A Conjugate Direction Method for Geophysical Inversion Problems

In geophysical tomography, algebraic methods are often used to linearize the nonlinear problem of determining the characteristics of an underground region given measurements of the earth´s attenuation to electromagnetic or seismic waves. In this way, a set of linear equations is developed such that the unknowns are the picture elements (pixels) of the region being scanned.Classically, these linear equations have been solved using the algebraic reconstruction technique (ART) algorithm. In this paper, a new algorithm that is a member of the set of conjugate direction (CD) methods is developed and comparisons are made between this algorithm and the ART algorithm for data arising from simulated electromagnetic probing. This new method, which we call the constrained conjugate gradient (CCG) algorithm, is shown to have a much faster convergence to a final solution than the ART algorithm. In addition, for applications involving high-contrast anomalies (for example, tunnel detection) the CCG is shown to have superior performance in locating the anomalous region for almost all test cases considered.