We present a joint seismic inverse scattering and finite-frequency (reflection) tomography program, formulated as a coupled set of optimization problems, in terms of inhomogeneous Helmholtz equations. We use a higher order finite difference scheme for these Helmholtz equations to guarantee sufficient accuracy. We adapt a structured approximate direct solver for the relevant systems of algebraic...

We develop a computational method based on the Debye scalar potential representation, which efficiently reduces the solution of Maxwell’s equations to the solution of two scalar Helmholtz equations. One of the key contributions of this paper is a theory for the translation of Maxwell solutions using such a representation, since the scalar potential form is not invariant with respect to translat...

Perfectly matched layers (PMLs) are formulated and applied to numerically solve the nonlocal Helmholtz equations in one two dimensions. In dimension, we present a PML modification for equation with general kernel demonstrate theoretically how effective it is some sense. dimensions, modifications both Cartesian polar coordinates. Based on modifications, truncated dimensional spaces, an asymptoti...

The finite difference method discretization of Helmholtz equations usually leads to the large spare linear systems. Since the coefficient matrix is frequently indefinite, it is difficult to solve iteratively. In this paper, a modified symmetric successive overrelaxation MSSOR preconditioning strategy is constructed based on the coefficient matrix and employed to speed up the convergence rate of...

A parallelization of a sweeping preconditioner for 3D Helmholtz equations without large cavities is introduced and benchmarked for several challenging velocity models. The setup and application costs of the sequential preconditioner are shown to be O(γN) and O(γN logN), where γ(ω) denotes the modestly frequency-dependent number of grid points per Perfectly Matched Layer. Several computational a...

Elastic wave propagation in anisotropic media is well represented by elastic wave equations. Modeling based on elastic wave equations characterizes both kinematics and dynamics correctly. However, because Pand S-modes are both propagated using elastic wave equations, there is a need to separate Pand S-modes to efficiently apply single-mode processing tools. In isotropic media, wave modes are us...