The problem of detecting one Rayleigh wave in the presence of the coda of another larger Rayleigh wave is considered. A detection method is proposed in which a high-resolution, wave number analysis technique is applied to prefiltered data from the Large Aperture Seismic Array (LASA) to determine the direction of arrival of the 40-sec-period Rayleigh-wave group at the appropriate arrival time. The performance of this detection method is considered in great detail. A necessary concomitant of the study of the detection method is the determination of the phases which comprise the coda. It is shown that one component of the coda consists of fundamental-mode Rayleigh waves which propagate along multiple paths and may be caused by either reflections at continental margins or diffraction effects. As has been demonstrated many times, the coda is shown to consist also of fundamental-mode Rayleigh waves which have propagated around the Earth in the direction of the back azimuth. Multiply reflected P and S waves, which propagate primarily in the upper mantle, are detected easily.

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