Earthquake statistics at Parkfield: 1. Stationarity of b values

Abstract

In this paper (paper 1), we quantitatively show that the heterogeneous pattern of b values (of the Gutenberg‐Richter relation) in the Parkfield segment of the San Andreas fault is to a high degree stationary for the past 35 years. This prepares the grounds for paper 2, where we test the hypothesis that our model of spatially varying b values forecasts future seismicity more accurately than the approach in which one assumes a constant b value equal to the average regional value. The method we develop to measure stationarity in the presence of spatial heterogeneity consists of the following steps: (1) Determine the optimal dimensions of the sampling volume by mapping b values with a wide range of radii and selecting the largest radius that gives the most detailed resolution of the b value heterogeneity. Along the selected fault segment, the high data density permits the definition of the dominant dimensions of the seismotectonic fabric, which is about 8–10 km. (2) Map the difference in b value between two periods, selecting numerous possible catalog divisions. (3) Identify significant changes of b values by the Utsu test (Utsu, 1992). Along the studied fault segment of 110 km length, only one patch of radius 5 km showed a significant increase in b, from below average to above, as a function of time. This change in b initiates around 1993 and thus correlates in space and time with a well‐documented episode of creep at depth. Using the derived spatial variable b value distributions, we find that the highest probability for earthquakes with magnitude M ≥ 6 is in the Middle Mountain asperity, where the 1966 Parkfield earthquake nucleated and where all M ≥ 4.5 events in the data set occurred. In contrast, if only the regional average b value of 0.92 is used to predict future seismicity, the creeping segment north of Parkfield should produce major earthquakes most frequently, a conclusion that contradicts the observations.