Determination of teleseismic relative phase arrival times using multi-channel cross-correlation and least squares

We have developed a semi-automated method of determining accurate relative phase arrival times and uncertainty estimates for teleseisms recorded on regional networks. Our analysis begins by obtaining preliminary arrival times with a single-trace phase-picking algorithm. For each possible pair of traces we then perform a search for the maximum of their cross-correlation function in order to obtain relative delay times. Depending on event magnitude, the best results are obtained by using correlation windows containing 2 to 4 sec of the initial energy pulse of the phase. The cross-correlation derived delay times are then used to generate an overdetermined system of linear equations whose solution is an optimized set of relative arrival times. We solve for these times using least squares. Cycle skipping is eliminated through the automatic re-evaluation of cross-correlation functions which yield high equation residuals. Quantitative estimates of timing uncertainty are obtained from the variance of equation residuals associated with each trace. Using data from the Washington Regional Seismograph Network, we have found that for reasonably high-quality events, the rms uncertainty in arrival time estimates is on the order of the sample interval (0.01 sec). Reproducibility of delay anomalies is excellent for events from the same geographic locations despite significant differences in waveform character. In connection with a study of the deep structure of the Cascadia Subduction Zone, we include a preliminary examination of the variation of residual patterns with azimuth.