b-Values as a Proxy for Stress - Inferences for Dynamic Modeling of the 2004 Parkfield Earthquake

Previous studies of the frequency-magnitude distribution of earthquakes in different tectonic settings have shown that the b-value in the frequency-magnitude distribution can vary significantly in the range 0.4-2.0 (Wiemer and Wyss, 2002). In particular, active faults are characterized by a high spatial variability of the b- value (e.g., Parkfield, San Jacinto-Elsinore, Kanto-Tokai, North Anatolian Fault, Mexican subduction zone). Furthermore, the regions on active faults that exhibit anomalously low b-values seem to correlate very well with asperities (regions that are strongly coupled, i.e., locked, and which generate large amplitudes of slip co- seismically). Thus, it has been hypothesized that fault asperities may be mapped by maxima in local earthquake probability, which in turn can be computed from the a- and b-values of the frequency-magnitude distribution. One possible explanation for the strong correlation between b-values and asperities is that patches of the faults that are weakly coupled (low level of friction) cannot build up stress and thus slip in frequent small earthquakes (high b-value), whereas regions that are strongly coupled (high level of friction) can remain locked under larger stresses, and slip only in more infrequent large earthquakes (low b-value). Further support to the hypothesis that b-values contain information on the state of stress of the crust comes from the recent observation that normal faulting earthquakes (which are expected to occur under the lowest stress levels) present the highest b-values, whereas strike-slip earthquakes have intermediate b-values, and thrust earthquakes (expected to occur under the highest stresses) present the lowest b-values. In view of the strong correlations between b-values and state of stress across different stress regimes, one question arises: "Can b- values actually be used to predict the state of stress of the crust in a quantitative way?" In order to answer this question, we will study the 2004 Parkfield, California, earthquake. The Parkfield region has been extensively studied in terms of b-values, and the 2004 earthquake generated a seismic dataset of great quality it is thus the ideal opportunity to study a possible quantitative relation between b-values and stress. We will model 2004 Parkfield earthquake based on a stress condition that is a direct function of the b-values, we will then let the earthquake propagate dynamically through the stress field established by the b-values and finally check whether the waveforms thus produced agree with the observed ground-motion.