Objective Estimation of Spatially Variable Parameters of Epidemic Type Aftershock Sequence Model: Application to California

Abstract

The ETAS model is widely employed to model the spatio-temporal 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 ANSS catalog that occurred within the time period 1981-2015 in a spatial polygon around California. The results indicate a 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.

References in corpus (20)

• Power-law distributions in empirical data
• Aftershock identification
• Sub-critical and Super-critical Regimes in Epidemic Models of Earthquake Aftershocks
• Importance of small earthquakes for stress transfers and earthquake triggering
• Foreshocks Explained by Cascades of Triggered Seismicity
• Is Earthquake Triggering Driven by Small Earthquakes?
• Mainshocks are aftershocks of conditional foreshocks: How do foreshock statistical properties emerge from aftershock laws
• Diffusion of Earthquake Aftershock Epicenters, Omori's Law and Generalized Continuous-Time Random Walk Models
• Bath's law Derived from the Gutenberg-Richter law and from Aftershock Properties
• Apparent Clustering and Apparent Background Earthquakes Biased by Undetected Seismicity
• Constraints on the Size of the Smallest Triggering Earthquake from the ETAS Model, Baath's Law, and Observed Aftershock Sequences
• Magnitude-Dependent Omori Law: Empirical Study and Theory
• Power Law Distributions of Offspring and Generation Numbers in Branching Models of Earthquake Triggering
• Nonstationary ETAS models for nonstandard earthquakes
• Anomalous Power Law Distribution of Total Lifetimes of Branching Processes Relevant to Earthquakes
• Systematic Assessment of the Static Stress-Triggering Hypothesis using Inter-earthquake Time Statistics
• Segmentation of Fault Networks Determined from Spatial Clustering of Earthquakes
• The Barycentric Fixed Mass Method for Multifractal Analysis
• Automatic reconstruction of fault networks from seismicity catalogs including location uncertainty
• Persistence and Quiescence of Seismicity on Fault Systems

Cited by in corpus (9)

• The Effect of Declustering on the Size Distribution of Mainshocks
• A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications
• Embracing Data Incompleteness for Better Earthquake Forecasting
• Is seismicity operating at a critical point?
• Forecasting the rates of future aftershocks of all generations is essential to develop better earthquake forecast models
• Magnitude Of Earthquakes Controls The Size Distribution Of Their Triggered Events
• Question-driven ensembles of flexible ETAS models
• Topological properties of epidemic aftershock processes
• Revisiting Seismicity Criticality: A New Framework for Bias Correction of Statistical Seismology Model Calibrations