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Abstract Quantifying the size of earthquakes is a foundational task in seismology, and over the years several magnitude scales have been developed. Of these, only scales based on seismic moment or potency can properly characterize changes in event size without saturation. Here, we develop empirical potency–magnitude scaling relations for earthquakes in the western United States, allowing us to translate instrumental magnitude estimates into uniform measures of earthquake size. We use synthetic waveforms to validate the observed scaling relations and to provide additional insight into the differences between instrumental and physics-based magnitude scales. Each earthquake in our catalog is assigned a clustering designation distinguishing mainshocks from triggered seismicity, along with a potency-based magnitude estimate that is comparable to moment magnitude and that can be easily converted into other magnitude scales as needed. The developed catalog and associated scaling relations have broad applications for fundamental and applied studies of earthquake processes and hazards.
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Invariant Galton–Watson branching process for earthquake occurrence
SUMMARY We propose a theoretical modelling framework for earthquake occurrence and clustering based on a family of invariant Galton–Watson (IGW) stochastic branching processes. The IGW process is a rigorously defined approximation to imprecisely observed or incorrectly estimated earthquake clusters modelled by Galton–Watson branching processes, including the Epidemic Type Aftershock Sequence (ETAS) model. The theory of IGW processes yields explicit distributions for multiple cluster attributes, including magnitude-dependent and magnitude-independent offspring number, cluster size and cluster combinatorial depth. Analysis of the observed seismicity in southern California demonstrates that the IGW model provides a close fit to the observed earthquake clusters. The estimated IGW parameters and derived statistics are robust with respect to the catalogue lower cut-off magnitude. The proposed model facilitates analyses of multiple quantities of seismicity based on self-similar tree attributes, and may be used to assess the proximity of seismicity to criticality.
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- PAR ID:
- 10368736
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Geophysical Journal International
- Volume:
- 231
- Issue:
- 1
- ISSN:
- 0956-540X
- Format(s):
- Medium: X Size: p. 567-583
- Size(s):
- p. 567-583
- Sponsoring Org:
- National Science Foundation
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