Multi-channel estimation of time residuals from broadband seismic data using multi-wavelets

We describe a new multi-channel procedure for estimating arrival time resid uals from seismic array data. It incorporates aspects of three traditional array processing methods: frequency-domain beamforming, time-domain beamfor ming and principal-component analysis. We start by applying the multi-wavel et transform to the data, which yields a suite of narrow-band seismograms. We use the multi-wavelet transform, instead of the windowed Fourier transfo rm, for superior control over both the time and frequency resolution. We em ploy a beamforming procedure that uses principal component analysis on the transformed, time-aligned data. The values in the principal component vecto r 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 c ontained in the phase differences in the principal component vector. The ph ase differences can be converted directly to time residuals, but they are o nly resolvable to a fraction of the analyzing wavelength. Hence, our method is a staged process that moves from lower to higher analyzing frequency ba nds. We present two data examples that illustrate the wide range of spatial and temporal scales over which this approach can be applied. First, we det ermine 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 s tack the data to over 1.0 Hz, Second, we study a local event recorded by hi gh-frequency sensors at an array in Turkmenistan with an aperture of less t han 1 km, We found that the time residuals only had a range of 0.02 sec, bu t by removing them, we significantly improved the stack of the data for the arrival's dominant frequency.