ALBERT

Description: The peak ground acceleration (PGA) and peak ground velocity (PGV) from 5058 ruptures of a foam rubber stick-slip model are not distributed according to a lognormal probability distribution function. PGA and PGV values are decomposed using the method of Anderson and Uchiyama (2011) . The statistically significant deviations from the lognormal distribution occur near the peak of the distribution. In some cases, high-amplitude tails differ by a much greater ratio, but the statistical significance of this effect is low. This result is true of both raw data and data adjusted for site and magnitude. Event terms are also not lognormal but can be modeled as a sum of three or four lognormal subdistributions, which possibly represent different preferred rupture initiation points rather than a uniform distribution of initiation points. The event term subdistributions with highest median values have small standard deviations, so if shapes of this nature were used in ground-motion prediction equations (GMPEs) during a probabilistic seismic-hazard analysis, the effect of the long tail of the lognormal distribution in controlling the hazard would be weakened considerably. Static stress drop was recorded for each event, and event terms for PGA and PGV are well correlated with static stress drop. Unlike Next Generation Attenuation-West 2 GMPEs, residual variances for the foam model are dominated by variability in the source slip function, rather than the path and site effects. This difference in the variance budget results from the way in which the source and site residuals are defined in this study; the source uncertainty includes variation in the rupture size (magnitude) and location, along with deviations in distance and path. We do not know if these results apply to earthquakes, but we do think tests of repeating stick-slip events in a physical system are useful to expand the set of credible hypotheses regarding possible behavior modes of earthquake faults.

Description: Field studies of historic rupture traces show that fault stepovers commonly serve as endpoints to earthquake ruptures. This is an effect that is corroborated by past dynamic modeling studies. However, field studies also show a great deal of complexity in fault-zone structure within a stepover, which is often simplified out of modeling studies. In the present study, we use the 3D finite-element method to investigate the effect of one type of smaller-scale complexity on the rupture process: a smaller fault segment positioned between the two primary strands of a strike-slip fault stepover. We find that such small faults can have a controlling effect on whether or not a rupture is able to jump the stepover and on the resulting ground motions from these ruptures. However, this effect is neither straightforward nor linear: the length of the intermediate segment and its basal depth, as well as whether the stepover is extensional or compressional, all contribute to the rupture behavior and ground-motion distribution. These results have important implications for assessing the probability of a rupture propagating through small- and large-scale discontinuities in faults, as well as for evaluating ground-motion intensities near fault stepovers. Because of the sensitivity of results to so many parameters, these results also suggest that modeling studies on idealized fault geometries may not be sufficient to describe the rupture behaviors of specific complex fault systems. Site-specific modeling studies, where possible, will provide better inputs and constraints for probabilistic rupture length assessments as well as for ground-motion estimates.

Description: The Southern California San Jacinto fault is geometrically complex, consisting of several major strands with smaller scale complexity within each strand. The two northernmost strands, the Claremont and the Casa Loma–Clark, are separated by a 25-km-long extensional stepover with an average of 4 km separation between the strands. We use a combined modeling method to assess probable rupture and ground-motion behaviors for this stepover. First, dynamic rupture modeling on geometrically complex fault strands embedded in a state-of-the-art 3D crustal velocity model is used to generate a series of scenario earthquakes. We then use the resulting near-fault low-frequency (〈1 Hz) ground-motion time histories to generate broadband synthetic seismograms with a hybrid approach. These synthetics are then compared with a distribution of precariously balanced rocks (PBRs) near the fault to constrain our results and assess shaking hazard for the region surrounding the fault. Our dynamic models produce sources between M w  5.4 and 6.9, with rupture limits imposed by sharp contrasts in fault stress or by geometrical barriers. The main stepover serves as a primary barrier to rupture in our model, producing event sizes that are consistent with the historical behavior of the San Jacinto fault. The largest broadband synthetics are a good match to leading ground-motion prediction equations and are generally consistent with the distribution of PBRs, none of which experience accelerations that produce toppling probabilities significantly higher than zero. Thus, although the PBRs do not rule out any of our model scenarios, they confirm that our models produce realistic rupture extents and shaking. Online Material: Figures of total slip for additional rupture models, low-frequency intensity plots, synthetic seismograms, and comparison with ground-motion prediction equations.

Description: We use the 3D finite-element method to conduct dynamic models of rupture and resulting ground motion on the Claremont–Casa Loma stepover of the northern San Jacinto fault. We incorporate complex fault geometry (from the U.S. Geological Survey [USGS] Quaternary Faults Database; see Data and Resources ), a realistic velocity structure (the Southern California Earthquake Center Community Velocity Model-S), a realistic regional stress field with an orientation taken from seismicity relocation literature, and several stochastic self-similar shear stress distributions. As we incorporate more types of complexity, the specific effects of any individual factor become less apparent within the overall rupture behavior. We also find that the distribution of high and low shear stress that arises from combining regional and stochastic stress fields has the strongest control over where the rupture terminates. Using a regional stress field alone, as well as with the combined regional and stochastic stress realization, we find that the stepover presents a significant barrier to rupture, regardless of our choice of initial nucleation point and that it is difficult for rupture to propagate the full length of either fault segment. Greater heterogeneity of stresses tends to produce shorter ruptures. Within this result, we find that the Claremont strand is more favorable for long ruptures than the Casa Loma–Clark strand. Low-frequency ground-motion intensity and distribution are controlled largely by the velocity structure rather than by stress heterogeneity. The strongest motions produced in these models are in the San Bernardino basin. Although directivity effects do contribute to the low-frequency ground-motion distribution, particularly in the near field, they are secondary to the effects of the velocity structure. Online Material: Figures of ground motions from models used to calibrate the stress conditions for dynamic rupture propagation.

Description: In a recent study of microearthquakes along the Parkfield segment of the San Andreas fault, Nadeau et al. (1995) have found that much of the seismicity in the region is characterized by quasi-periodic repeating sequences of small earthquakes that are essentially identical in waveform, size and, location. Nadeau and Johnson (1998) interpreted these as repeated slip on a given asperity driven by a steady slip rate of 2.3 cm/yr and concluded that the stress drops needed to be extremely high, of the order of 20 kilobars. We propose another explanation for these small repeating events, namely that an inner asperity is surrounded by a larger creeping zone, which in turn is surrounded by a still larger locked zone. This geometry produces a local slip velocity much less than the overall creep velocity observed on a still larger scale (slip velocity shielding). We have constructed a foam rubber model to illustrate the phenomenon. The time sequences of small events at the asperity, punctuated by large events which rupture the whole block, look very similar to the cumulative moment plots of Nadeau and Johnson. The actual dynamic stress drops are of the same order as for the large events. Thus the results of the model correspond to the observations of Nadeau and Johnson and suggest that the model may be appropriate to explain their observations, without requiring super strong asperities.

Description: The overturning fragility of a freestanding block such as a precariously balanced rock (PBR) has been parameterized as a function of a vector of ground-motion intensity measures. Methodologies are outlined to estimate the failure probabilities of such objects given their residence times. For deterministic seismic hazard analyses (DSHAs), a PBR is exposed to the scenario earthquakes that occur during its exposure time providing an estimate of the probability that the PBR survives the ensemble of events. For probabilistic seismic hazard analyses (PSHAs), the PBR overturning fragility is multiplied by the ground-motion occurrence rate from a vector-valued probabilistic seismic hazard analysis (VPSHA), yielding the marginal overturning rate for each ground-motion bin. Summing the marginal rates over all ground-motion bins produces the total overturning rate. For time-independent Poisson-based PSHA estimates, the probability of block failure can be easily calculated as a function of exposure time. This latter method is used to test VPSHA estimates similar to the 2002 U.S. Geological Survey (USGS) National Seismic Hazard Maps via PBR residence times. PBR overturning fragilities are estimated at sites in southern California near the San Andreas fault, between the San Jacinto and Elsinore faults, and near the White Wolf fault. The resulting failure probabilities for several of the PBRs are very high, suggesting that they are inconsistent with the 2002 USGS ground motions. An investigation of the hazard calculated with zero aleatory variability in the ground-motion prediction equations (GMPEs) suggests that the median ground motions or the earthquake rupture rates are too high at certain PBR sites.