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 by way of Elsevier (2000, 2002) dealt generally 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). * incidence of actual reasoning on formal mathematical derivations * Readers would not have to have a powerful historical past in arithmetic and mathematical physics * specific research of wave phenomena in quite a few different types of elastic and liquid-elastic media

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

**Example text**

With some time delay, the wave arrives at the front face of the volume, S(x+ dx/2). Force F(x, t), which accompanies the wave, has the same direction at both crosssections, but may differ in magnitude. 2 LONGITUDINAL WAVES IN A THIN BAR 17 takes place. The force at points of the section S(x + dx/2) acts on a medium located in front of the bar element. In accordance with Newton's third law, force Fx(x + dx/2), having the same magnitude and opposite direction, acts on the surface S(x + dx/2) of the elementary volume.

As follows from Hooke's law, eq. 64 can written in the form: u Xx — =—^ or Xx —— = E r— = ~VEP (1-65) By analogy with electrodynamics, the right side of 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.

From eqs. 64) 20 CHAPTER 1. HOOKE'S LAW, POISSON'S RELATION AND WAVES... that is, the ratio of velocities of the particle and wave defines the strain with an accuracy of a sign. As was mentioned earlier and in Appendix D the strain exx is usually very small: (exx

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