A Comparison of Seismic Array Processing Schemes

It is our purpose in this note to discuss three of the many approaches to seismic array processing from the theoretical point of view. The three are: 1) maximumlikelihood processing, 2) the minimum-variance, unbiased estimator (MVU) approach used by Levin, and 3) multichannel Wiener filtering. A feature common to these techniques is the formation of a single output waveform which serves as an estimator of the unknown signal coming from a fixed direction. We refer to such an output as a "beam." It will be shown that 1) reduces to 2) in the case of gaussian noise and known signal parameters (i. e. , known epicenter) and that 3) is related very simply to 2). In fact, the Wiener filtering output can be obtained directly from the MVU output. We treat both the sampled-data and continuous-time cases. The note contains no new results. Accepted for the Air Force Stanley J. Wisniewski Lt Colonel, USAF Chief, Lincoln Laboratory Office