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ETAS-positive: An Epidemic-Type Aftershock Model That Is Insensitive to Catalog Incompleteness

Description: 

Earthquake catalogs provide incomplete records of the earthquakes that occur, due to saturation of the network during periods of high activity. Incompleteness typically manifests as an early-time plateau in the aftershock rate, during which the rate exceeds the maximum detection rate of the seismic network. This complicates the generation and testing of aftershock forecasts, which need to consider all of the earthquakes that occur, not just those that make it into the catalog. Traditional attempts to recover unbiased statistics involve modeling the time-dependent completeness magnitude, but such models are non-unique and introduce their own biases and uncertainty.

In previous work, I demonstrated how to set up the estimation of common seismicity parameters in a way that minimizes sensitivity to incomplete data. Using the ‘positive’ statistics approach, parameters are estimated within nominally complete intervals, defined by pairs of earthquakes where the second is larger than the first. The first earthquake in the pair sets a reference magnitude above which subsequent earthquakes are likely to be detected, and a small positive magnitude adjustment ensure arbitrarily high detection probability. This definition makes no reference to an absolute magnitude of completeness. I previously applied this method to the estimation of the a and b-value of the Gutenberg-Richter distribution; here I extend the approach to the epidemic-type aftershock sequence (ETAS) model. I define pairs following the same scheme used for a-positive, where every earthquake defines the start of a ‘complete’ interval terminated by the next larger earthquake. In situations where there is no next larger earthquake, the open interval is used. The ETAS+ likelihood is then maximized only over these complete intervals.

Applying ETAS+ to global aftershock sequences reveals little evidence for an early-time plateau in rate, with an Omori c-value of 60 seconds following magnitude 6.5 and larger mainshocks. This is coincident with the times of the earliest cataloged aftershocks.

Session: New Insights into the Development, Testing and Communication of Seismicity Forecasts [Poster Session]

Type: Poster

Date: 5/2/2024

Presentation Time: 08:00 AM (local time)

Presenting Author: Nicholas

Student Presenter: No

Invited Presentation: 

Authors