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

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 in general 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 types, and media with cylindrical inclusions (boreholes). * occurrence of actual reasoning on formal mathematical derivations * Readers shouldn't have to have a powerful historical past in arithmetic and mathematical physics * distinct research of wave phenomena in quite a few varieties of elastic and liquid-elastic media

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108) Ci where u(x,t) is the particle displacement of the bar, A and B are constants, and / and g are practically arbitrary functions of distance and time. Thus, all results obtained in the previous section are completely applied to the sinusoidal waves. At the same time it is also useful to consider them separately (Parts I and II), taking into account their special role in the theory of wave phenomena and numerous practical applications. As is well known, the convenient use of sinusoidal functions is related to the following factors: 1.

The thin line corresponds to this wave. Superposition of both waves shows that at the beginning the resultant wave (thick line) is still extensional. 6: (a) The incident wave is an arbitrary function of x (b-g) A superposition of the incident and reflected waves at different instances near the free end. [After Kolsky, 1963] 34 CHAPTER 1. HOOKE'S LAW, POISSON'S RELATION AND WAVES... because near the bar end, the magnitude of the reflected wave is smaller than that of the incident wave. With an increase of time, we start to observe an appearance of the compressional wave, which becomes more and more noticeable, Fig.

Of course, as in a general case of nonstationary waves, eqs. 113 give vJx2t1 C\ = _XAx2t)_ E or _Xx(x,t)t Z 40 CHAPTER 1. EOOKE'S LAW, POISSON'S RELATION AND WAVES... where Z = pci is the bar impedance. The reflected and transmitted waves are also sinusoidal waves with the same frequency as the incident wave, and the reflection and transmission coefficients Z\ — Zi ZJ\ -\- £11 1Z\ ZJ\ -\- Z2 are independent of a frequency. Both of these features greatly simplify the study of wave behavior. Now let us consider one example.

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