Frequency‐dependent effects of rupture for the 2004 Parkfield main shock, results from UPSAR

The frequency‐dependent effects of rupture propagation of the Parkfield, California, earthquake (28 September 2004, M6) to the northwest along the San Andreas Fault can be seen in acceleration records at UPSAR (USGS Parkfield Seismic Array) in at least two ways. First, we can see the effects of directivity in the acceleration traces at UPSAR, which is about 11.5 km from the epicenter. Directivity or the seismic equivalent of a Doppler shift has been documented in many cases by comparing short‐duration, high‐amplitude pulses (P or S) in the forward direction with longer‐duration body waves in the backward direction. In this case we detect a change from a relatively large amplitude, coherent, high‐frequency signal at the start of rupture to a low‐amplitude, low‐coherent, low‐frequency signal at about the time the rupture front transfers from the forward azimuth to the back azimuth at about 34–36 s (time is UTC and is the seconds after day 272 and 17 h and 15 min. S arrival is just after 30 s) for rays leaving the fault and propagating to UPSAR. The frequency change is obvious in the band about 5 to 30 Hz, which is significantly above the corner frequency of the earthquake (about 0.11 Hz). From kinematic source models, the duration of faulting is about 9.2 s, and the change in frequency is during faulting as the rupture extends to the northwest. Understanding the systematic change in frequency and amplitude of seismic waves in relation to the propagation of the rupture front is important for predicting strong ground motion. Second, we can filter the acceleration records from the array to determine if the low‐frequency energy emerges from the same part of the fault as the high‐frequency signal (e.g., has the same back azimuth and apparent velocity at UPSAR), an important clue to the dynamics of rupture. Analysis of sources of strong motion (characterized by relatively high frequencies) compared to kinematic slip models (relatively low frequency) for the 11 March 2011 Tohoku earthquake as well as Maule (27 February 2010) and Chi‐Chi (20 September 1999) earthquakes show that high‐ and low‐frequency sources do not have the same locations on the fault. In this paper we filter the accelerograms from UPSAR for the 2004 main shock in various passbands and then recompute the cross correlations to determine the vector slowness of the incoming waves. At Parkfield, it appears that for seismic waves with frequencies above 1 Hz, there is no discernible frequency‐dependent difference in source position (up to 8 Hz) based on estimates of back azimuth and apparent velocity. However, at lower frequencies, sources appear to be from shallower depths and trail the high frequencies as the rupture proceeds down the fault. This result is greater than one standard deviation of an estimate of error, based on a new method of estimating error that is a measure of how broad the peak in correlation is and an estimate of the variance of the correlation values. These observations can be understood in terms of a rupture front that is more energetic and coherent near the front of rupture (radiating higher frequencies) and less coherent and less energetic (radiating in a lower frequency band) behind the initial rupture front. This result is a qualitative assessment of changes in azimuth and apparent velocity with frequency and time and does not include corrections to find the source location on the fault.