Abstract

We describe a new multi-channel procedure for estimating arrival time residuals from seismic array data. It incorporates aspects of three traditional array processing methods: frequency-domain beamforming, time-domain beamforming, and principal-component analysis. We start by applying the multi-wavelet transform to the data, which yields a suite of narrow-band seismograms. We use the multi-wavelet transform, instead of the windowed Fourier transform, for superior control over both the time and frequency resolution. We employ a beamforming procedure that uses principal component analysis on the transformed, time-aligned data. The values in the principal component vector and value pair are used to calculate a measure of coherence analogous to semblance. A measure of the misfit of the data to our plane-wave model is contained in the phase differences in the principal component vector. The phase differences can be converted directly to time residuals, but they are only resolvable to a fraction of the analyzing wavelength. Hence, our method is a staged process that moves from lower to higher analyzing frequency bands. We present two data examples that illustrate the wide range of spatial and temporal scales over which this approach can be applied. First, we determine time residuals for the deep-focus Bolivian earthquake of 1994 for a set of broadband stations spread over most of southern California. The time residuals had a range of 2 sec, and after their removal, we were able to stack the data to over 1.0 Hz. Second, we study a local event recorded by high-frequency sensors at an array in Turkmenistan with an aperture of less than 1 km. We found that the time residuals only had a range of 0.02 sec, but by removing them, we significantly improved the stack of the data for the arrival's dominant frequency.

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