Efficient preconditioned least-squares wave-equation migration

Abstract

Since the appearance of wave-equation migration (WEM), many have tried to improve the resolution and effectiveness of this technology. Least-squares wave-equation migration is one of those attempts that try to fill the gap between migration assumptions and reality in an iterative manner. However, these iterations do not come cheap. A proven solution to limit the number of least-squares iterations is to correct the gradient direction within each iteration via the action of a preconditioner that approximates the inverse Hessian. However, the Hessian computation, or even the Hessian approximation computation, in large-scale seismic imaging problems involves an expensive computational bottleneck, making it unfeasible. Therefore, we develop an efficient computation of the Hessian approximation operator in the context of one-way WEM in the space-frequency domain. We build the Hessian approximation operator depth by depth, considerably reducing the operator size each time it is calculated. We prove the validity of our method with two numerical examples. We then extend our proposal to the framework of full-wavefield migration, which is based on WEM principles but includes interbed multiples. Finally, this efficient preconditioned least-squares full-wavefield migration is successfully applied to a data set with strong interbed multiple scattering.