Get Acoustic and Elastic Wave Fields in Geophysics, III PDF

By Alex A. Kaufman, A.L. Levshin

ISBN-10: 0080457681

ISBN-13: 9780080457680

ISBN-10: 0444519556

ISBN-13: 9780444519559

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 as a rule with wave propagation in liquid media.

The 3rd quantity is devoted to propagation of airplane, round and cylindrical elastic waves in several 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 would not have to have a robust heritage in arithmetic and mathematical physics * precise research of wave phenomena in quite a few kinds of elastic and liquid-elastic media

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

Sample text

Case two: simple shear Now we study deformation that accompanies propagation of shear waves, as is shown in Fig. 9c. In this case, face d\C\ does not move and the distortion angle 7 coincides with a. As before, it is assumed that forces producing a deformation, are parallel to diagonals in their vicinity, and they cause either their extension or shortening. For instance, as follows from Hooke's law (eq. 137), the relative change of diagonal D Fig. 9c, is At the same time from the triangle aid\a\ we have S tan 7 = —— aidi Also didi — Dcos — and 5 — a\a\ — 4 -rCOS7T/4 Since 7 is small, eq.

66) Cl As is also the case in acoustics, impedance plays an important role in describing reflection and transmission of waves. Incoming wave In accordance with eq. 62 we have in this case u(x,i) = Bg[a(t+-)], u(x. t) = Bag'[a{t + -)] ci , . , exx(x, t) = —g'[a(t + -)], Cl u exx = — ci . BaE . . 67) ci ' Ci u Xx —= — ci E or Q As — = Z u Since the wave propagates toward the origin, (x > 0), both the wave and particle velocities have the same direction in places where compression occurs. However, the directions arc opposite to each other in places where tension occurs.

Here 5V/V = 0 = divs is a dilatation (Appendix D). 42) 14 CHAPTER 1. HOOKE'S LAW, POISSON'S RELATION AND WAVES... where (L43) M -W^) is the bulk modulus. As follows from eq. 41 Poisson's ratio, a, cannot exceed 1/2; otherwise, with an increase of pressure, volume would increase too. Note that the velocity of propagation in a fluid is defined by the density p and the bulk modulus M (Part I). T-axis that produce a bar extension. There are also forces applied to faces perpendicular to the y-axis, so that these faces of the bar cannot move in this direction.

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


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