Improving local earthquake locations using the L1 norm and waveform cross correlation: Application to the Whittier Narrows, California, aftershock sequence

Experiments with different earthquake location methods applied to aftershocks of the October 1, 1987, Whittier Narrows earthquake in California ( M L =5.9) suggest that local event locations can be greatly improved through the use of the L1 norm, station corrections and waveform cross correlation. The Whittier Narrows sequence is a compact cluster of over 500 events at 12 to 18 km depth located within the dense station coverage of the Southern California Seismic Network (SCSN), a telemetered network of several hundred short‐period seismographs. SCSN travel time picks and waveforms obtained through the Southern California Earthquake Center are examined for 589 earthquakes between 1981 and 1994 in the vicinity of the mainshock. Using a smoothed version of the standard southern California velocity model and the existing travel time picks, improved location accuracy is obtained through use of the L1 norm rather than the conventional least squares (L2 norm) approach, presumably due to the more robust response of the former to outliers in the data. A large additional improvement results from the use of station terms to account for three‐dimensional velocity structure outside of the event cluster. To achieve greater location accuracy, waveforms for these events are resampled and low‐pass filtered, and the P and S wave cross‐correlation functions are computed at each station for every event pair. For those events with similar waveforms, differential times may be obtained from the cross‐correlation functions. These times are then combined with the travel time picks to invert for an adjusted set of picks that are more consistent than the original picks and include seismograms that were originally unpicked. Locations obtained from the adjusted picks show a further improvement in accuracy. Location uncertainties are estimated using a bootstrap technique in which events are relocated many times for sets of picks in which the travel time residuals at the best fitting location are used to randomly perturb each pick. Improvements in location accuracy are indicated by the reduced scatter in the residuals, smaller estimated location errors, and the increased tendency of the locations to cluster along well‐defined fault planes. Median standard errors for the final inversion are 150 m in horizontal location and 230 m in vertical location, although the relative locations within localized clusters of similar events are better constrained. Seismicity cross sections resolve the shallow dipping fault plane associated with the mainshock and a steeply dipping fault plane associated with a M L =5.3 aftershock. These fault planes appear to cross, and activity began on the secondary fault plane prior to the large aftershock.