Nonlinear wave propagation in sandstone: A numerical study

Abstract

Elastic nonlinear effects in rocks are observed widely in laboratory experiments. For example, Toksöz et al. (1976) measured the pressure dependence of wave speed in the rocks. In crystalline rock and sandstone, Johnson et al. (1987) and Johnson and Shankland (1989) have demonstrated the nonlinear generation of elastic waves. The importance of nonlinear effects in seismic waves in the earth in regard to models of the source is given in Johnson and McCall (1994). The evolution of the harmonic spectrum of a single frequency wave propagated in Berea Sandstone was shown in Meegan et al. (1993). The structural defects contained in rock, such as microcracks and grain‐to‐grain contacts, give rise to this strong elastic nonlinearity (e.g., Gist, 1994). A new theoretical model is developed in McCall and Guyer (1994) to describe elastic behavior of hysteretic nonlinear materials, such as rock. In general, the third‐order elastic constants of the rocks have much larger values than ordered solids.