Stable solutions in Marchenko iterative scheme with Beyond Neumann
J. Maciel, Reynam C. Pestana, D. Barreira · 2021
Summary The solution of the Marchenko equations is usually obtained by iterative methods based on the Neumann series expansion. In the iterative method, if the matrix has eigenvalues smaller than one, we have ensured a convergent solution. However, seismic data acquired in geologies with strong impedance contrast can fail in the convergence condition. In this case, it is necessary to scale down the dataset amplitude, which is normally done using an empirical procedure. In this work, we present the Beyond Neumann method as an alternative method to avoid such convergence problems. The method is based on the preconditioning of the matrix to be inverted and this is obtained by scaling it with a relaxation parameter, coming from the minimization of the residue square, and the product of a conditioning matrix. To test and demonstrate the applicability of our proposed method, we show the comparison of the Beyond Neumann and conventional Neumann solutions using a synthetic dataset obtained from a modified Sigsbee2B model.