Reflection Tomography: Vees in Midpoint-Offset Space , by Marta Jo Woodward

In reflection seismic experiments, localized velocity anomalies cast shadows on underlying reflectors---creating vee-shaped time-shift patterns in midpoint-offset space. Ray-theoretic, tomographic inversion of reflection seismic data for small velocity anomalies typically consists in the four-step identification of these patterns. A background velocity model is assumed; vees for point velocity anomalies at all midpoints are found by ray-tracing through the model; anomalous traveltimes are determined by picking crosscorrelation peaks, and the picked time shifts are backprojected into midpoint-depth space through integration over all possible vees on the midpoint-offset plane. This paper proposes two modifications to this four-step scheme. First, the reconstruction of small velocity anomalies is reformulated as an optimization problem. By shifting traces underlying precalculated vee-patterns up and down in time to maximize a semblance objective function, the algorithm estimates traveltime and velocity anomalies simultaneously---without intermediate picking. Second, wave effects noted through comparison of equivalent wave and ray-theoretic data sets are incorporated into the algorithm through modification of the ray-trace derived vee-patterns. Smearing the vees in midpoint and damping them in offset yielded improved inversion results for wave-theoretic data.


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