Download Acoustic and Elastic Wave Fields in Geophysics, III by Alex A. Kaufman, A.L. Levshin PDF

By Alex A. Kaufman, A.L. Levshin

This monograph is the final quantity within the sequence 'Acoustic and Elastic Wave Fields in Geophysics'. the former volumes released through Elsevier (2000, 2002) dealt often with wave propagation in liquid media.

The 3rd quantity is devoted to propagation of aircraft, round and cylindrical elastic waves in numerous media together with isotropic and transversely isotropic solids, liquid-solid versions, and media with cylindrical inclusions (boreholes). * occurrence of actual reasoning on formal mathematical derivations * Readers shouldn't have to have a powerful history in arithmetic and mathematical physics * special research of wave phenomena in quite a few varieties of elastic and liquid-elastic media

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Extra resources for Acoustic and Elastic Wave Fields in Geophysics, III

Sample text

In the approximation of a thin bar, it is assumed that all functions describing the wave u(x,t), exx(x,t), u(x,t), Xx(x,t) are the same at all points of any cross-section of the bar. Besides, the strains eyy and ezz, caused by the stress Xx, are uniformly distributed over each cross-section S. Because of symmetry, components of the displacement v and w are equal to zero along the middle line of the bar (x-axis), and then they linearly increase toward the lateral surface. Because of all these assumptions, we can only approximately describe the displacement, field s.

Because of this, the wave almost instantly reaches the back and front faces of the volume. Correspondingly, external forces acting on both faces have the same magnitude but opposite directions. Therefore, the total force is equal to zero, and this element moves at a constant velocity. Thus, stress, strain, and particle velocity behave as step-functions, whereas displacement is a linear function, Fig. 3c. In other words, functions, u, exx, and Xx remain constant behind the wave front, but the distance of the particle from the original position changes linearly.

Suppose that at some instant t — 0, one face of a rectangular parallelepiped inside a medium is subjected to the action of the tangential force Fy, Fig. 8a. Because of this force, a wave arises and propagates toward the opposite face. Since the volume is very small, the wave reaches the back face very quickly and the same force Fy acts on a medium behind the volume. 4 HOOKE'S LAW FOR SHEAR STRESSES AND TORSIONAL WAVES... 8: (a) Transmission of the shear force (b) Illustration of eqs. 128 (c) Stresses inside elementary volume (d) Forces acting on the rectangular parallelepiped aibiCidi 44 CHAPTER 1.

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