The authors present a second order explicit finite-difference scheme for elastic waves in 2-D nonhomogeneous media. These schemes are based on integrating the equations of motion and the stress-free surface conditions across the discontinuities before discretizing them on a grid. As an alternative for the free-surface treatment, a scheme using zero density above the surface is suggested. This scheme is first order and is shown to be a natural consequence of the integrated equations of motion and is called a vacuum formalism. These schemes remove instabilities encountered in earlier integration schemes. The consistency study reveals a close link between the vacuum formalism and the integrated/ discretized stress-free condition, giving priority to the vacuum formalism when a material discontinuity reaches the free surface. The two presented free-surface treatments coincide in the sense of the limit (grid size --> 0) for lateral homogeneity at or near the free surface.

This content is PDF only. Please click on the PDF icon to access.

First Page Preview

First page PDF preview
You do not currently have access to this article.