Elastic finite difference modelling with stability and dispersion corrections

Peter M. Manning and Gary F. Margrave

ABSTRACT

This paper presents a very general method to limit the dispersion and instability inherent within finite-difference elastic modelling in two dimensions. The method is based on an extension of the Von Neumann stability analysis. For a fixed frequency an analytic relationship is derived between the continuous derivatives in the elastic wave equation and their second order finite-difference approximations. Typically, the continuous derivative is equal to a finite-difference result divided by a correction factor that is a squared sinc function dependant on frequency and grid size. When the continuous derivatives are replaced by these expressions, an exact formulation of the elastic wave equation results that involves finite differences and correction factors. These correction factors are all frequency dependent. The frequency dependence can be converted to wavenumber dependence using P and S wave velocities. This allows the correction factors to be applied as spatial filters. Numerical tests show that these correction factors compensate for a wide range of dispersion and instability.

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