New solution methods were considered for migration deconvolution in seismic imaging problems. It is well known that direct migration methods, using the adjoint operator L*, yield a lower-resolution or blurred image, and that the linearized inversion of seismic data for the reflectivity model usually requires solving a (regularized) least-squares migration problem. We observed that the (regularized) least-squares method is computationally expensive, which becomes a severe obstacle for practical applications. Iterative gradient-descent methods were studied and an efficient method for migration deconvolution was developed. The problem was formulated by incorporating regularizing constraints, and then a nonmonotone gradient-descent method was applied to accelerate the convergence. To test the potential of the application of the developed method, synthetic two-dimensional and three-dimensional seismic-migration-deconvolution simulations were performed. Numerical performance indicates that this method is promising for practical seismic migration imaging.

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