Migration deconvolution using domain decomposition

Abstract

Least-squares migration (LSM) is an effective technique for mitigating blurring effects and migration artifacts generated by limited data frequency bandwidth, incomplete coverage of geometry, source signature, and unbalanced amplitudes caused by complex wavefield propagation in the subsurface. Migration deconvolution (MD) is an image-domain approach for LSM that approximates the Hessian operator using a set of precomputed point spread functions. We have developed a new workflow by integrating the MD and domain decomposition (DD) methods. DD techniques aim to solve large and complex linear systems by splitting problems into smaller parts, facilitating parallel computing, and providing a higher convergence in iterative algorithms. We suggest that instead of solving the problem in a unique domain, as conventionally performed, splitting the problem into subdomains that overlap and solve each of them independently. We accelerate the convergence rate of the conjugate-gradient solver by applying the DD methods to retrieve better reflectivity, which is mainly visible in regions with low amplitudes. Moreover, using the pseudo-Hessian operator, the convergence of the algorithm is accelerated, suggesting that the inverse problem becomes better conditioned. Experiments using the synthetic Pluto model demonstrate that our algorithm dramatically reduces the required number of iterations while providing a considerable enhancement in image resolution and better continuity of poorly illuminated events.