 | (5) |
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Particle Motion for P Waves |
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37 | (3) |
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Particle Motion for Elliptical and Linear S Waves |
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40 | (6) |
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Type-I or Elliptical S (SI) Wave |
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42 | (3) |
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Type-II or Linear S (SII)Wave |
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45 | (1) |
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Energy Characteristics of P, SI, and SII Waves |
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46 | (11) |
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Mean Energy Flux (Mean Intensity) |
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46 | (4) |
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50 | (3) |
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53 | (1) |
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Mean Rate of Energy Dissipation |
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54 | (1) |
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Reciprocal Quality Factor, Q-1 |
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55 | (2) |
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Viscoelasticity Characterized by Parameters for Homogeneous P and S Waves |
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57 | (2) |
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Characteristics of Inhomogeneous Waves in Terms of Characteristics of Homogeneous Waves |
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59 | (16) |
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Wave Speed and Maximum Attenuation |
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60 | (4) |
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Particle Motion for P and SI Waves |
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64 | (3) |
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Energy Characteristics for P, SI, and SII Waves |
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67 | (8) |
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P, SI, and SII Waves in Low-Loss Viscoelastic Media |
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75 | (7) |
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P, SI, and SII Waves in Media with Equal Complex Lame Parameters |
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82 | (2) |
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P, SI, and SII Waves in a Standard Linear Solid |
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84 | (2) |
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Displacement and Volumetric Strain |
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86 | (10) |
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Displacement for General P and SI Waves |
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86 | (6) |
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Volumetric Strain for a General P Wave |
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92 | (1) |
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Simultaneous Measurement of Volumetric Strain and Displacement |
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93 | (3) |
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96 | (2) |
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Framework for Single-Boundary Reflection-Refraction and Surface-Wave Problems |
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98 | (9) |
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Specification of Boundary |
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98 | (1) |
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99 | (7) |
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106 | (1) |
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General P, SI, and SII Waves Incident on a Viscoelastic Boundary |
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107 | (36) |
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Boundary-Condition Equations for General Waves |
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107 | (2) |
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109 | (14) |
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Specification of Incident General SI Wave |
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109 | (2) |
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Propagation and Attenuation Vectors; Generalized Snell's Law |
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111 | (3) |
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114 | (1) |
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Conditions for Homogeneity and Inhomogeneity |
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115 | (5) |
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Conditions for Critical Angles |
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120 | (3) |
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123 | (7) |
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Specification of Incident General P Wave |
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123 | (2) |
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Propagation and Attenuation Vectors; Generalized Snell's Law |
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125 | (1) |
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126 | (1) |
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Conditions for Homogenity and Inhomogeneity |
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127 | (2) |
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Conditions for Critical Angles |
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129 | (1) |
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Incident General SII Wave |
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130 | (11) |
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Specification of Incident General SII Wave |
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130 | (1) |
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Propagation and Attenuation Vectors; Generalized Snell's Law |
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131 | (2) |
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133 | (1) |
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Conditions for Homogeneity and Inhomogeneity |
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134 | (1) |
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Conditions for Critical Angles |
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134 | (1) |
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Energy Flux and Energy Flow Due to Wave Field Interactions |
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135 | (6) |
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141 | (2) |
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Numerical Models for General Waves Reflected and Refracted at Viscoelastic Boundaries |
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143 | (27) |
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General SII Wave Incident on a Moderate-Loss Viscoelastic Boundary (Sediments) |
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144 | (11) |
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Incident Homogeneous SII Wave |
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145 | (6) |
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Incident Inhomogeneous SII Wave |
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151 | (4) |
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P Wave Incident on a Low-Loss Viscoelastic Boundary (Water, Stainless-Steel) |
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155 | (14) |
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Reflected and Refracted Waves |
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156 | (7) |
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Experimental Evidence in Confirmation of Theory for Viscoelastic Waves |
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163 | (2) |
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Viscoelastic Reflection Coefficients for Ocean, Solid-Earth Boundary |
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165 | (4) |
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169 | (1) |
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General SI, P, and SII Waves Incident on a Viscoelastic Free Surface |
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170 | (36) |
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Boundary-Condition Equations |
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170 | (2) |
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172 | (20) |
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Reflected General P and SI Waves |
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172 | (4) |
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Displacement and Volumetric Strain |
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176 | (5) |
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Numerical Model for Low-Loss Media (Weathered Granite) |
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181 | (11) |
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192 | (11) |
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Reflected General P and SI Waves |
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192 | (4) |
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Numerical Model for Low-Loss Media (Pierre Shale) |
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196 | (7) |
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Incident General SII Wave |
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203 | (1) |
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204 | (2) |
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Rayleigh-Type Surface Wave on a Viscoelastic Half Space |
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206 | (40) |
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206 | (4) |
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210 | (15) |
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Velocity and Absorption Coefficient |
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210 | (1) |
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Propagation and Attenuation Vectors for Component Solutions |
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211 | (1) |
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Displacement and Particle Motion |
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212 | (5) |
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217 | (2) |
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Media with Equal Complex Lame Parameters (Λ=M) |
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219 | (6) |
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Numerical Characteristics of Rayleigh-Type Surface Waves |
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225 | (16) |
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Characteristics at the Free Surface |
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227 | (5) |
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Characteristics Versus Depth |
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232 | (9) |
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241 | (5) |
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General SII Waves Incident on Multiple Layers of Viscoelastic Media |
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246 | (16) |
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Analytic Solution (Multiple Layers) |
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247 | (7) |
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Analytic Solutin (One Layer) |
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254 | (1) |
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Numerical Response of Viscoelastic Layers (Elastic, Earth's Crust, Rock, Soil) |
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255 | (6) |
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261 | (1) |
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Love-Type Surface Waves in Multilayered Viscoelastic Media |
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262 | (17) |
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Analytic Solution (Multiple Layers) |
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262 | (3) |
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Displacement (Multiple Layers) |
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265 | (2) |
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Analytic Solution and Displacement (One Layer) |
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267 | (3) |
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Numerical Characteristics of Love-Type Surface Waves |
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270 | (8) |
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278 | (1) |
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279 | (13) |
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Appendix 1 - Properties of Riemann-Stieltjes Convolution Integral |
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279 | (1) |
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Appendix 2 - Vector and Displacement-Potential Identities |
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279 | (1) |
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279 | (1) |
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Displacement-Potential Identities |
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280 | (1) |
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Appendix 3 - Solution of the Helmholtz Equation |
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280 | (4) |
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Appendix 4 - Roots of Squared Complex Rayleigh Equation |
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284 | (2) |
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Appendix 5 - Complex Root for a Rayleigh-Type Surface Wave |
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286 | (2) |
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Appendix 6 - Particle-Motion Characteristics for a Rayleigh-Type Surface Wave |
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288 | (4) |
References |
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292 | (3) |
Additional Reading |
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295 | (1) |
Index |
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296 | |