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A-Positive: An Improved Estimator of the Earthquake Rate That Is Robust Against Catalog Incompleteness

Description: 

Earthquake rate and magnitude distribution are the fundamental quantities of statistical seismology. Long term rate models inform our hazard and building codes, and short-term models provide situational awareness during aftershock sequences. There is even hope that the temporal evolution of the rate may provide some information about larger earthquakes to come. Earthquake catalogs are at the core of these estimates, but catalogs are imperfect due to both sparse network coverage and to saturation of the network during periods of high activity. Traditional attempts to address incompleteness center on modeling the time-varying magnitude of completeness, but such models are non-unique and introduce additional uncertainty.

Here I present a method for estimating the earthquake rate that is insensitive to catalog incompleteness and does not depend on a completeness model. This method is rooted in the assumption that catalogs improve monotonically in time between any two earthquakes and that small earthquakes do not obscure larger ones. I define an estimate for the earthquake rate, ‘a-positive,’ that is based on interevent times between successive earthquakes where the second earthquake is larger than the first. I show how to use this approach to generate a non-parametric estimate of the earthquake rate and magnitude frequency distribution, as well as a parametric rate estimate using a modified definition of the Epidemic Type Aftershock Sequence model that considers only the time between successive earthquakes. When applied to aftershock data, the improved rate estimate finds essentially no evidence for a plateau in the early aftershock rate, even at the times of the earliest detected aftershocks in a sequence. The early time plateau modeled by the c-value in the modified Omori’s law is most likely a statistical feature of the earthquake catalog and is unlikely to encode anything about the aftershock nucleation process.

Session: New Methods and Models for More Informative Earthquake Forecasting

Type: Oral

Date: 4/19/2023

Presentation Time: 08:15 AM (local time)

Presenting Author: Nicholas van der Elst

Student Presenter: No

Invited Presentation: 

Authors