Computer Science Technical Report Automated Velocity Picking: A Computer Vision and Optimization Approach

\Velocity Picking" is the problem of picking velocity-time pairs based on a coherence metric between multiple seismic signals. Coherence as a function of velocity and time can be expressed as a 2-D color image representing the \Semblance Velocity." Currently, humans pick velocities by looking at the Semblance Velocity image; picking velocities for a seismic survey can take days or even weeks. Automating the process as pure optimization without exploiting the Semblance Velocity image yields an essentially intractable problem. The problem can also be posed as a geometric feature matching problem similar to those used in computer vision. A feature extraction algorithm can recognize islands (peaks) of maximal power corresponding to velocities in the Semblance Velocity image: a heuristic combinatorial matching process can then be used to nd a subset of peaks which maximizes the coherence metric. Our results indicate this combinatorial approach has many advantages. It is fast, in as much as the evaluation process is restricted to a small nite set of line segments connecting peaks in the image. It also allows the peak selection process to be interactive. Users can hand select peaks; the search then is restricted to solutions consistent with the peaks selected by the user. Our experience indicates that selecting even a single peak is enough to restrict the search to guide it to very good solutions. We also introduce another way to di erentiate competing solutions. We compute an initial set of solutions, then compute a composite median solution across the set. Because geology is such that we generally expect gradual change in rock strata over short distances in space, solutions far away from the median are likely to be incorrect. After obtaining the median, we do a second pass of optimization in which "closeness to the median" is included as an additional optimization criterium. The nal results are similar to those produced by humans and in fact produce a higher evaluation than human picks in terms of the resulting coherence across the seismic signals.