Diffraction Tomography: Perturbed Vees in Midpint-Offset Space?
, by Marta Jo Woodward
In reflection seismic experiments, localized velocity anomalies cast shadows
on underlying reflectors--creating anomalous time-shift patterns on expected arrival horizons in midpoint-offset space. When the velocity anomalies are larger than the dominant source wavelength of the experiment, these time-shift patterns may be predicted by ray-tracing and the time delays inverted for the velocity field using ray-theoretic, reflection tomography. When the velocity anomalies are on the order of the dominant source wavelength of the experiment, ray theory breaks fown and wave effects must be incorporated in the inversion. The theory of diffection tomography has been developed for this latter problem: it inverts the full, forward-scattered wavefield after linearlization of the scalar wave equation through application of either the Born of Rytov approximations. SEP-51 contained an article proposing a simplified form of diffreaction tomography, based on the perturbation of ray-theoretic time-shigt patterns to account for diffraction effects instead of on full wavefield inversion. The results in that paper were promising but not perfect. This paper examines a slightly different method of modifying the ray-theoretic vee-patterns for wave phenomena than that described in SEP-51. The results are inferior to those of the previous paper; they fail to conclusively evaluate the potential of the approach.