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 via Elsevier (2000, 2002) dealt in most cases 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 wouldn't have to have a robust history in arithmetic and mathematical physics * certain research of wave phenomena in a variety of varieties of elastic and liquid-elastic media

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

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However, in the presence of the primary source, the resultant wave contains all frequencies. This happens because the effect of a destructive interference at some frequencies is compensated by an action of the primary source which generates waves at such frequencies. Completely different behavior is observed when this source ceases to act, since only the interference of waves moving in the opposite directions defines the frequency content of the resultant wave. In other words, the resultant oscillations are formed only by sinusoidal waves that experience the constructive interference.

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.

Since with an increase of time the same value of the argument t — x/ci is observed at greater distances, the function / [a(t — X/Q)] describes the outgoing wave that is traveling away from the origin, if x > 0. In contrast, the function g[a(t + X/Q)] characterizes the incoming wave, if x > 0, because with a decrease of distance the same value of the argument t + x/ci takes place later. It may happen that the wave field is described by either by the outgoing or incoming waves or by the superposition of them.

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