A-positive: How to get unbiased rates out of real earthquake catalogs without knowing the magnitude of completeness

Nicholas J. van der Elst, & Morgan T. Page

Submitted September 10, 2023, SCEC Contribution #12778, 2023 SCEC Annual Meeting Poster #158

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. The time evolution of rate may even provide some predictive 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 we 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. We define an estimate for the earthquake rate, ‘a-positive,’ that is based on interevent times between each earthquake and the next earthquake larger than itself. We show how to use this approach to generate a non-parametric estimate of the earthquake rate and magnitude frequency distribution. 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.

van der Elst, N. J., & Page, M. T. (2023, 09). A-positive: How to get unbiased rates out of real earthquake catalogs without knowing the magnitude of completeness. Poster Presentation at 2023 SCEC Annual Meeting.

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