Seismic modelling by Fresnel diffraction theory with application to wide-aperture data from SW Oklahoma

Abstract

SUMMARY A numerical, 2-D modelling algorithm for seismic P-waves, based on Fresnel diffraction theory, has been developed. This algorithm uses Huygens’ principle: every point on the wavefront may act as an independent secondary source for the subsequent behaviour of the wave. Huygens’ principle implies that a seismogram, which is the seismic response of a medium to a source, can be calculated as the sum of responses of secondary sources on a wavefront. The Fresnel approximation of diffraction is used to calculate the seismic responses. This modelling algorithm is an integral method that is applicable to laterally inhomogeneous models. Ray tracing is used to determine the travel time from each individual secondary source to the receiver. Since the response at the receiver is the accumulation of responses from all secondary sources instead of that from a single source, diffractions and caustics can be modelled in addition to reflections and transmissions. The algorithm is verified by comparison with acoustic finite difference computations, and applied to modelling of data from a wide-aperture seismic survey conducted in SW Oklahoma in 1985. The structure in the survey area is highly laterally inhomogeneous with igneous rocks to the SW, sedimentary rocks to the NE, and a series of thrust faults between.