Reply to Arthur Frankel's "comment on 'rupture Process of the 1987 Superstition Hills Earthquake from the Inversion of Strong-motion Data'"

We thank Art Frankel for his continuing interest in unraveling the details of the complicated source process of the 1987 Superstition Hills earthquake. His insightful comments and subsequent modeling on our part has helped to resolve some of the differences between the rupture model presented in Wald et al. (1990), hereafter referred to as WEA, and that published by Frankel and Wennerberg (1989), hereafter F&W. The main issue raised by Frankel (1992) is the discrepancy between the two estimates for the location of high-frequency radiation during the third, largest subevent of this earthquake. According to Frankers (1992) comment, the model of F&W limits slip during subevent 3 to a zone less than 8 km long southeast of the hypocenter. Thus, the portion of the fault beginning at the fault step-over (Fig. 1) and southeast of that point did not generate high-frequency ground motions. The model WEA favor requires highfrequency radiation from both the northern segment of the fault (where F&W require slip) as well as from the step-over region and the immediately adjacent southern fault segment. We agree that the clarification of this issue is extremely important considering that the link between high-frequency (damaging) strong motions and observations made at longer periods is often made to infer or estimate potential seismic hazards. Although we would like to resolve this issue definitively, we must be realistic and open to the possibility that the answer may be within the grey zone of resolution from this data set and our modeling sophistication, perhaps the very reason that there is a controversy at all. Frankel's (1992) comment addresses three main observations: (1) the consistency of timing of observed subevent 3 arrivals at various azimuths, (2) the inability of the WEA model to match the timing of some subevent 3 arrivals, and (3) the possibility that station PTS pulls slip towards that station due to its proximity to the rupture area. We will first review some observations concerning the Superstition Hills earthquake, clarify a few attributes of both the F&W and WEA models, and then, in turn, address each of the above issues. In addressing these issues, results of subsequent inversions prompted by this discussion will be presented. There is no question as to whether or not slip occurred during this earthquake along the southern portion (southeast of fault step-over) of the Superstition Hills Fault. In fact, at the surface, co-seismic displacement was as great as it was north of the step-over (Sharp et al., 1989; Williams and Magistrale, 1989). Further, teleseismic studies that address the spatial distribution of the longer period energy release (Bent et al. , 1989; Hwang et al., 1990) require greater than 10 km of separation between subevents 2 and 3, placing the third subevent on the southern segment of the fault. In addition, geodetic inversions by Larson (1991) require nearly comparable dislocation on the northwest and southeast fault segments down to depths compatible with the WEA strong-motion inversion estimates. The question we are concerned with here is whether or not the strong-motion data require that high-frequency radiation occurred during the