Mapping of the high‐frequency source radiation for the Loma Prieta Earthquake, California

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Abstract
Waveform inversion has been successfully applied to map the spatial distribution of earthquake fault slip from strong motion records. But its application has been restricted to a relatively lower frequency range of the data (ƒ< 2.0–3.0 Hz) essentially due to the difficulties in calculating the high‐frequency Green's function; these difficulties arise specifically from the small‐scale complexity of source, path and station site, and insufficient numbers of observations. However, we can avoid these difficulties by simply looking at the seismic wave energy envelopes instead of the complicated high‐frequency wave phases. By assuming that the slip responsible for high‐frequency wave (e.g.,ƒ> 5 Hz) generation is incoherent between neighboring patches on the fault, we formulated an analytical model for calculating the envelope time history of the squared high‐frequency displacement seismogram. This envelope time history is found through the line integration of the squared energy radiation intensity over the isochron. Using a recursive stochastic inversion scheme, we determined both the lower‐frequency slip distributions from the low‐pass‐filtered strong motion displacement data and the higher‐frequency energy radiation intensity from the envelope of the squared high‐frequency displacement data on an extended fault for the 1989 Loma Prieta earthquake, respectively. Our resulting lower‐frequency slip model shows that there are two main slip patches and little slip directly updip of the hypocenter. One major slip zone located 10 km northwest of the hypocenter with predominant dip‐slip and the other located 12 km southeast of the hypocenter with predominant oblique slip. Our preliminary results of the high‐frequency energy radiation intensity inversion indicate three large high‐frequency sources and few smaller ones located on the outer periphery of the large slip zones. This suggests that the high‐frequency energy sources are located along or near the boundaries of large slip zones, which is consistent with the theoretical consideration that high frequencies are primarily generated from the rupture stopping areas or places with large slip variation.