California Earthquake Rupture Models

We present a stochastic earthquake source model for intermediate-to long-term forecasts. The model is based on fundamental observations: the frequency-magnitude distribution, slip rates on major faults, long-term strain rates, and source parameter values of instrumentally-recorded and historic earthquakes. The basic building blocks of the model are two pairs of probability density maps. The first pair consists of smoothed seismicity and weighted focal mechanisms based on observed earthquakes. The second pair contains the same type of information for faults. We construct from the model a “stochastic event set”, i.e. a large set of simulated earthquakes that are relevant for seismic hazard calculations and model testing. Their complete descriptions are determined in the following order: magnitude, epicenter, moment tensor, length, displacement, and down-dip width. Our approach assures by construction that the simulated magnitudes are consistent with the observed frequency-magnitude distribution. We employ a magnitude-dependent weighting procedure that tends to place the largest simulated earthquakes near major faults with consistent focal mechanisms. Nevertheless, our stochastic model allows for surprises, such as large off-fault earthquakes, which comply with the observation that several recent destructive earthquakes occurred on previously unknown fault structures. We apply the model to California to illustrate its features. A common drawback of smoothed seismicity methods is that valuable knowledge of fault structures and deformation rates have no contribution to the estimate of future earthquake probabilities In currently quiet regions characterized by ample evidence of large historic earthquakes in the past few thousand years, geological data provide a vital contribution to the calculation of earthquake potentials. We therefore present a method to construct a stochastic earthquake source model that benefits from applying the kernel-smoothing method to earthquakes and mapped fault structures with associated deformation rates. Building on the kernel-smoothing concept, we objectively combine geologically estimated data with seismological data. The concept is modular in that one could similarly introduce knowledge on deformation rates from recent GPS data or inferred strain rates. In this context, we use the stochastic earthquake source model to simulate a set of hazard-relevant earthquakes based on a four step procedure: (1) the starting point is the frequency-magnitude distribution, therefore our model solves the bulge problem by construction; (2) epicentral locations are assigned at random from a magnitude-dependent location probability density map based on past earthquakes and strain rate; (3) the moment tensor is then estimated from a weighted combination of nearby actual earthquakes and nearby fault moment tensor rates; (4) the rupture length, displacement, and width are assigned using a magnitude scaling relationship. The procedure ensures that properties of larger simulated earthquakes are stochastically more dependent on the fault information, and the properties of smaller simulated earthquakes are more likely to be estimated from past seismicity. The resulting set of simulated earthquakes can be used for seismic hazard calculations and other research that requires a large set of big earthquakes. The model requires two types of input data for a chosen region: a well defined earthquake catalog that includes the location, magnitude, and focal mechanism of past earthquakes and a fault database that specifies the spatial three-dimensional geometry of active faults and provides their average long-term deformation. The basic building blocks of our model are two pairs of probability density maps. The first pair consists of smoothed seismicity and observed focal mechanisms based on the earthquake catalog. We use the kernel smoothing method to smooth seismicity, i.e. to transform discrete earthquake epicenters into spatially continuous probability distributions. The focal mechanism density is estimated by distance-weighted combinations of observed moment tensors. The second pair of maps contains the same type of information for mapped faults. To apply the same smoothing methods to faults, we convert fault sections to moment rate point sources with focal mechanisms inferred from the fault section geometry For a complete description of each moment rate tensor, we estimate the strike and dip angle from the corresponding fault section geometry and used the rake angle given in the fault database. In this way we simplify all faults to a series of point sources. By collecting these, we have a “catalog” of moment rate point sources that is purely based on fault geometry and slip rates. In other words, we transform the fault network representation to something like an earthquake catalog.