THE PERFECTLY REFLECTING WEDGE USED AS A CONTROL MODEL IN SEISMIC DIFFRACTION MODELLING*

Abstract

ABSTRACTThe numerical modelling of seismic diffraction, e.g., at faults and other discontinuities, generally requires the use of fast approximate methods. The geophysicist responsible for the development of such numerical methods has a real need of exact solutions to certain ideal geometries to check the accuracy of his calculations.One such exact solution, which is available, is the acoustic wave solution to the perfectly reflecting wedge. The solution is three‐dimensional and the source is an explosive point source. This model is ideal for seismic diffraction; the solution has the advantage of being exact, truly three‐dimensional and of being in the convenient form of the temporal and spatial impulse response. More complicated sources which are extended in either space or time can, therefore, be modelled exactly by numerical integration.This paper presents some examples of the use of the perfectly reflecting wedge as a control model for an asymptotic high frequency diffraction modelling method. This control model has revealed that certain survey and wedge configurations can yield significant disagreement with, e.g., the Kirchhoff approximation. Such configurations could occur during VSP modelling when the survey lies in the near field or in the shadow zone of a high contrast fault. This control model has also been instructive in demonstrating why the high frequency, asymptotic, approximation is generally very good and has indicated a possible improvement to the Kirchhoff approximation for edge diffraction.