Introduction

In seismic modeling adaptive techniques are well known. Usually the adaption of a quantity is in the direction of a physical dimension like time or space. In general, adaption is guided by criteria to improve numerical accuracy and stability or to increase the speed of the calculation. In his Ph.D. thesis Cunha-Filho 1992 discussed the notion of treating the propagating elastic wave field differently to the underlying medium. His aim was to improve accuracy of reflected and transmitted amplitudes across an interface. He derived his technique in combination with an averaging scheme across the interface and made use of an unstaggered grid.

When examining the accuracy and stability of finite difference operators, the staggered grid finite difference equation can be separated into components that interpolate to the points where derivatives are evaluated. For anisotropic media Igel et. al 1992 showed an error analysis of FD operators and their spatial distribution. Usual implementations have implicit interpolations of medium and wave field properties built into the wave equation operator. Splitting the wave equation operator and explicitly controlling the interpolation gives a well determined and more accurate wave propagation description.