Diffraction tomography applied to crosshole and VSP seismic data

Abstract

Diffraction tomography is an approach to seismic inversion which is analogous to f-k migration. It differs from f-k migration in that it attempts to obtain a more quantitative rather than qualitative image of the Earth's subsurface. Diffraction tomography is based on the generalized projection-slice theorem which relates the scattered wave field to the Fourier spectrum of the scatterer. Factors such as the survey geometry and the source bandwidth determine the data coverage in the spatial Fourier domain which in turn determines the image resolution. Limited view-angles result in regions of the spatial Fourier domain with no data coverage, causing the solution to the tomographic reconstruction problem to be nonunique. The simplistic approach is to assume the missing samples are zero and perform a standard reconstruction but this can result in images with severe artefacts. Additional a priori information can be introduced to the problem in order to reduce the nonuniqueness and increase the stability of the reconstruction. This is the standard approach used in ray tomography but it is not commonly used in diffraction tomography applied to seismic data.This paper shows the application of diffraction tomography to crosshole and VSP seismic data. Using synthetic data, the effects on image resolution of the survey geometry and the finite source bandwidth are examined and techniques for improving image quality are discussed.