ALM: An Asperity-based Likelihood Model for California

Abstract

In most earthquake hazard models, the b -value of the Gutenberg-Richter law plays a central role in forecasting future seismicity based on the observed history. The cumulative earthquake-size distribution is commonly described by a power law: log10( N ) = a - bM , where N is the cumulative number of earthquakes of magnitude M or greater, a is the earthquake productivity of a volume, and b is the relative size distribution (Gutenberg and Richter 1944; Ishimoto and Iida 1939). The slope of this power law, the b -value, is a critical parameter in seismology that describes the size distribution of events. A high b -value indicates a relatively larger proportion of small events, and vice versa. In earthquake forecasting projects such as the source-related probabilistic seismic hazard assessment (PSHA), an underlying fundamental question is: What do the (numerous) smaller earthquakes tell us about the (infrequent) larger ones? Embedded into this question is also the question of stationarity: Can one trust recent small earthquakes to convey accurate information about infrequent large ones? It is these questions of scaling and stationarity that our model fundamentally addresses. In PSHA projects, the b -value is either chosen as a regional constant or varies spatially between local zones. However, there is currently no obvious scientific basis for choosing either of these approaches. The model we propose, the Asperity-based Likelihood Model (ALM), assumes that the earthquake-size distribution, and specifically the b -value of recent micro-earthquakes, is the most important information for forecasting future events of M 5+. Below we first briefly review the evidence that leads us to propose the ALM model, and then we describe the actual steps involved in deriving the model parameters. Most of the evidence in support of ALM stems from observational data from a variety of tectonic regimes as well …