PLANE COMPRESSIONAL VOIGT WAVES

Abstract

The Voigt wave equation, long considered a possible mathematical model for seismic waves, was extensively studied in 1943 by Norman Ricker, who developed an asymptotic solution applicable at sufficiently large distances from the shotpoint. Ricker’s solution does not agree with his field results (1953) in all respects. For example, Van Melle (1954) has shown that Ricker’s wavelets decay too rapidly with distance to be consistent with the experimental data. This particular difference between theory and observation may arise from the form of the wave source implicitly assumed by Ricker, a doublet impulse of displacement. A single impulse of pressure seems a more reasonable first approximation to the shot. For this source a complete solution for plane waves is developed, valid for all distances and times. A method similar to Ricker’s is then outlined for obtaining an asymptotic solution suitable for computations at large distances. The wavelets from the pressure impulse do not decay as rapidly as Ricker’s doublet displacement solutions. This is a move toward better agreement with experiment. On the other hand, the pressure impulse wavelets have only a single lobe, a definite move away from the observations. There is some reason to believe, however, that the corresponding spherical waves would be more oscillatory than the plane waves. More mathematical work is needed for further tests of the Voigt solid as a theoretical model for earth waves. The next step suggested is the computation of spherical waves from a pressure impulse.