Wave Fields in Real Media, Volume 38, Second Edition.part1.rar

Wave Fields in Real Media, Volume 38, Second Edition: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media (Handbook of Geophysical … Exploration: Seismic Exploration)
By J. Jose M. Carcione


Publisher: Elsevier Science
Number Of Pages: 538
Publication Date: 2007-03-15
ISBN-10 / ASIN: 0080464084
ISBN-13 / EAN: 9780080464084
Binding: Hardcover


This book examines the differences between an ideal and a real description of wave propagation, where ideal means an elastic (lossless), isotropic and single-phase medium, and real means an anelastic, anisotropic and multi-phase medium. The analysis starts by introducing the relevant stress-strain relation. This relation and the equations of momentum conservation are combined to give the equation of motion. The differential formulation is written in terms of memory variables, and Biot’s theory is used to describe wave propagation in porous media. For each rheology, a plane-wave analysis is performed in order to understand the physics of wave propagation. The book contains a review of the main direct numerical methods for solving the equation of motion in the time and space domains. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock acoustics, and material science - including many branches of acoustics of fluids and solids - may also find this text useful.

* Presents the fundamentals of wave propagation in anisotropic, anelastic and porus media
* Contains a new chapter on the analogy between acoustic and electromagnetic waves, incorporating the subject of electromagnetic waves
* Emphasizes geophysics, particularly, seismic exploration for hydrocarbon reservoirs, which is essential for exploration and production of oil

不是很清晰

[ 本帖最后由 drjiachen 于 2008-12-24 11:20 编辑 ]

Contents
Preface xiii
About the author xix
Basic notation xx
Glossary of main symbols xxi
1 Anisotropic elastic media 1
1.1 Strain-energy density and stress-strain relation 1
1.2 Dynamical equations 4
1.2.1 Symmetries and transformation properties 6
Symmetry plane of a monoclinic medium 7
Transformation of the stiffness matrix 9
1.3 Kelvin-Christoffel equation, phase velocity and slowness 10
1.3.1 Transversely isotropic media 11
1.3.2 Symmetry planes of an orthorhombic medium 13
1.3.3 Orthogonality of polarizations 14
1.4 Energy balance and energy velocity 15
1.4.1 Group velocity 17
1.4.2 Equivalence between the group and energy velocities 18
1.4.3 Envelope velocity 20
1.4.4 Example: Transversely isotropic media 20
1.4.5 Elasticity constants from phase and group velocities 22
1.4.6 Relationship between the slowness and wave surfaces 24
SH-wave propagation 24
1.5 Finely layered media 25
1.6 Anomalous polarizations 29
1.6.1 Conditions for the existence of anomalous polarization 29
1.6.2 Stability constraints 32
1.6.3 Anomalous polarization in orthorhombic media 33
1.6.4 Anomalous polarization in monoclinic media 33
1.6.5 The polarization 34
1.6.6 Example 35
1.7 The best isotropic approximation 38
1.8 Analytical solutions for transversely isotropic media 40
1.8.1 2-D Green's function 40
v
vi CONTENTS
1.8.2 3-D Green's function 42
1.9 Reflection and transmission of plane waves 42
1.9.1 Cross-plane shear waves 45
2 Viscoelasticity and wave propagation 51
2.1 Energy densities and stress-strain relations 52
2.1.1 Fading memory and symmetries of the relaxation tensor 54
2.2 Stress-strain relation for 1-D viscoelastic media 55
2.2.1 Complex modulus and storage and loss moduli 55
2.2.2 Energy and significance of the storage and loss moduli 57
2.2.3 Non-negative work requirements and other conditions 57
2.2.4 Consequences of reality and causality 58
2.2.5 Summary of the main properties 60
Relaxation function 60
Complex modulus 60
2.3 Wave propagation concepts for 1-D viscoelastic media 61
2.3.1 Wave propagation for complex frequencies 65
2.4 Mechanical models and wave propagation 68
2.4.1 Maxwell model 68
2.4.2 Kelvin-Voigt model 71
2.4.3 Zener or standard linear solid model 74
2.4.4 Burgers model 77
2.4.5 Generalized Zener model 79
Nearly constant Q 80
2.4.6 Nearly constant-Q model with a continuous spectrum 82
2.5 Constant-Q model and wave equation 83
2.5.1 Phase velocity and attenuation factor 84
2.5.2 Wave equation in differential form. Fractional derivatives 85
Propagation in Pierre shale 86
2.6 The concept of centrovelocity 87
2.6.1 1-D Green's function and transient solution 88
2.6.2 Numerical evaluation of the velocities 89
2.6.3 Example 90
2.7 Memory variables and equation of motion 92
2.7.1 Maxwell model 92
2.7.2 Kelvin-Voigt model 94
2.7.3 Zener model 95
2.7.4 Generalized Zener model 95
3 Isotropic anelastic media 97
3.1 Stress-strain relation 98
3.2 Equations of motion and dispersion relations 98
3.3 Vector plane waves 100
3.3.1 Slowness, phase velocity and attenuation factor 100
3.3.2 Particle motion of the P wave 102
3.3.3 Particle motion of the S waves 104
3.3.4 Polarization and orthogonality 106
CONTENTS vii
3.4 Energy balance, energy velocity and quality factor 107
3.4.1 P wave 108
3.4.2 S waves 114
3.5 Boundary conditions and Snell's law 114
3.6 The correspondence principle 116
3.7 Rayleigh waves 116
3.7.1 Dispersion relation 117
3.7.2 Displacement field 118
3.7.3 Phase velocity and attenuation factor 119
3.7.4 Special viscoelastic solids 120
Incompressible solid 120
Poisson solid 120
Hardtwig solid 120
3.7.5 Two Rayleigh waves 120
3.8 Reflection and transmission of cross-plane shear waves 121
3.9 Memory variables and equation of motion 124
3.10 Analytical solutions 126
3.10.1 Viscoacoustic media 126
3.10.2 Constant-Q viscoacoustic media 127
3.10.3 Viscoelastic media 128
3.11 The elastodynamic of a non-ideal interface 129
3.11.1 The interface model 130
Boundary conditions in differential form 131
3.11.2 Reflection and transmission coefficients of SH waves 132
Energy loss 133
3.11.3 Reflection and transmission coefficients of P-SV waves 133
Energy loss 135
Examples 136
4 Anisotropic anelastic media 139
4.1 Stress-strain relations 140
4.1.1 Model 1: Effective anisotropy 142
4.1.2 Model 2: Attenuation via eigenstrains 142
4.1.3 Model 3: Attenuation via mean and deviatoric stresses 144
4.2 Wave velocities, slowness and attenuation vector 145
4.3 Energy balance and fundamental relations 147
4.3.1 Plane waves. Energy velocity and quality factor 149
4.3.2 Polarizations 154
4.4 The physics of wave propagation for viscoelastic SH waves 155
4.4.1 Energy velocity 155
4.4.2 Group velocity 156
4.4.3 Envelope velocity 157
4.4.4 Perpendicularity properties 157
4.4.5 Numerical evaluation of the energy velocity 159
4.4.6 Forbidden directions of propagation 161
4.5 Memory variables and equation of motion in the time domain 162
viii CONTENTS
4.5.1 Strain memory variables 163
4.5.2 Memory-variable equations 165
4.5.3 SH equation of motion 166
4.5.4 qP-qSV equation of motion 166
4.6 Analytical solution for SH waves in monoclinic media 168
5 The reciprocity principle 171
5.1 Sources, receivers and reciprocity 172
5.2 The reciprocity principle 172
5.3 Reciprocity of particle velocity. Monopoles 173
5.4 Reciprocity of strain 174
5.4.1 Single couples 174
Single couples without moment 177
Single couples with moment 177
5.4.2 Double couples 177
Double couple without moment. Dilatation 177
Double couple without moment and monopole force 178
Double couple without moment and single couple 178
5.5 Reciprocity of stress 179
6 Reflection and transmission of plane waves 183
6.1 Reflection and transmission of SH waves 184
6.1.1 Symmetry plane of a homogeneous monoclinic medium 184
6.1.2 Complex stiffnesses of the incidence and transmission media . . . .186
6.1.3 Reflection and transmission coefficients 187
6.1.4 Propagation, attenuation and energy directions 190
6.1.5 Brewster and critical angles 195
6.1.6 Phase velocities and attenuations 199
6.1.7 Energy-flux balance 201
6.1.8 Energy velocities and quality factors 203
6.2 Reflection and transmission of qP-qSV waves 205
6.2.1 Propagation characteristics 205
6.2.2 Properties of the homogeneous wave 207
6.2.3 Reflection and transmission coefficients 208
6.2.4 Propagation, attenuation and energy directions 209
6.2.5 Phase velocities and attenuations 210
6.2.6 Energy-flow balance 210
6.2.7 Umov-Poynting theorem, energy velocity and quality factor 212
6.2.8 Reflection of seismic waves 213
6.2.9 Incident inhomogeneous waves 224
Generation of inhomogeneous waves 225
Ocean bottom 226
6.3 Reflection and transmission at fluid/solid interfaces 228
6.3.1 Solid/fluid interface 228
6.3.2 Fluid/solid interface 229
6.3.3 The Rayleigh window 230
6.4 Reflection and transmission coefficients of a set of layers 231
CONTENTS ix
7 Biot's theory for porous media 235
7.1 Isotropic media. Strain energy and stress-strain relations 237
7.1.1 Jacketed compressibility test 237
7.1.2 Unjacketed compressibility test 238
7.2 The concept of effective stress 240
7.2.1 Effective stress in seismic exploration 242
Pore-volume balance 244
Acoustic properties 246
7.2.2 Analysis in terms of compressibilities 246
7.3 Anisotropic media. Strain energy and stress-strain relations 250
7.3.1 Effective-stress law for anisotropic media 254
7.3.2 Summary of equations 255
Pore pressure 256
Total stress 256
Effective stress 256
Skempton relation 256
Undrained-modulus matrix 256
7.3.3 Brown and Korringa's equations 256
Transversely isotropic medium 257
7.4 Kinetic energy 257
7.4.1 Anisotropic media 260
7.5 Dissipation potential 262
7.5.1 Anisotropic media 263
7.6 Lagrange's equations and equation of motion 263
7.6.1 The viscodynamic operator 265
7.6.2 Fluid flow in a plane slit 265
7.6.3 Anisotropic media 270
7.7 Plane-wave analysis 271
7.7.1 Compressional waves 271
Relation with Terzaghi's law 274
The diffusive slow mode 276
7.7.2 The shear wave 276
7.8 Strain energy for inhomogeneous porosity 278
7.8.1 Complementary energy theorem 279
7.8.2 Volume-averaging method 280
7.9 Boundary conditions 284
7.9.1 Interface between two porous media 284
Deresiewicz and Skalak's derivation 284
Gurevich and Schoenberg's derivation 286
7.9.2 Interface between a porous medium and a viscoelastic medium . . . 288
7.9.3 Interface between a porous medium and a viscoacoustic medium . . 289
7.9.4 Free surface of a porous medium 289
7.10 The mesoscopic loss mechanism. White model 289
7.11 Green's function for poro-viscoacoustic media 295
7.11.1 Field equations 295
7.11.2 The solution 296
x CONTENTS
7.12 Green's function at a fluid/porous medium interface 299
7.13 Poro-viscoelasticity 303
7.14 Anisotropic poro-viscoelasticity 307
7.14.1 Stress-strain relations 308
7.14.2 Biot-Euler's equation 309
7.14.3 Time-harmonic fields 309
7.14.4 Inhomogeneous plane waves 312
7.14.5 Homogeneous plane waves 314
7.14.6 Wave propagation in femoral bone 316
8 The acoustic-electromagnetic analogy 321
8.1 Maxwell's equations 323
8.2 The acoustic-electromagnetic analogy 324
8.2.1 Kinematics and energy considerations 329
8.3 A viscoelastic form of the electromagnetic energy 331
8.3.1 Umov-Poynting's theorem for harmonic fields 332
8.3.2 Umov-Poynting's theorem for transient fields 333
The Debye-Zener analogy 337
The Cole-Cole model 341
8.4 The analogy for reflection and transmission 342
8.4.1 Reflection and refraction coefficients 342
Propagation, attenuation and ray angles 343
Energy-flux balance 343
8.4.2 Application of the analogy 344
Refraction index and Fresnel's formulae 344
Brewster (polarizing) angle 345
Critical angle. Total reflection 346
Reflectivity and transmissivity 349
Dual fields 349
Sound waves 350
8.4.3 The analogy between TM and TE waves 351
Green's analogies 352
8.4.4 Brief historical review 355
8.5 3-D electromagnetic theory and the analogy 356
8.5.1 The form of the tensor components 357
8.5.2 Electromagnetic equations in differential form 358
8.6 Plane-wave theory 359
8.6.1 Slowness, phase velocity and attenuation 361
8.6.2 Energy velocity and quality factor 363
8.7 Analytical solution for anisotropic media 366
8.7.1 The solution 368
8.8 Finely layered media 369
8.9 The time-average and CRIM equations 372
8.10 The Kramers-Kronig dispersion relations 373
8.11 The reciprocity principle 374
8.12 Babinet's principle 375
CONTENTS xi
8.13 Alford rotation 376
8.14 Poro-acoustic and electromagnetic diffusion 378
8.14.1 Poro-acoustic equations 378
8.14.2 Electromagnetic equations 380
The TM and TE equations 380
Phase velocity, attenuation factor and skin depth 381
Analytical solutions 381
8.15 Electro-seismic wave theory 382
9 Numerical methods 385
9.1 Equation of motion 385
9.2 Time integration 386
9.2.1 Classical finite differences 388
9.2.2 Splitting methods 389
9.2.3 Predictor-corrector methods 390
The Runge-Kutta method 390
9.2.4 Spectral methods 390
9.2.5 Algorithms for finite-element methods 392
9.3 Calculation of spatial derivatives 392
9.3.1 Finite differences 392
9.3.2 Pseudospectral methods 394
9.3.3 The finite-element method 396
9.4 Source implementation 397
9.5 Boundary conditions 398
9.6 Absorbing boundaries 400
9.7 Model and modeling design - Seismic modeling 401
9.8 Concluding remarks 404
9.9 Appendix 405
9.9.1 Electromagnetic-diffusion code 405
9.9.2 Finite-differences code for the SH-wave equation of motion 409
9.9.3 Finite-differences code for the SH-wave and Maxwell's equations . . 415
9.9.4 Pseudospectral Fourier Method 422
9.9.5 Pseudospectral Chebyshev Method 424
Examinations 427
Chronology of main discoveries 431
Leonardo's manuscripts 443
A list of scientists 447
Bibliography 457
Name index 491
Subject index 503

Wave Fields in Real Media, Volume 38, Second Edition.part1

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[ 本帖最后由 drjiachen 于 2008-12-24 11:37 编辑 ]

Wave Fields in Real Media, Volume 38, Second Edition.part2-5

[ 本帖最后由 drjiachen 于 2008-12-24 11:33 编辑 ]

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knaknkakna

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Wave Fields in Real Media

不是很清晰吗？？？是很不清晰

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