OpenFile Report 96532
Recurrence Models for FaultsNow we add the hazard from specific faults. This is the right side of Figure 17. We divided the faults into types A and B, roughly following the nomenclature of WGCEP (1995). We classify a fault as Atype if there have been sufficient studies of it to produce models of fault segmentation. In California the Atype faults are: San Andreas, San Jacinto, Elsinore, Hayward, Rodgers Creek, and Imperial (M. Petersen, C. Cramer, and W. Bryant, written comm., 1996). The only fault outside of California that we classified as Atype is the Wasatch Fault. We assumed singlesegment ruptures on the Wasatch Fault (see below). Note that we have not included uncertainty in segment boundaries for these hazard maps. For California, we followed the rupture scenarios specified by Petersen, Cramer and Bryant of CDMG, with input from Lienkaemper of USGS for northern California. We assumed singlesegment, characteristic rupture for the San Jacinto and Elsinore faults. For the San Andreas fault, multiplesegment ruptures were included in the hazard calculation, including repeats of the 1906 and 1857 rupture zones, and a scenario with the southern San Andreas fault rupturing from San Bernardino through the Coachella segment. Both singlesegment and doublesegment ruptures of the Hayward Fault were included. For California faults, we used characteristic magnitudes derived by CDMG from the fault area using the relations in Wells and Coppersmith (1994). For the remainder of the WUS, we determined characteristic magnitude from the fault length using the relations of Wells and Coppersmith (1994) appropriate for that fault type. For the Btype faults, we felt there were insufficient studies to warrant specific segmentation boundaries. For these faults, we followed the scheme of Petersen et al. (1996) and used both characteristic and GutenbergRichter (GR; exponential) models of earthquake occurrence. These recurrence models were weighted equally. The GR model basically accounts for the possibility that a fault is segmented and may rupture only part of its length. We assume that the GR distribution applies from a minimum moment magnitude of 6.5 up to a moment magnitude corresponding to rupture of the entire fault length. In the Pasadena workshop, we showed that without the M6.5 minimum, southern California faults would produce far too many M45 events compared to the historic record. For this comparison we determined the predicted rates of M45 events using fault slip rates and the equation for avalue given next. Given a geologic slip rate and a characteristic magnitude of M$$_{c} we solve for the avalue for a fault by requiring that the calculated annual moment sum of earthquakes equals the geologic moment rate , where the recurrence rate is determined from the GR relation. We do not use the observed rate of earthquakes near the fault to determine the avalue. Using the geologic moment rate produces where µ is shear modulus, N(M) is the annual number of events in a magnitude bin from M0.05 to M+0.05, L is fault length and W is fault width. Equation (1) is rearranged to determine the avalue for each fault. We used a bvalue of 0.8 for all of the faults (except for California faults where we used b=0.9), based on the bvalue derived from the regional seismicity (see above). Equation (1) is a discrete version of similar equations to find avalues by Anderson (1979). The procedure for calculating hazard using the GR model involves looping through magnitude increments. For each magnitude we calculate a rupture length using Wells and Coppersmith (1994). Then a rupture zone of this length is floated along the fault trace. For each site, we find the appropriate distance to the floating ruptures and calculate the frequency of exceedance (FE). The FE's are then added for all the floating rupture zones. Of course we normalize the rate of occurrence of the floating rupture zones to maintain the proper overall rate. As we apply it, the characteristic earthquake model (Schwartz and Coppersmith, 1984) is actually the maximum magnitude model of Wesnousky (1986) Here we assume that the fault only generates earthquakes that rupture the entire fault. Smaller events along the fault would be incorporated by models 1 and 2 with the distributed seismicity or by the GR model described above. Following Wesnousky (1986) we find a recurrence rate for the characteristic event with moment M_{0c} as It should be noted that using the GR model generally produces higher probabilistic ground motions than the characteristic earthquake model, because of the more frequent occurrence of earthquakes with magnitudes of about 6.5. Fault widths (except for California)were determined by assuming a seismogenic depth of 15 km and then using the dip, so that the width equaled 15 km divided by the sine of the dip. For most normal faults we assumed a dip of 60 degrees. Dip directions were taken from the literature. For the Wasatch, Lost River, Beaverhead, Lemhi, and Hebgen Lake faults, the dip angles were taken from the literature (see fault parameter table on Website). Strikeslip faults were assigned a dip of 90 degrees. For California faults, widths were often defined using the depth of seismicity (J. Lienkaemper, written comm., 1996; M. Petersen, C. Cramer, and W. Bryant, written comm., 1996). Fault length was calculated from the total length of the digitized fault trace.

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