Towards a Physics Based Epidemic Type Aftershock Sequence Model

Abstract

Recent years have seen a growing emphasis on developing models for earthquake forecasting and quantifying their predictive skills in order to augment our understanding of the processes leading to seismogenesis. Two extensively used models to describe the spatial and temporal distribution of earthquakes are Rate and State and Epidemic Type Aftershock Sequence model. They are respectively based on the static stress triggering hypothesis and empirically observed statistical laws (namely Omori law, Gutenberg Richter law and Productivity law). Both models have been successful to some extent in describing many empirical observations related to seismicity as well as in forecasting the rate of the future earthquakes. However, several key issues related to both remain unaddressed. For instance, (i) impact of secondary stress changes caused by small earthquakes is completely ignored while assessing the static stress triggering hypothesis as well as in forecasting the rate of future earthquakes based on Coulomb stress change from the past events; (ii) often simplistic assumptions are made about the orientation of the fault planes that cause static deformations as well as the recipient fault planes of these deformations; (iii) influence of uncertainties in the data are rarely considered while computing the static stress changes; (iv) parameters of the ETAS model are often assumed to be spatially homogeneous; (v) very few attempts are made to understand the physical origin of the ETAS parameters, and (vi) possibility of a self-consistent hybrid of the two models remains unexplored.We attempt to address these issues in a systematic manner with attention on statistical rigor, realistic synthetic tests and generalized data-driven approaches. We first conduct a rigorous test of the static stress triggering hypothesis with the aim to tackle the first three points outlined above. In particular, we investigate the correlation between the time variation of the seismicity rate and the sign (and amplitude) of Coulomb stress changes. We also quantify the Coulomb Index (CI), the fraction of events that received net positive Coulomb stress changes compared to the total number of events. We find compelling evidence supporting the static triggering (with stronger evidence after resolving the focal plane ambiguity) above significantly small (about 10 Pa) but consistently observed stress thresholds. Furthermore, we find evidence for the static triggering hypothesis to be robust with respect to the choice of the friction coefficient, Skempton’s coefficient, and magnitude threshold. However, our analysis suffers from the imprecise assumption that all earthquakes following a source event are its direct aftershocks. To ameliorate the effects of the preceding assumption on our analysis, we infer the full triggering genealogy of the ANSS catalog of the Californian earthquakes by defining and implementing an ETAS model with space varying parameters using the Expectation Maximization (EM) algorithm and spatial Voronoi tessellation ensembles. We use the penalized Log-Likelihood to rank the inverted models and select the best ones to eventually compute an ensemble model at any location. Prior to analyzing the results obtained from the application of the proposed method to earthquakes in and around California, we verified the reliability of this method using realistic synthetic catalogs. Results obtained on this earthquake catalog suggest that ETAS (productivity and background) parameters are far from uniform in the study region. We also find that the efficiency of earthquakes to trigger future ones (quantified by the branching ratio) positively correlates with the local surface heat flow measurements. In contrast, the rate of earthquakes triggered by far-field tectonic loading (or background seismicity rate) shows no such correlation, suggesting the relevance of dynamic triggering possibly through fluid-induced activation. Furthermore, we find the branching ratio and background seismicity rate to be uncorrelated with hypocentral depths, indicating that the seismic coupling remains invariant of hypocentral depths in the study region. Additionally, we find pieces of evidence suggesting that the earthquake triggering is mostly dominated by small earthquakes, convincing us further that the static stress change studies should not only focus on the Coulomb stress changes caused by specific moderate to large earthquakes but should also account for the secondary static stress changes caused by smaller events. We then quantify the forecasting skill of the ETAS model with spatially varying parameters by comparing the former to the forecasting skills of other smoothed seismicity models. Our results indicate that by taking account of both background and aftershock components of the seismicity rate, our model (ETAS-SV2) easily outperforms models that are based on just smoothing the declustered seismicity. Furthermore, we also find that when forecasting the rate of future M4.95 earthquakes, the smoothed seismicity model based only on a catalog that has been stochastically declustered using the ETAS model tends to outperform smoothed seismicity models based on declustered catalogs obtained from two widely used declustering methods. We then use the genealogy tree of earthquakes obtained from the spatially heterogeneous ETAS model to quantify the compatibility of the latter with the static stress triggering hypothesis. Using this tree, we obtain conditional Coulomb Indices (CI values conditioned on the probability of being a direct aftershock) for different source models available for the Landers earthquake. These conditional CI values are then compared to previously defined unconditional CI values, which serve as the null hypothesis. We find statistically significant enrichment in the evidence supporting the static triggering hypothesis when using the genealogy tree obtained from the improved ETAS model pointing towards at least partial compatibility of the former with the static stress triggering hypothesis. Finally, we estimate time-varying ETAS parameters in the Salton Sea geothermal area and Geysers geothermal field. Our observations suggest that the main fault segment in the Salton Sea geothermal area is more favorably oriented to the underlying background stress field than its remaining three subsidiary conjugate fault segments. Our results also allow us to evidence the influence of fluid injection (and/or extraction) on the background seismicity rate in the regions located around the Salton Sea geothermal facility and the Geysers geothermal facility. While in the case of the former we are not able to deduce if the fluid injection or extraction drives the human-induced seismic activity, our results clearly indicate that the fluid injection rate seems to dominate the seismicity triggering in the case of the latter. --> Recent years have seen a growing emphasis on developing models for earthquake forecastingand quantifying their predictive skills in order to augment our understandingof the processes leading to seismogenesis. Two extensively used models to describethe spatial and temporal distribution of earthquakes are Rate and State and Epidemic Type AftershockSequence model. They are respectively based on the static stress triggering hypothesisand empirically observed statistical laws (namely Omori law, Gutenberg Richter law and Productivitylaw). Both models have been successful to some extent in describing many empiricalobservations related to seismicity as well as in forecasting the rate of the future earthquakes.However, several key issues related to both remain unaddressed. For instance, (i) impact of secondarystress changes caused by small earthquakes is completely ignored while assessing thestatic stress triggering hypothesis as well as in forecasting the rate of future earthquakes basedon Coulomb stress change from the past events; (ii) often simplistic assumptions are made aboutthe orientation of the fault planes that cause static deformations as well as the recipient faultplanes of these deformations; (iii) influence of uncertainties in the data are rarely consideredwhile computing the static stress changes; (iv) parameters of the ETAS model are often assumedto be spatially homogeneous; (v) very few attempts are made to understand the physicalorigin of the ETAS parameters, and (vi) possibility of a self-consistent hybrid of the two modelsremains unexplored.We attempt to address these issues in a systematic manner with attentionon statistical rigor, realistic synthetic tests and generalized data-driven approaches.We first conduct a rigorous test of the static stress triggering hypothesis with the aim totackle the first three points outlined above. In particular, we investigate the correlation betweenthe time variation of the seismicity rate and the sign (and amplitude) of Coulomb stresschanges. We also quantify the Coulomb Index (CI), the fraction of events that received net positiveCoulomb stress changes compared to the total number of events. We find compelling evidencesupporting the static triggering (with stronger evidence after resolving the focal planeambiguity) above significantly small (about 10 Pa) but consistently observed stress thresholds.Furthermore, we find evidence for the static triggering hypothesis to be robust with respect tothe choice of the friction coefficient, Skempton’s coefficient, and magnitude threshold. However,our analysis suffers from the imprecise assumption that all earthquakes following a source eventare its direct aftershocks.To ameliorate the effects of the preceding assumption on our analysis, we infer the full triggeringgenealogy of the ANSS catalog of the Californian earthquakes by defining and implementingan ETAS model with space varying parameters using the Expectation Maximization (EM)algorithm and spatial Voronoi tessellation ensembles. We use the penalized Log-Likelihood torank the inverted models and select the best ones to eventually compute an ensemble model atany location. Prior to analyzing the results obtained from the application of the proposed methodto earthquakes in and around California, we verified the reliability of this method using realisticsynthetic catalogs. Results obtained on this earthquake catalog suggest that ETAS (productivityand background) parameters are far from uniform in the study region. We also find that theefficiency of earthquakes to trigger future ones (quantified by the branching ratio) positivelycorrelates with the local surface heat flow measurements. In contrast, the rate of earthquakestriggered by far-field tectonic loading (or background seismicity rate) shows no such correlation,suggesting the relevance of dynamic triggering possibly through fluid-induced activation.Furthermore, we find the branching ratio and background seismicity rate to be uncorrelatedwith hypocentral depths, indicating that the seismic coupling remains invariant of hypocentraldepths in the study region. Additionally, we find pieces of evidence suggesting that the earthquake triggering is mostly dominated by small earthquakes, convincing us further thatthe static stress change studies should not only focus on the Coulomb stress changes caused by specific moderate to large earthquakes but should also account for the secondary static stresschanges caused by smaller events.We then quantify the forecasting skill of the ETAS model with spatially varying parametersby comparing the former to the forecasting skills of other smoothed seismicity models. Ourresults indicate that by taking account of both background and aftershock components of theseismicity rate, our model (ETAS-SV2) easily outperforms models that are based on just smoothingthe declustered seismicity. Furthermore, we also find that when forecasting the rate of futureM4.95 earthquakes, the smoothed seismicity model based only on a catalog that has beenstochastically declustered using the ETAS model tends to outperform smoothed seismicity modelsbased on declustered catalogs obtained from two widely used declustering methods.We then use the genealogy tree of earthquakes obtained from the spatially heterogeneousETAS model to quantify the compatibility of the latter with the static stress triggering hypothesis.Using this tree, we obtain conditional Coulomb Indices (CI values conditioned on theprobability of being a direct aftershock) for different source models available for the Landersearthquake. These conditional CI values are then compared to previously defined unconditionalCI values, which serve as the null hypothesis. We find statistically significant enrichment in the evidencesupporting the static triggering hypothesis when using the genealogy tree obtained fromthe improved ETAS model pointing towards at least partial compatibility of the former with thestatic stress triggering hypothesis.Finally, we estimate time-varying ETAS parameters in the Salton Sea geothermal area andGeysers geothermal field. Our observations suggest that the main fault segment in the SaltonSea geothermal area is more favorably oriented to the underlying background stress field thanits remaining three subsidiary conjugate fault segments. Our results also allow us to evidencethe influence of fluid injection (and/or extraction) on the background seismicity rate in the regionslocated around the Salton Sea geothermal facility and the Geysers geothermal facility.While in the case of the former we are not able to deduce if the fluid injection or extractiondrives the human-induced seismic activity, our results clearly indicate that the fluid injectionrate seems to dominate the seismicity triggering in the case of the latter.