A New Blind Beamforming Technique for the Alignment and Enhancement of Seismic Signals

Abstract

Blind beamforming constitutes a unified framework for the solution of two very important problems in seismological applications involving ensembles of similar signals, namely the signal alignment and signal enhancement problems. The former problem translates into the estimation of the time delays that exist between the signals, while the second problem deals with the optimal weighting of the signals, so that the SNR of their weighted average is maximized. A global optimization technique for the solution of the alignment problem with a sample-level accuracy, is proposed in this manuscript. The sample-level alignment problem is formulated as a combinatorial optimization problem and an approximate solution is proposed by using the technique of SDP relaxation. Finally, the signal enhancement problem is formulated as a quadratic maximization problem which in the vast majority of cases has an analytical solution, while in more challenging conditions can be approximately solved via SDP relaxation. The superior performance of the technique compared to other similar approaches is demonstrated through a number experiments involving numerical simulations with several signal and noise models.