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Elastic waves in layered media
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CONTENTS Preface V List of Symbols .... . xi 1. Fundamental Equations and Solutions .... 1 1-1. Equations of Motion .... 1 The Equation of Continuity . ... 5 1-2. Elastic Media . . . . 5 Isotropic Elastic Solid 5 Ideal Fluid . . . . 6 1-3. Imperfectly Elastic Media 7 1-4. Boundary Conditions 7 1-5. Reduction to Wave Equations 7 1-6. Solutions of the Wave Equation 10 Plane Waves 10 Spherical Waves 12 Poisson and Kirchhoff Solutions 16 General Solution of Wave Equation 17 Some Special Forms Used 18 References .... 20 2 Homogeneous and Isotropic Half Space 24 2-1 Reflection of Plane Waves at a Free Surface 24 Incident P Waves 26 Incident S Waves 28 Partition of Reflected Energy 28 Reflection at Critical Angles 29 2-2. Free Rayleigh Waves 31 2-3. Integral Solutions for a Line Source .... 34 Surface Source . . ... 34 Internal Source . ... 36 2-4 Integral Solutions for a Point Source 38 Surface Source 38 Internal Source 42 2-5. Evaluation of Integral Solutions 44 Application of Contour Integration 44 Residues 47 Branch Line Integrals: Line Source 49 Application of the Method of Steepest Descent 59 2-6. Generalization for an Arbitrary Time Variation 61 2-7. Other Investigations ... . . 64 2-8 Traveling Disturbance . 67 2-9 Experimental Study of Lamb's Problem . . 69 References . 71 3. Two Semi-infinite Media in Contact 74 3-1. Reflection and Refraction of Plane Waves at an Interface . . 74 Rigid Boundary . . . 74 General Equations . . 76 Liquid-Liquid Interface .78 Liquid-Solid Interface 79 Solid-Solid Interface 83 3-2. Reflection of a Pulse Incident beyond the Critical Angle 93 3-3. Propagation in Two Semi-infinite Media: Point Source . 93 Two Liquids . 94 Fluid and Solid Half Spaces . . 105 Two Solids . . 107 Stoneley Waves . Ill 3-4. Further Remarks on Waves Generated at an Interface 113 3-5. Other Investigations . 115 References 121 4. A Layered Half Space . . 124 4-1 General Equations for an n-Layered Elastic Half Space . 124 4-2. Two-layered Liquid Half Space 126 Discussion of Solutions . . . . 137 Generalization for a Pulse . 142 4-3. Three-layered Liquid Half Space 151 4—1. Liquid Layer on a Solid Bottom 156 Compressional-wave Source in the Solid Substratum 157 Suboceanic Rayleigh Waves. First Mode 166 Compressional-wave Source in the Liquid Layer 174 Leaking Modes . 184 Some Aspects of Microseisms . . 185 4-5. Solid Layer over Solid Half Space 189 Rayleigh Waves General Discussion . ... 189 Propagation of Rayleigh Waves across Continents 196 Ground Roll 200 Theoretical Rayleigh-wave Dispersion Curves 204 Love Waves' General Discussion 205 Love Waves across Continents 213 Love Waves across Oceans 216 Lg and Rg Waves 219 Other Investigations 222 4-6. Three-layered Half Space 224 Oceanic Rayleigh Waves with Layered Substratum 225 Love Waves 227 4—7. Air-coupled Rayleigh Waves 230 Air-coupled Ground Roll 236 4-8. Remarks Concerning the Problem of an n-Layered Half Space .... 238 References . 245 5. The Effects of Gravity, Curvature, and Viscosity 255 6-1. Gravity Terms in General Equations 255 5-2. Effect of Gravity on Surface Waves 257 Rayleigh Waves- Incompressible Half Space 257 Gravitating and Compressible Liquid Layer over Solid Half Space . . . 260 5-3. Effect of Curvature on Surface Waves ... 263 Cylindrical Curvature 263 Sperical Curvature 265 5-4. General Solutions for a Spherical Body ... 266 Wave Propagation in a Gravitating Compressible Planet 269 5-5. The Effect of Internal Fiiction . . . . 272 Voigt Solid 272 Maxwell Solid 276 Internal Friction in Earth Materials 277 References . . 278 6. Plates and Cylinders 281 6-1. Plate in a Vacuum 281 Symmetric Vibrations (Mi) 283 Antisymmetric Vibrations (Af2) 285 Interpretation in Terms of P and SV Waves 286 Impulsive Sources 286 Other Investigations 28S 6-2 Plate in a Liquid 288 Symmetric Vibrations 292 Antisymmetric Vibrations 293 Other Investigations 293 6-3 Floating Ice Sheet 293 SH Waves 293 SV and P Waves 295 Crary Waves 299 Flexural Waves from an Impulsive Source .... 301 6-4 Cylindrical Rod in a Vacuum 305 Longitudinal Vibrations 306 Torsional and Flexural Vibrations 311 6-5 Cylindrical Rod in a Liquid 314 6-6 Cylindrical Hole in an Infinite Solid 314 6-7 Liquid Cylinder in an Elastic Medium 317 6-8 Cylindrical Tube 319 References . 323 7 Wave Propagation in Media with Vabiablb Velocity 328 7-1. Wave Propagation in Heterogeneous Iaotropic Media 328 7-2. Sound Propagation in a Fluid Half Space . 330 SOFAR Propagation 335 The T Phase 341 7—3. Love Waves in Heterogeneous Isotropic Media '. 341 Homogeneous Layer over Heterogeneous Half Space: Matuzawa'a Case . 343 Sat6's Case 344 Jeffreys' Case 346 Meissner's Case 347 7-4. Rayleigh Waves in Heterogeneous Isotropic Media 349 Mantle Rayleigh Waves 353 7-5. Aeolotropic and Other Media 358 References 360 Appendix A. Method op Steepest Descent 365 References 369 Appendix B. Ratleiqh's Pbinciple 370 References 374 Index 375 Download link：http://www.isload.com.cn/store/d5fcoaf8iv3fb [ Last edited by zhq025 on 2008-1-16 at 10:23 ] |
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