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Image Domain Least-Squares Migration with Hessian Estimated by Non-Stationary Matching Filters

The key to image domain least-squares migration is the explicit calculation of the Hessian matrix. However, the full Hessian matrix is too big and expensive to compute and save. Guitton (2004) directly approximates the non-diagonal inverse of the Hessian with a bank of non-stationary matching filters, which can be seen as a low-rank approximation of the true inverse Hessian. The filters have the amplitude-balancing effect, but the ability to increase the resolution is missing. In this paper, to capture as much effect of least-squares migration as possible, we use non-stationary matching filters to approximate the non-diagonal Hessian first, and then solve a constrained optimization problem with the sparse and TV regularization for the result of the image domain least-squares migration. Numerical examples illustrate that the inverted images of the proposed method have both more balanced amplitudes and higher resolution than conventional migration images.