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 as a rule 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 should not have to have a robust heritage in arithmetic and mathematical physics
* designated research of wave phenomena in a variety of varieties of elastic and liquid-elastic media

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Additional info for Acoustic and Elastic Wave Fields in Geophysics, III, Volume 39 (Methods in Geochemistry and Geophysics)

Sample text

Of course, if the external force Fx varies slowly, the influence of harmonics is strongly reduced even at earlier times. This analysis shows that the wave "informs" the low end of the bar about its original length /. 95) is applied to the left end of the bar, which has a length I and the cross-section S, Fig. 5a. At this moment, the pulse of the compressional wave arises and moves with the velocity Q. We assume that ciSt -C I and that a change of the bar length due to either a compression or extension is extremely small.

As follows from cqs. 140) since ezz = 0, and therefore volume does not change. In accordance with eqs. 141) and rotation is absent. , the angle 7, and the stress r 4 (Tyy). After deformation (Fig. ) - \T^ ob\ 4 2' d-142) l+e99 Note that for small 7 tanrall -1)= M 2'~ tan7r / 4 ~ t a n 7 / 2 _ 1 - 7/2 _ 1 + tanTT/4tan7/2 ~ 1 + 7/2 ~ _ 7 ' 48 CHAPTER 1. EOOKE'S LAW, POISSON'S RELATION AND WAVES... eq. 142 becomes 1 " 7 = T — — = 1 " 2eyy, 1 -|- tyy since exx = — eyy (eq. 137), and e w < 1. 143) Substitution of eq.

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. The similarity for outgoing waves is obvious. 2 LONGITUDINAL WAVES IN A THIN BAR 21 Displacement field In accordance with Poisson's relation dv dy dw dz du dx wave propagation along the x-axis is accompanied by motion of particles along all axes.

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