Rate‐Dependent Incompleteness of Earthquake Catalogs

Abstract

Important information about the earthquake generation process can be gained from instrumental earthquake catalogs, but this requires complete recordings to avoid biased results. The local completeness magnitude M c is known to depend on general conditions such as the seismographic network and the environmental noise, which generally limit the possibility of detecting small events. The detectability can be additionally reduced by an earthquake-induced increase of the noise level leading to shortterm variations of M c , which cannot be resolved by traditional methods relying on the analysis of the frequency-magnitude distribution. Based on simple assumptions, I propose a new method to estimate such temporal excursions of M c solely based on the estimation of the earthquake rate resulting in a high temporal resolution of M c . The approach is shown to be in agreement with the apparent decrease of the estimated Gutenberg-Richter b-value in high-activity phases of recorded data sets and the observed incompleteness periods after mainshocks. Furthermore, an algorithm to estimate temporal changes of M c is introduced and applied to empirical aftershock and swarm sequences from California and central Europe, indicating that observed b-value fluctuations are often related to rate-dependent incompleteness of the earthquake catalogs.Online Material: MATLAB code to compute rate-dependent completeness magnitude, and figures showing variation in the estimated M c values in equalized time scale.

Estimating ETAS: The effects of truncation, missing data, and model assumptions

“…The value of max( M c ( t )) strongly depends on the estimation method. Hainzl [] found for sample sizes of 10 a maximum of approximately M c = 4.5 for the Landers and Hector Mine sequences. Other studies found max ( M c ( t )) ≈ 4–4.5 with different methods [ Kagan , ; Helmstetter et al ., ].…”

Data completeness of the Kumamoto earthquake sequence in the JMA catalog and its influence on the estimation of the ETAS parameters

“…One observational approach is to use waveformbased earthquake detection methods (e.g., Enescu et al 2007Enescu et al , 2009Peng et al 2007;Marsan and Enescu 2012;Hainzl 2016). These methods found many aftershocks that are unrecorded in the catalog.…”

Statistical analysis of the 2012–2013 Torreperogil–Sabiote seismic series, Spain

“…The resulting µ-value shows some strong fluctuations which might suggest an episodic character of the aseismic forcing. Nevertheless some fluctuations could also be partially related to missing events in phases of activity (Hainzl 2016).…”

“…Detailed aftershock studies showed that the delay parameter c is very small, in the order of one to several minutes or even less (.e.g. Peng et al 2006;Enescu et al 2007), while larger estimations often result from incomplete recordings directly after the occurrence of larger earthquakes (Kagan 2004, Hainzl 2016. Note that for single aftershock decay according to the Omori-Utsu law, the probability density function of the interevent-times decays with an exponent of 2 − 1 p (see above).…”