Objective estimation of spatially variable parameters of epidemic type aftershock sequence model: Application to California

Abstract

The Epidemic Type Aftershock Sequence (ETAS) model is widely employed to model the spatiotemporal distribution of earthquakes, generally using spatially invariant parameters. We propose an efficient method for the estimation of spatially varying parameters, using the expectation maximization (EM) algorithm and spatial Voronoi tessellation ensembles. We use the Bayesian information criterion (BIC) to rank inverted models given their likelihood and complexity and select the best models to finally compute an ensemble model at any location. Using a synthetic catalog, we also check that the proposed method correctly inverts the known parameters. We apply the proposed method to earthquakes included in the Advanced National Seismic System catalog that occurred within the time period 1981–2015 in a spatial polygon around California. The results indicate significant spatial variation of the ETAS parameters. We find that the efficiency of earthquakes to trigger future ones (quantified by the branching ratio) positively correlates with surface heat flow. In contrast, the rate of earthquakes triggered by far‐field tectonic loading or background seismicity rate shows no such correlation, suggesting the relevance of triggering possibly through fluid‐induced activation. Furthermore, the branching ratio and background seismicity rate are found to be uncorrelated with hypocentral depths, indicating that the seismic coupling remains invariant of hypocentral depths in the study region. Additionally, triggering seems to be mostly dominated by small earthquakes. Consequently, the static stress change studies should not only focus on the Coulomb stress changes caused by specific moderate to large earthquakes but also account for the secondary static stress changes caused by smaller earthquakes.

Deconvolving the Fate of Carbon in Coastal Sediments

“…The algorithm developed by Nandan et al (2017) for the estimation of spatially variable parameters of an Epidemic-type aftershock sequence was modified and applied to the available TOC and 14 C data for the CMS by assuming a log-normal distribution of these parameters (Seiter et al, 2004). Previous studies have also assumed a log-normal distribution of TOC and other parameters (Diggle & Ribeiro, 2007;Gosheva et al, 2017;Nussbaum et al, 2014;Seiter et al, 2004).…”

“…Overall, there is a strong imperative to find effective methods that deconvolve the complex patterns in OC content and composition, and to provide a mechanistic understanding of the underlying processes responsible for this heterogeneity. In this study, we apply a clustering algorithm adapted from Nandan et al (2017) as a novel way of classifying swaths of ocean floor into distinct "carbon impact" regions. We then apply statistical analyses to assess the region-specific factors impacting the carbon dynamics.…”

Forecasting the Rates of Future Aftershocks of All Generations Is Essential to Develop Better Earthquake Forecast Models

“…Recently, we introduced an objective method to invert spatially variable parameters of the ETAS model (Nandan et al, ). We found that the three parameters K , a , and μ show substantial spatial variation, which could be explained by the spatial variation of the surface heat flow in the study region.…”

“…We found that the three parameters K , a , and μ show substantial spatial variation, which could be explained by the spatial variation of the surface heat flow in the study region. In Nandan et al (), however, we considered the parameters of the temporal (Omori) and spatial kernels to be spatially invariant for reasons of computational and mathematical simplicity. In the present work, we have extended our previous method to invert the spatial variation of the Omori parameters as well, while still assuming the parameters of the spatial kernel to be spatially invariant.…”

“…For an incorrect choice of M c for the training catalog, the scaling may lead to inappropriate forecasts. For the area under study, Nandan et al () found that the ANSS catalog is complete for M ≥ 2.95 during the years 1981 to 2016. This choice of M c = 2.95 is justified by estimating independent temporal and spatial variation of magnitudes of completeness in the study region.…”