Transmission‐reflection tomography: Application to reverse VSP data

Abstract

A multiphase tomographic algorithm is presented that allows 2-D and 3-D slowness (inverse of velocity) and variable reflector depth to be reconstructed simultaneously from both transmission and reflection traveltimes. We analyze the ambiguity in the determination of velocity and depth in transmission and reflection data and realize that depth perturbation is more sensitive to reflection traveltime anomalies than slowness perturbation, whereas the reverse is true of transmission traveltime anomalies. Because of the constraints on velocity and depth provided by the different wave types, this algorithm reduces the ambiguity substantially between velocity and depth prevalent in reflection tomography and also avoids the undetermined problem in transmission tomography. The linearized inversion was undertaken iteratively by decoupling velocity parameters from reflector depths. A rapid 2-D and 3-D ray‐tracing algorithm is used to compute transmission and reflection traveltimes and partial derivatives with respect to slowness and reflector depth. Both depth and velocity are parameterized in terms of cubic B‐spline functions. Synthetic examples indicate the improvement in tomographic results when both transmission and reflection times are included. The method has been applied to a reverse vertical seismic profile (VSP) data set recorded on the British coal measures along a crossed‐linear array. Traveltimes were picked automatically by the simultaneous determination of time delays and stacking weights using a waveform matching technique. The tomographic inversion of the observed reverse VSP images two fault‐zones of lower velocity than the surrounding media. The location of the faults was confirmed by near‐by reflection lines. The technique can be applied to offset VSPs or reverse VSPs and coincident VSP and surface reflection data.