A separable-kernel decomposition method for approximating the DSR continuation operator

Abstract

We develop a separable-kernel decomposition method for approximating the double-square-root (DSR) continuation operator in one-way migrations in this paper. This new approach is a further development of separable approximations of the single-square-root (SSR) operator. The separable approximation of the DSR operator generally involves solving a complicated nonlinear system of integral equations. Instead of solving this nonlinear system directly, our new method consists of repeatedly applying the separable-kernel technique developed for the two-variable SSR operator to the multivariable DSR operator. Numerical experiments demonstrate the efficiency of the proposed method. We illustrate the fast convergence of the obtained separable approximation. We also demonstrate the capability of this novel approximation for imaging an area with geologic complexities through synthetic data.