Tomographic modeling of a cross-borehole data set

In this paper we describe a methodology for estimating P-wave velocities from a cross-borehole seismic survey that uses straight-ray tomography, ray tracing, and finite-difference wave-equation modeling to produce velocity models that fit the first-break traveltimes. After a starting model is established by straight-ray tomography, the velocity model is checked by ray tracing and wave-equation modeling. Since the models for each procedure show consistent results and the modeled traveltimes closely match those traveltimes from the actual data, we felt our interpretation was confirmed.However, the fitting of cross-well first break traveltimes is only a necessary validity check and is not sufficient to guarantee that the true solution has been found. Two wells were drilled through the areas that were anomalous on the derived tomogram and check-shot velocity surveys were run. Due primarily to a lateral ambiguity in velocity estimation caused by too few near-vertical raypaths, the check-shot surveys did not agree with the tomogram velocities. However, subsequently the check-shot traveltimes were used to place bounds on velocity in a constrained least-squares procedure; the combined modeling of uphole and cross-well rays produced an optimum velocity model which satisfies all available data.