Prestack migration velocity estimation using nonlinear methods

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We describe here methods of estimating interval velocities based on two nonlinear optimization methods; very fast simulated annealing (VFSA) and a genetic algorithm (GA). The objective function is defined using prestack seismic data after depth migration. This inverse problem involves optimizing the lateral consistency of reflectors between adjacent migrated shot records. In effect, the normal moveout correction in velocity analysis is replaced by prestack depth migration. When the least‐squared difference between each pair of migrated shots is at a minimum, the true velocity model has been found. Our model is parameterized using cubic‐B splines distributed on a rectangular grid. The main advantages of using migrated data are that they do not require traveltime picking, knowledge of the source wavelet, and expensive computation of synthetic waveform data to assess the degree of data‐model fit. Nonlinear methods allow automated determination of the global minimum without relying on estimates of the gradient of the objective function, the starting model, or making assumptions about the nature of the objective function itself. For the velocity estimation problem, the VFSA converges 4 to 5 times faster than the GA for both a 2-D synthetic example and a structurally complex real data example from the Gulf of Mexico. Though computationally intensive, this problem requires few model parameters, and use of a fast traveltime code for Kirchhoff migration makes the algorithm tractable for real earth problems.