Automatic cross‐well tomography: an application of the differential semblance optimization to two real examples

An automatic tomography algorithm, based on differential semblance optimization (DSO), has been used to invert real cross‐well seismic data for the background velocity. The method relies on the first‐arrival transmitted waves. Given a background velocity model, the traveltimes between the sources and the receivers are computed, then semblance panels are created by back‐propagating the data traces. If the velocity model is correct all the first‐arrival transmitted waves will be aligned in the semblance panels. The DSO method consists of finding the background velocity by minimizing the L2‐norm of the difference between adjacent back‐propagated traces. Thanks to the good behaviour of this DSO cost function about the solution, a local (gradient) optimization can be performed. This provides a relatively fast algorithm when ray tracing and analytic computation of the gradient are used. Unfortunately the method fails in the presence of caustics in the data. However, this difficulty can be circumvented by applying suitable masks to the data. This approach is first applied to a synthetic example then to two real data sets: the McElroy data set recorded in West Texas and the NIMR data set recorded in Oman. The results are quite encouraging and similar to those obtained with classical tomography.