Iterative Synthesis Methods for a Seismic Array Processor

Two methods for the iterative synthesis of an array processor are discussed: the method of steepest descent and the method of conjugate gradients with projection. These methods require no intermediate statistics such as the covariance matrix function or the cross-power spectral matrix, and therefore, require less storage space than the conventional synthesis methods. A bound for the rate of convergence is obtained for these iterative procedures and it is shown that the convergence is geometric. The algorithms are then applied to seismic data of the Montana large aperture seismic array. Simulation results indicate that the convergence is so fast that a few iterations are enough from the practical viewpoint. Therefore, these methods can also save significant computation time as well.