Critical Invariant Galton-Watson Branching Process for Earthquake Occurrence

Ilya Zaliapin, Yevgeniy Kovchegov, & Yehuda Ben-Zion

Published September 11, 2022, SCEC Contribution #12499, 2022 SCEC Annual Meeting Poster #213 (PDF)

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We propose a new theoretical modeling framework for seismicity based on a recently introduced family of invariant Galton-Watson (IGW) stochastic branching processes. The IGW framework overcomes some well-recognized problems in existing approaches while preserving the main postulates of stochastic branching models. Informally, the IGW model is the only family that is invariant with respect to multiple operations that represent imprecise observations and estimations of parameters in real data. The IWG framework provides a convenient approximation to modeling observed data with branching processes similar to the Epidemic Type Aftershock Sequence (ETAS) model. The theory of IGW processes suggests explicit distributions for multiple clustering statistics, including magnitude-dependent and magnitude-independent offspring number, cluster size, and cluster combinatorial depth. The framework provides a one-parametric model that can fit observed clusters of all sizes (not only the largest ones), and it suggests new observed statistics based on the Horton-Strahler analysis of earthquake clusters. We show that the IGW model closely approximates the ETAS model, while allowing for a comprehensive theoretical analysis and more robust estimates of parameters. Analysis of seismicity in southern California demonstrates that the IGW model provides a very close fit to observed earthquake clusters, and that the estimated IWG parameters and derived statistics are robust with respect to the lower magnitude threshold used in the analysis. The proposed model facilitates analyses of additional quantities of seismicity based on self-similar tree attributes, and may be used to assess the proximity of seismicity to criticality.

Reference:
Kovchegov, Y., I. Zaliapin, and Y. Ben-Zion (2022) Invariant Galton-Watson Branching Process for Earthquake Occurrence. Geophysical Journal International, ggac204, doi:10.1093/gji/ggac204

Citation
Zaliapin, I., Kovchegov, Y., & Ben-Zion, Y. (2022, 09). Critical Invariant Galton-Watson Branching Process for Earthquake Occurrence. Poster Presentation at 2022 SCEC Annual Meeting.


Related Projects & Working Groups
Earthquake Forecasting and Predictability (EFP)