An Helmholtz iterative solver for the three-dimensional seismic imaging problem?

During the last three decades high-frequency approximations or paraxial (one-way) approximations of the wave equation have been successfully used to process seismic data in two-dimensional or three-dimensional spaces. With the increase of computer power and the need to take into account complex geological structures, solutions of the exact wave...

A new iterative solver for the time-harmonic wave equation

The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can be solved efficiently by a direct method. In...

Resistivity imaging with controlled-source electromagnetic data: Depth and data weighting

We discuss some computational aspects of resistivity imaging by inversion of offshore controlled-source electromagnetic data. We adopt the classic approach to imaging by formulating it as an inverse problem. A weighted least-squares functional measures the misfit between synthetic and observed data. Its minimization by a quasi-Newton algorithm...

An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies

In this work, we present a new numerical framework for the efficient solution of the time-harmonic elastic wave equation at multiple frequencies. We show that multiple frequencies (and multiple right-hand sides) can be incorporated when the discretized problem is written as a matrix equation. This matrix equation can be solved efficiently...