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E-raamat: Viscoelastic Waves and Rays in Layered Media

(United States Geological Survey, California)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 22-Oct-2020
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108852241
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Viscoelastic Waves and Rays in Layered MediaSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 22-Oct-2020
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108852241
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This second edition extends the rigorous, self-contained exposition of the theory for viscoelastic wave propagation in layered media to include head waves and general ray theory. The theory, not published elsewhere, provides solutions for fundamental wave-propagation and ray-theory problems valid for any media with a linear response, elastic or anelastic. It explains measurable variations in wave speed, particle motion, and attenuation of body waves, surface waves, and head waves induced at anelastic material boundaries that do not occur for elastic waves. This book may be used as a textbook for advanced university courses and as a research reference in seismology, exploration geophysics, engineering, solid mechanics, and acoustics. It provides computation steps for ray-tracing computer algorithms to develop a variety of tomography inferred anelastic models, such as those for the Earth's deep interior and petroleum reserves. Numerical results and problem sets emphasize important aspects of the theory for each chapter.

Arvustused

'As noted by R. A. Stephen, Borcherdt's book is a tour de force that can serve as a vanguard for the study of viscoelastic properties of the Earth and other layered media. With its instructive problems sets for each chapter and complementary numerical results, the book is an excellent stand-alone or complementary textbook for advanced courses or research in seismology, exploration geophysics, engineering, solid mechanics, and acoustics. The book fills a void not covered in other texts.' Andreas Fichtner, Seismological Research Letters 'This work is very impressive and the very coherent description of wave propagation in viscoelastic layered (solid) media is exceptional. The main contribution from my point of view is the detailed understanding of physical features of waves when they propagate into lossy media. This book would be a valuable contribution to a research library. Advanced students and researchers will find in this book answers to questions they may face when considering effects in lossy materials, quite different from effects in lossless media.' Pr Emeritus Jean Virieux, Geophysical Journal International 'Bound to become one of the most sought-after references on the subject. Roger Borcherdt has worked on the subject since his PhD days, and his mastery of the subject is something to behold.' Sven Treitel, The Leading Edge, Society of Exploration Geophysicists

Muu info

A rigorous self-contained exposition of the mathematical theory for wave propagation and general ray theory in layered viscoelastic media.
Preface xiii
Historical Prologue xix
1 One-Dimensional Viscoelasticity
1(18)
1.1 Constitutive Law
1(4)
1.2 Stored and Dissipated Energy
5(2)
1.3 Physical Models
7(8)
1.4 Equation of Motion
15(2)
1.5 Problems
17(2)
2 Three-Dimensional Viscoelasticity
19(13)
2.1 Constitutive Law
19(1)
2.2 Stress-Strain Notation
20(3)
2.3 Equation of Motion
23(2)
2.4 Correspondence Principle
25(1)
2.5 Energy Balance
26(4)
2.6 Problems
30(2)
3 Viscoelastic P, SI, and SH Waves
32(66)
3.1 Solutions of Equation of Motion
32(5)
3.2 Particle Motion for P Waves
37(3)
3.3 Particle Motion for Elliptical and Linear S Waves
40(6)
3.3.1 Type-I or Elliptical S (SI) Wave
42(3)
3.3.2 Type-II or Linear S (SII) Wave
45(1)
3.4 Energy Characteristics of P, SI, and SII Waves
46(11)
3.4.1 Mean Energy Flux (Mean Intensity)
46(4)
3.4.2 Mean Energy Densities
50(2)
3.4.3 Energy Velocity
52(1)
3.4.4 Mean Rate of Energy Dissipation
53(1)
3.4.5 Reciprocal Quality Factor, Q-1
54(3)
3.5 Viscoelasticity Characterized by Parameters for Homogeneous P and S Waves
57(2)
3.6 Characteristics of Inhomogeneous Waves in Terms of Characteristics of Homogeneous Waves
59(16)
3.6.1 Wave Speed and Maximum Attenuation
59(5)
3.6.2 Particle Motion for P and SI Waves
64(2)
3.6.3 Energy Characteristics for P, SI, and SII Waves
66(9)
3.7 P, SI, and SII Waves in Low-Loss Viscoelastic Media
75(7)
3.8 P, SI, and SII Waves in Media with Equal Complex Lame Parameters
82(2)
3.9 P, SI, and SII waves in a Standard Linear Solid
84(2)
3.10 Displacement and Volumetric Strain
86(10)
3.10.1 Displacement for General P and SI Waves
86(6)
3.10.2 Volumetric Strain for a General P Wave
92(1)
3.10.3 Simultaneous Measurement of Volumetric Strain and Displacement
93(3)
3.11 Problems
96(2)
4 Framework for Single-Boundary Reflection-Refraction and Surface-Wave Problems
98(9)
4.1 Specification of Boundary
98(2)
4.2 Specification of Waves
100(6)
4.3 Problems
106(1)
5 General P, SI, and SII Waves Incident on a Viscoelastic Boundary
107(36)
5.1 Boundary-Condition Equations for General Waves
107(2)
5.2 Incident General SI
109(14)
5.2.1 Specification of Incident General SI Wave
109(2)
5.2.2 Propagation and Attenuation Vectors; Generalized Snell's Law
111(3)
5.2.3 Amplitude and Phase
114(1)
5.2.4 Conditions for Homogeneity and Inhomogeneity
115(5)
5.2.5 Conditions for Critical Angles
120(3)
5.3 Incident General P Wave
123(7)
5.3.1 Specification of Incident General P Wave
123(2)
5.3.2 Propagation and Attenuation Vectors; Generalized Snell's Law
125(1)
5.3.3 Amplitude and Phase
126(1)
5.3.4 Conditions for Homogeneity and Inhomogeneity
127(1)
5.3.5 Conditions for Critical Angles
128(2)
5.4 Incident General SII Wave
130(11)
5.4.1 Specification of Incident General SII Wave
130(1)
5.4.2 Propagation and Attenuation Vectors; Generalized Snell's Law
131(2)
5.4.3 Amplitude and Phase
133(1)
5.4.4 Conditions for Homogeneity and Inhomogeneity
134(1)
5.4.5 Conditions for Critical Angles
134(1)
5.4.6 Energy Flux and Energy Flow Due to Wave Field Interactions
135(6)
5.5 Problems
141(2)
6 Numerical Models for General Waves Reflected and Refracted at Viscoelastic Boundaries
143(27)
6.1 General SII Wave Incident on a Moderate-Loss Viscoelastic Boundary (Sediments)
144(11)
6.1.1 Incident Homogeneous SII Wave
145(6)
6.1.2 Incident Inhomogeneous SII Wave
151(4)
6.2 P Wave Incident on Low-Loss Viscoelastic Boundary (Water, Stainless-Steel)
155(8)
6.2.1 Reflected and Refracted Waves
156(7)
6.3 Experimental Confirmation of Viscoelastic Wave Theory
163(2)
6.4 Viscoelastic Reflection Coefficients for Ocean, Solid-Earth Boundaries
165(3)
6.5 Problems
168(2)
7 General SI, P, and SII Waves Incident on a Viscoelastic Free Surface
170(33)
7.1 Boundary-Condition Equations
170(2)
7.2 Incident General SI Wave
172(19)
7.2.1 Reflected General P and SI Waves
172(4)
7.2.2 Displacement and Volumetric Strain
176(5)
7.2.3 Numerical Model for Low-Loss Media (Weathered Granite)
181(10)
7.3 Incident General P Wave
191(9)
7.3.1 Reflected General P and SI Waves
191(4)
7.3.2 Numerical Model for Low-Loss Media (Pierre Shale)
195(5)
7.4 Incident General SII Wave
200(2)
7.5 Problems
202(1)
8 Rayleigh-Type Surface Wave on a Viscoelastic Half Space
203(38)
8.1 Analytic Solution
203(4)
8.2 Physical Characteristics
207(15)
8.2.1 Velocity and Attenuation Coefficient
207(1)
8.2.2 Propagation and Attenuation Vectors for Component Solutions
208(1)
8.2.3 Displacement and Particle Motion
209(5)
8.2.4 Volumetric Strain
214(2)
8.2.5 Media with Equal Complex Lame Parameters (A = M)
216(6)
8.3 Numerical Characteristics of Rayleigh-Type Surface Waves
222(17)
8.3.1 Characteristics at the Free Surface
224(4)
8.3.2 Characteristics versus Depth
228(11)
8.4 Problems
239(2)
9 General SII Waves Incident on Multiple Layers of Viscoelastic Media
241(17)
9.1 Analytic Solution (Multiple Layers)
242(7)
9.2 Analytic Solution (One Layer)
249(1)
9.3 Numerical Response of Viscoelastic Layers (Elastic, Earth's Crust, Rock, Soil)
250(6)
9.4 Problems
256(2)
10 Love-Type Surface Waves in Multilayered Viscoelastic Media
258(18)
10.1 Analytic Solution (Multiple Layers)
258(3)
10.2 Displacement (Multiple Layers)
261(2)
10.3 Analytic Solution and Displacement (One Layer)
263(3)
10.4 Numerical Characteristics of Love-Type Surface Waves
266(8)
10.5 Problems
274(2)
11 General Viscoelastic Ray Theory
276(157)
11.1 General SII Rays in Horizontal Layered Viscoelastic Media
277(62)
11.1.1 Viscoelastic Ray Parameters for Phase and Attenuation
287(2)
11.1.2 Viscoelastic Solution of Forward Ray-Tracing Problem
289(5)
11.1.3 Ray-Path, Wave-Propagation, and Travel-Time Characteristics
294(8)
11.1.4 Amplitude Attenuation Characteristics
302(4)
11.1.5 General Viscoelastic Head Waves
306(10)
11.1.6 Critical, Reversal, and Turning Points for Viscoelastic Rays
316(7)
11.1.7 Computation Steps (Forward Ray-Tracing Algorithm)
323(5)
11.1.8 Ray Characteristics in a Surface Layer
328(4)
11.1.9 Ray Characteristics in Underlying Layers; "Wide" Angle Refractions across Anelastic Boundaries (Earth's Mantle, Rock, Soil)
332(7)
11.2 General SII Rays in Horizontal Viscoelastic Media with Vertical Material Gradients
339(16)
11.2.1 Viscoelastic Ray Parameters for Phase and Attenuation
341(1)
11.2.2 Viscoelastic Solution of Forward Ray-tracing Problem
342(3)
11.2.3 Ray-Path, Wave-Propagation, and Travel-Time Characteristics
345(5)
11.2.4 Amplitude Attenuation Characteristics
350(2)
11.2.5 Critical, Reversal, and Turning Points for Viscoelastic Rays
352(3)
11.3 General SII Rays in Spherical Layered Viscoelastic Media
355(24)
11.3.1 Viscoelastic Ray Parameters for Phase and Attenuation
360(1)
11.3.2 Viscoelastic Solution of Forward Ray-Tracing Problem
361(3)
11.3.4 Ray- Path, Wave-Propagation, and Travel-Time Characteristics
364(7)
11.3.4 Amplitude-Attenuation Characteristics
371(3)
11.3.5 General Viscoelastic Head Waves (Spherical Layers)
374(2)
11.3.6 Critical, Reversal, and Turning Points for Viscoelastic Rays
376(3)
11.4 General SII Rays in Spherical Viscoelastic Media with Radial Material Gradients
379(18)
11.4.1 Viscoelastic Ray Parameters for Phase and Attenuation 3
81(301)
11.4.2 Viscoelastic Solution of Forward Ray-tracing Problem
382(2)
11.4.3 Ray-Path, Wave-Propagation, and Travel-Time Characteristics
384(8)
11.4.4 Amplitude-Attenuation Characteristics
392(2)
11.4.5 Critical, Reversal, and Turning Points for Viscoelastic Rays
394(3)
11.5 Forward Ray-Tracing Algorithms and Earth-Flattening Transformations for Horizontal and Spherical Viscoelastic Media
397(11)
11.6 Inverse-Problem Solutions for Viscoelastic Media
408(18)
11.6.1 Horizontal Media (Single and Multiple Layers)
409(1)
11.6.1.1 Viscoelastic Material Parameters Inferred for Single Layer from Reflected Waves
409(4)
11.6.1.2 Viscoelastic Material Parameters Inferred for Multiple Layers from Reflected Waves
413(3)
11.6.1.3 Viscoelastic Material Parameters Inferred for Multiple Layers from Head Waves
416(2)
11.6.2 Horizontal and Spherical Media with Material Gradients (Solution of Viscoelastic Herglotz-Wiechert Integral)
418(1)
11.6.2.1 Viscoelastic Material Parameters Inferred for Half Space with Vertical Material Gradients
418(5)
11.6.2.2 Viscoelastic Material Parameters Inferred for Sphere with Radial Material Gradients
423(3)
11.7 Implications of Using Elastic Models to Describe General Rays in Anelastic Viscoelastic Media
426(2)
11.8 Problems
428(5)
12 Appendices
433(35)
12.1 Appendix 1 - Properties of Riemann-Stieltjes Convolution Integral
433(1)
12.2 Appendix 2 - Vector and Displacement-Potential Identities
433(1)
12.2.1 Vector Identities
433(1)
12.2.2 Displacement-Potential Identities
434(1)
12.3 Appendix 3 - Solution of the Helmholtz Equation
434(4)
12.4 Appendix 4 - Roots of Squared Complex Rayleigh Equation
438(2)
12.5 Appendix 5 - Complex Root for a Rayleigh-Type Surface Wave
440(2)
12.6 Appendix 6 Particle Motion Characteristics for a Rayleigh-Type Surface Wave
442(3)
12.7 Appendix 7 - Characteristics of General Waves in a Viscoelastic Surface Layer
445(20)
12.7.1 General SII Reflected Wave
445(7)
12.7.2 General SII Head Wave
452(8)
12.7.3 General SII Direct Wave
460(5)
12.8 Appendix 8 - Viscoelastic Herglotz-Wiechert Integral for Spherical Media with Radial Gradients
465(3)
References 468(5)
Additional Reading - first edition 473(1)
Additional Reading - second edition (Observations, Empirical Interpretations, and Applications of the Theory of Viscoelastic Waves in Layered Media) 474(4)
Index 478
Roger Borcherdt is a research seismologist, scientist emeritus at the US Geological Survey, and past consulting and visiting Shimizu professor at Stanford University, California. Dr Borcherdt is the author of more than 200 scientific publications, including several on the theoretical and empirical aspects of seismic wave propagation pertaining to problems in seismology, exploration geophysics, and earthquake engineering. He is the recipient of the Distinguished Service award, the highest honor of the Department of Interior, for seminal contributions in seismology and engineering; the Bruce A. Bolt Medal awarded jointly by the Seismological Society of America, the Earthquake Engineering Research Institute, and COSMOS; and the 1994 and 2002 Outstanding Paper Awards of Earthquake Spectra. He is an honorary member of the Earthquake Engineering Research Institute, a past journal editor, a co-inventor of the General Earthquake Observation System (GEOS, patent 4,603,486), as well as an active member of several professional societies.
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