Wave-equation Migration Velocity Analysis (MVA) is emerging as a plausible alternative to reflection tomography for velocity model construction and updating. The use of a wave-equation propagator means that it is thought to be applicable in areas of complex geology where ray-tracing may be unstable and Kirchhoff-style gathers are hard to pick. However, the scale and non-linearity of the problem means that it requires multiple iterations of descents type optimization, which makes it expensive. Furthermore, acquisition limitations and variations in reflection amplitudes and illumination typically extend the null space beyond the natural limits of resolution imposed by the source, resulting in uncertainties in the model and associated image. Appropriate regularization can stabilize and even accelerate convergence to models which are a priori more satisfying than others which fit the data. Under the assumption that the velocity variations are conformal with the seismic reflectivity, we propose structure-oriented smoothing for such regularization. Synthetic and real-data examples demonstrate that this is a good choice.

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