We show that it is possible to estimate the background velocity for prestack depth migration in 2D laterally varying media using a non‐linear optimization technique called very fast simulated annealing (VFSA). We use cubic splines in the velocity model parametrization and make use of either successive pairs of shot gathers or several constant‐offset sections as input data for the inversion. A Kirchhoff summation scheme based on first‐arrival traveltimes is used to migrate/model the input data during the velocity analysis. We evaluate and compare two different measures of error. The first is defined in the recorded data or (x,t) domain and is based on a reflection‐tomography criterion. The second is defined in the migrated data or (x,z) domain and is based on a migration‐misfit criterion. Depth relaxation is used to improve the convergence and quality of the velocity analysis while simultaneously reducing the computational cost. Further, we show that by coarse sampling in the offset domain the method is still robust. Our non‐linear optimization approach to migration velocity analysis is evaluated for both synthetic and real seismic data. For the velocity‐analysis method based on the reflection‐tomography criterion, traveltimes do not have to be picked. Similarly, the migration‐misfit criterion does not require that depth images be manually compared. Interpreter intervention is required only to restrict the search space used in the velocity‐analysis problem. Extension of the proposed schemes to 3D models is straightforward but practical only for the fastest available computers.

At the present time, proper solutions for absorption modeling are based on wavefield extrapolation techniques which, in some instances, may be considered expensive. Two alternative, low cost, but incomplete solutions exist in the literature. The first models dispersion in the frequency domain in accordance with the Futterman dispersive relations but does not consider attenuation. The second models both attenuation and dispersion in the time domain but assumes a digital minimum‐phase formulation that results in an inadequate treatment of the dispersion. We show that this second solution can be adapted to perform attenuation and/or dispersion modeling in agreement with the Futterman attenuation‐dispersion relationships thus obviating the shortcoming mentioned above. Synthetic and real data examples are shown to illustrate the performance of the proposed algorithm.

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