Abstract Evaluating the performance of finite-difference algorithms typically uses a technique known as von Neumann analysis. For a given algorithm, application of the technique yields both a dispersion relation valid for the discrete timespace grid and a mathematical condition for stability. In practice, a major shortcoming of conventional von Neumann analysis is that it can be applied only to an idealized numerical model — that of an infinite, homogeneous whole space. Experience has shown that numerical instabilities often arise in finite-difference simulations of wave propagation at interfaces address this issue, I generalize von Neumann analysis for a model of two half-spaces. I perform the analysis for the case of acoustic wave propagation using a standard staggered-grid finite-difference numerical scheme. By deriving expressions for the discrete reflection and transmission coefficients, I study under what conditions the discrete reflection and transmission coefficients become unbounded. I find that instabilities encountered in numerical modeling near interfaces with strong material contrasts are linked to these cases and develop a modified stability criterion that takes into account the resulting instabilities. I test and verify the stability criterion by executing a finite-difference algorithm under conditions predicted to be stable and unstable.

Abstract On a 2D profile of subsurface permittivity structure derived from guided GPR pulses recorded in the Kuparuk River watershed, Alaska, the transition from a stream channel to a peat layer is interpreted. Although multi-channel data are used, guided waves are analyzed using single-channel analysis, which sidesteps assumptions regarding lateral homogeneity within receiver arrays. As a result, 2D structure is obtained along a profile using an inversion procedure. These data were processed in three steps: (1) picking group traveltimes, (2) performing tomography in the lateral direction, and (3) inverting local group-velocity dispersion curves. When the permittivity profile obtained from the guided waves is compared to a GPR reflection profile, it is clear that the guided waves capture shallow structure near a stream channel that is not imaged accurately on the reflection profile. This demonstrates the utility of using guided waves to provide information on shallow structure that cannot be obtained from reflections.