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.