Frequency domain coherent processing of regional seismic signals at small arrays

It can be shown that most currently used methods for enhancing regional signals at small arrays are special cases of a more general frequency domain processing scheme designed to optimize the signal/noise power gain for the processor once the signal and noise power spectral matrices are given. The optimum processor makes use of the coherence structures of the signal and noise, and can be simply derived by simultaneous diagonalization of these power spectral matrices. Curiously enough, the optimum processors are not weighted beams but include phase-shifting different from the array beam steers. Such processing schemes can be programmed quite efficiently in the frequency domain and may, in some cases, be more efficient than weighted array beams.