By Jose Pujol
Publisher: Cambridge University Press
Print Publication Year: 2003
Online Publication Date:November 2009
Online ISBN:9780511610127
Hardback ISBN:9780521817301
Paperback ISBN:9780521520461
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511610127.007
Subjects: Solid Earth Geophysics, Fluid dynamics and solid mechanics
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Introduction
After the homogeneous infinite space, the next two simplest configurations are a homogeneous half-space with a free surface and two homogeneous half-spaces (or media, for short) with different elastic properties. The first case can be considered as a special case of the second one with one of the media a vacuum. In either case the boundary between the two media constitutes a surface of discontinuity in elastic properties that has a critical effect on wave propagation. To simplify the problem we will assume plane boundaries and wave fronts. Although in the Earth neither the wave fronts nor the boundaries satisfy these assumptions, they are acceptable approximations as long as the seismic source is sufficiently far from the receiver and/or the wavelength is much shorter than the curvature of the boundary. In addition, the case of spherical wave fronts can be solved in terms of plane wave results (e.g., Aki and Richards, 1980). Therefore, the theory and results described here have a much wider application than could be expected by considering the simplifying assumptions. For example, they are used in teleseismic studies, in the generation of synthetic seismograms using ray theory, and in exploration seismology, particularly in amplitude-versus-offset (AVO) studies.
The interaction of elastic waves with a boundary has a number of similarities with the interaction of acoustic and electromagnetic waves, so that it can be expected that a wave incident on a boundary will generate reflected and transmitted waves (the latter only if the other medium is not a vacuum).
pp. i-vi
pp. vii-xii
pp. xiii-xvii
pp. xviii-xviii
1 - Introduction to tensors and dyadics: Read PDF
pp. 1-39
2 - Deformation. Strain and rotation tensors: Read PDF
pp. 40-58
3 - The stress tensor: Read PDF
pp. 59-83
4 - Linear elasticity – the elastic wave equation: Read PDF
pp. 84-99
5 - Scalar and elastic waves in unbounded media: Read PDF
pp. 100-128
6 - Plane waves in simple models with plane boundaries: Read PDF
pp. 129-187
7 - Surface waves in simple models – dispersive waves: Read PDF
pp. 188-233
pp. 234-277
9 - Seismic point sources in unbounded homogeneous media: Read PDF
pp. 278-315
10 - The earthquake source in unbounded media: Read PDF
pp. 316-356
11 - Anelastic attenuation: Read PDF
pp. 357-390
pp. 391-406
Appendices
A - Introduction to the theory of distributions: Read PDF
pp. 407-418
B - The Hilbert transform: Read PDF
pp. 419-421
C - Green's function for the 3-D scalar wave equation: Read PDF
pp. 422-424
D - Proof of (9.5.12): Read PDF
pp. 425-427
E - Proof of (9.13.1): Read PDF
pp. 428-430
pp. 431-438
pp. 439-444