We present a methodology for conducting a site-specific probabilistic analysis of fault displacement hazard. Two approaches are outlined. The first relates the occurrence of fault displacement at or near the ground surface to the occurrence of earthquakes in the same manner as is done in a standard probabilistic seismic hazard analysis (PSHA) for ground shaking. The methodology for this approach is taken directly from PSHA methodology with the ground-motion attenuation function replaced by a fault displacement attenuation function. In the second approach, the rate of displacement events and the distribution for fault displacement are derived directly from the characteristics of the faults or geologic features at the site of interest. The methodology for probabilistic fault displacement hazard analysis (PFDHA) was developed for a normal faulting environment and the probability distributions we present may have general application in similar tectonic regions. In addition, the general methodology is applicable to any region and we indicate the type of data needed to apply the methodology elsewhere.

The U.S. Bureau of Reclamation's Paradox Valley Unit (PVU) extracts aquifer brine from nine shallow wells along the Dolores River, Paradox Valley, in southwestern Colorado and, after treating, high pressure injects the brine 4.3-4.8 km below the surface. PVU injects at rates between ϳ800 and ϳ1300 L/min. Since 1991, PVU has emplaced over 4 ‫ן‬ 10 6 m 3 of fluid and induced more than 4000 surfacerecorded seismic events. The events are recorded on the local 15-station Paradox Valley Seismic Network. The induced seismicity at Paradox separates into two distinct source zones: a principle zone (Ͼ95% of the events) asymmetrically surrounding the injection well to a maximum radial distance of ϳ3 km, and a secondary, ellipsoidal zone, ϳ2.5 km long and centered ϳ8 km northwest of the injection well. The expansion of these zones has stabilized since mid-1999, about three years after the onset of continuous injection. Within the principal zone, hypocenters align in distinct linear patterns, showing at-depth stratigraphy and the local Wray Mesa fracture and fault system. The primary faults of the Wray Mesa system are aseismic, striking subparallel to the inferred maximum principal stress direction, with one or more faults, probably, acting as fluid conduits to the secondary seismic zone. Individual seismic events, in both zones, do not discernibly correlate with short-term injection parameters; however, a 0.5 km 2 region immediately northwest of the injection well responds to long-term, large-scale changes in injection rate and the surpassing of a threshold injection pressure. Focal mechanisms of the induced events are consistent with simple double-couple, strike-slip moments and subhorizontal extension to the northeast. In addition, the fault planes are consistent with principal stress directions determined from borehole breakouts. More than 99.9% of the PVU seismicity is below human detection (ϳM 2.5). However, approximately 15 events have been felt locally, with the largest being a magnitude M 4.3. Because of the M 4.3 and two earlier-felt M ϳ3.5 events and injection economics, PVU changed injection strategies three times since 1996. These changes reduced seismicity from ϳ1100 events/year to as low as ϳ60 events/year.

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A seismic hazard evaluation for three dams in the Rocky Mountains of northern Colorado is based on a study of the historical seismicity. To model earthquake occurrence as a random process utilizing a maximum likelihood method, the catalog must exhibit random space-time characteristics. This was achieved using a declustering procedure and correction for completeness of recording. On the basis of the resulting a-and b-values, probabilistic epicentral distances for a 2 x 10 -5 annual probability were calculated. For a random earthquake of magnitude ML 6.0-6.5, this distance is 15 kin. Suggested ground motion parameters were estimated using a probabilistie seismic hazard analysis. Critical peak horizontal accelerations at the dams are 0.229 if median values are assumed and 0.399 if variable attenuation and seismicity rates are taken into account. For structural analysis of the dams, synthetic acceleration time series were calculated to match the empirical response spectra. In addition, existing horizontal strong motion records from two Mammoth Lakes, California earthquakes were selected and scaled to fit the target horizontal acceleration response spectra.