Search

A variety of nonparametric models have been proposed for estimating earthquake triggering. We investigate the ability of the model-independent stochastic declustering method developed by Marsan and Lengliné (2008) to estimate variable spatial triggering that can vary with direction, magnitude, and region. We develop an approach for local fault estimation and demonstrate forecasting methods that use the nonparametric estimates. Simulation studies are conducted to verify the effectiveness of the method, and the nonparametric estimates are applied to a California earthquake catalog. Model forecast performance is evaluated retrospectively by comparing our models with the long-term forecast of Helmstetter et al. (2007), using both deviance and Voronoi residuals. We show improved performance compared with Helmstetter et al. (2007) in various regions while using a full nonparametric estimation and forecasting approach.

Voronoi residuals, deviances, super-thinning, and some other residual analysis methods are applied to a selection of earthquake forecast models in the Collaboratory for the Study of Earthquake Predictability (CSEP). Unlike simple numerical summaries such as the N-test, L-test, or R-test, graphical residual methods are proposed which can be useful for comparing multiple models and for highlighting when and where a given model does not agree closely with the observed seismicity. For gridded forecasts, deviances seem ideally suited for model comparison, and Voronoi residuals seem preferable to simple grid-based residuals for assessing one model individually. For models outputting an estimated conditional rate at any particular space–time location, Voronoi residuals and super-thinning can be especially useful at identifying departures from the data.

Space–time Hawkes point process models for the conditional rate of earthquake occurrences traditionally make many parametric assumptions about the form of the triggering function for the rate of aftershocks following an earthquake. As an alternative, Marsan and Lengliné [Science 319 (2008) 1076–1079] developed a completely nonparametric method that provides an estimate of a homogeneous background rate for mainshocks, and a histogram estimate of the triggering function. At each step of the procedure the model estimates rely on computing the probability each earthquake is a mainshock or aftershock of a previous event. The focus of this paper is the improvement and assessment of Marsan and Lengliné’s method in the following ways: (a) the proposal of novel ways to incorporate a spatially inhomogeneous background rate; (b) adding error bars to the histogram estimates which quantify the sampling variability in the estimation of the underlying seismic process. A simulation study is designed to evaluate and validate the ability of our methods to recover the triggering function and spatially varying background rate. An application to earthquake data from the Tohoku District in Japan is discussed at the end, and the results are compared to a well-established parametric model of seismicity for this region.