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Tables of Contents for Acoustic and Elastic Wave Fields in Geophysics
Chapter/Section Title
Page #
Page Count
Introduction
ix
 
List of Symbols
xiii
 
Newton's laws and parlide motion
Newton's laws
1
12
Motion of system of particles
13
8
Free and forced vibrations
Hooke's law for springs
21
2
Free vibrations of the system: mass-spring
23
10
Forced vibrations of the system: mass-spring
33
10
Principles of measuring vibrations
43
6
Propagation
Propagation of waves along a system of masses and springs
49
7
Solution of 1-D wave equation. Bounder conditions
56
31
Transversal waves in a spring
87
13
Basic equations for dilatational waves
Introduction
99
1
Wave phenomena in gas and fluid
100
18
Wave equation and boundary conditions for dilatational waves
118
11
The kinetic and potential energy of the wave flux of the energy. Poynting vector
129
9
Boundary value problem. Theorem of uniqueness
138
8
Gravitational waves in a fluid
146
11
Waves in homogeneous medium
Spherical waves from an elementary source
157
25
Cylindrical waves from linear source in homogenous medium
182
12
Plane waves in homogeneous medium
194
11
Interference and diffraction
Superposition of waves in an uniform medium, caused by a system of primary sources
205
21
Helmholtz formula
226
9
Kirchhoff diffraction theory
235
10
Fraunhofer and Fresnel diffraction
245
20
Helmholtz - Kirchhoff formula
265
9
Huygens - Fresnel principles
274
14
Relationship of potential with initial conditions. Poisson's formula
288
10
Transition to geometrical acoustics
298
11
Eikonal and transportation equations
309
14
Superposition of sinusoidal waves with different frequencies and wave lengths
Wave group. Phase and group velocities
323
15
Superposition of sinusoidal waves and the method of stationary phase
338
27
Principles of geometrical acoustics
Introduction
365
1
Rays and their general features
365
15
Behavior of rays when velocity is a function of one cartesian coordinate
380
17
Behavior of rays when velocity is a function of one coordinate r
397
3
Rays near interfaces
400
20
Time fields
420
6
Appendices
1. Vector algebra
426
13
2. Scalar field and gradient
439
4
3. Vector fields
443
28
4. Complex numbers
471
9
5. Linear ordinary differential equations with constant coefficients
480
7
6. Fourier series
487
11
7. Fourier integral
498
10
8. Duhamel integral
508
2
References
510