Forward modelling in cross-hole seismic tomography using reciprocity

Abstract

Seismic transmission tomography provides means of direct estimation of compressional wave velocities using first arrival travel times from cross-hole data. Forward modelling in seismic tomography involves the computation of travel times at the receiver positions and the estimation of ray travel paths for a subsurface velocity model and source-receiver geometry. Conventional ray-tracing techniques face many difficulties when applied to real-life situations. These can be overcome to a great extent by using a ray-tracing technique based on the principle of reciprocity. In the present work, an algorithm is developed which makes use of the reciprocity principle and Fermat's principle for the estimation of raypaths. In this technique seismic travel-time calculation is based on a two-dimensional dynamic programming approach, involving the systematic mapping of travel times over a grid of constant-velocity cells. The algorithm is seen to work even for most complicated velocity models. First arrival seismic energy can travel either as transmitted waves, diffracted waves or head waves, and this technique simulates all of them. The algorithm is tested for various subsurface velocity models, some of which are presented in this paper. The results are represented as ray diagrams, superimposed over the actual velocity model. The isotime lines depicting the wavefronts are also presented, which clearly reveal the effect of velocity contrast on seismic wave propagation.