Multiple signal extraction by multiple interference attenuation in the presence of random noise in seismic array data

A vector of digital filters is derived for the multichannel processing of the signals acquired by an array of sensors with the objective of extracting multiple desired signals by the attenuation of multiple interferences and random noise. The signals and interferences are assumed to have arbitrary waveforms with no a priori knowledge of these waveforms. The time duration of the recorded array data is assumed to be long enough to incorporate all time delayed propagated waveforms at the sensors of the array. The derivation is for the general case of an arbitrary array geometric configuration and is not confined to the special case of a linear array of equispaced sensors. The rationale adopted in the derivation of the filters is to give first priority at each discrete frequency to passing the signals, a second priority to canceling the interferences, and a third priority to attenuating the random noise. This rationale well suits the case of seismic data that are dominantly corrupted by strong interferences rather than random noise. Solving a constrained minimization problem derives the vector of array filters. The computation of this vector requires the application of a powerful matrix decomposition technique for the detection of any redundant and/or inconsistent constraints at each discrete frequency. The simulation results demonstrate the extraction ability of the derived filters in both the multiple input single output and the multiple input multiple output processing schemes.