PLANE AND SPHERICAL TRANSIENT VOIGT WAVES

Abstract

The combination of high‐speed digital computers and recursive finite difference schemes has become a powerful tool in the theoretical analysis of seismic wave propagation. Using this tool, we have obtained solutions to the viscoelastic, or Voigt, wave equation under the following conditions: First, a pressure impulse is applied to the surface of a spherical cavity in a spherically symmetric system; and, second, an arbitrary function is applied to the surface of a semi‐infinite body in a rectangular system. At and near the cavity wall, the cavity radius appears to be the dominant factor in determining the wavelet shape. The viscosity of the medium plays a minor role. At large distances from the cavity, the pressure impulse response of the medium is controlled by the viscosity. Poisson’s ratio has a small but noticeable effect on the wavelet shape near the source. In the plane‐wave case, our results are in good agreement with those given by Collins (1960) near the source and those of Ricker (1943, 1953) at large distances from the source.