Adaptive Smoothing of Seismicity in Time, Space, and Magnitude for Time-Dependent Earthquake Forecasts for California

Abstract

We present new methods for short-term earthquake forecasting that employ space, time, and magnitude kernels to smooth seismicity. These methods are purely statistical and rely on very few assumptions about seismicity. In particular, we do not use Omori-Utsu law, and only one of our two new models assumes a Gutenberg-Richter law to model the magnitude distribution; the second model estimates the magnitude distribution nonparametrically with kernels. We employ adaptive kernels of variable bandwidths to estimate seismicity in space, time, and magnitude bins. To project rates over short time scales into the future, we simply assume persistence, that is, a constant rate over short time windows. The resulting forecasts from the two new kernel models are compared with those of the epidemic-type aftershock sequence (ETAS) model generated by . Although our new methods are simpler and require fewer parameters than ETAS, the obtained probability gains are surprisingly close. Nonetheless, ETAS performs significantly better in most comparisons, and the kernel model with a Gutenberg-Richter law attains larger gains than the kernel model that nonparametrically estimates the magnitude distribution. Finally, we show that combining ETAS and kernel model forecasts, by simply averaging the expected rate in each bin, can provide greater predictive skill than ETAS or the kernel models can achieve individually.

A Spatiotemporal Clustering Model for the Third Uniform California Earthquake Rupture Forecast (UCERF3‐ETAS): Toward an Operational Earthquake Forecast

“…In lieu of a detailed review of that model here, Table 1 indicates which types of constraints are embodied in STEP, together with those utilized in the UCERF3 epidemic-type aftershock sequence (ETAS) model presented here. Many other candidate OEF models have also been developed and tested since the introduction of STEP (e.g., Werner et al, 2011;Woessner et al, 2011;Nanjo et al, 2012, and references therein; Segou et al, 2013;Zechar et al, 2013, and references therein;Helmstetter and Werner 2014;Marzocchi et al, 2014;Gerstenberger et al, 2014). What makes UCERF3-ETAS unique to all of these is a more explicit and complete incorporation of geologic fault information, as well as the inclusion of elastic rebound (in which rupture probabilities are thought to drop on a fault after experiencing a large event and to grow back with time as tectonic stresses re-accumulate).…”

“…As mentioned, the model that specifies the longterm rate of smaller earthquakes in UCERF3-ETAS has demonstrated skill in the formal prospective tests conducted by the Collaboratory for the Study of Earthquake Predictability (CSEP, Helmstetter et al, 2007;Zechar et al, 2013;Helmstetter and Werner, 2014;Rhoades et al, 2014). However, we had to change these rates near several faults (via the ApplyGridSeisCorr parameter; Fig.…”

Forecasting the Full Distribution of Earthquake Numbers Is Fair, Robust, and Better

“…Note that LL and N respectively correspond to the expected maximum log-likelihood score obtained upon the calibration of the ETAS model using the EM algorithm and to the number of earthquakes used for the calibration of the ETAS model. 4. We then repeat the Steps 1-3 1000 times with different realisations of q Voronoi centres selected randomly from the list of the earthquakes and store the estimate parameters and BIC.…”

Intermediate‐term forecasting of aftershocks from an early aftershock sequence: Bayesian and ensemble forecasting approaches

“…In addition to the forecasting from each magnitude frequency model, we also examine the performance of an ensemble forecasting that combines the two forecasts from these models. Ensemble forecasting has been implemented in some studies for probabilistic earthquake forecasting [e.g., Gerstenberger et al, ; Marzocchi et al, ; Helmstetter and Werner, ; Rhoades et al, ]. Akaike [] suggested that natural weighting of each forecast is proportional to the factor exp[ln L ( X learn ) − p ], where L ( X learn ) and p are the likelihood function and the number of model parameters, respectively.…”