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 by means of Elsevier (2000, 2002) dealt often with wave propagation in liquid media.

The 3rd quantity is devoted to propagation of airplane, round and cylindrical elastic waves in numerous media together with isotropic and transversely isotropic solids, liquid-solid types, and media with cylindrical inclusions (boreholes). * incidence of actual reasoning on formal mathematical derivations * Readers wouldn't have to have a robust heritage in arithmetic and mathematical physics * targeted 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

In other words, their frequency remains the same. This fact greatly simplifies the study of sinusoidal waves. 2. The shape of transient waves is preserved when they propagate along a bar and attenuation is absent. , it is impossible to describe this process by either single function f[a(t — x/c[] or g[a(t + x/ci\, or by a sum of them. At the same time, even in the presence of attenuation, the sinusoidal wave as a function of time preserves the same frequency. This is the second reason why it is very convenient to study wave phenomena using sinusoidal waves even when part of an elastic energy is transformed into heat.

For instance, if an acceleration, ax, of the center of mass of some bar is higher than for some other bar, velocity V(t) grows more rapidly, and we 36 CHAPTER 1. HOOKE'S LAW, POISSON'S RELATION AND WAVES... usually say that inertia of this body is smaller. Also, proceeding from Newton's second law, it is conventional to consider mass, m, as the parameter that characterizes inertia. In other words, mass m defines a time interval during which the center of mass of the moving bar reaches a certain value of the velocity, if Fx = const.

It is impossible to describe this process by either single function f[a(t — x/c[] or g[a(t + x/ci\, or by a sum of them. At the same time, even in the presence of attenuation, the sinusoidal wave as a function of time preserves the same frequency. This is the second reason why it is very convenient to study wave phenomena using sinusoidal waves even when part of an elastic energy is transformed into heat. 3. The use of Fourier's integral allows us to treat an arbitrary transient wave as superposition of sinusoidal waves (Part I).

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