Abstract
We present a non-stationary epidemic-type aftershock sequence (ETAS) model in which the usual assumption of stationary background rate is relaxed. Such a model could be used for modeling seismic sequences affected by aseismic transients such as fluid/magma intrusion, slow slip earthquakes (SSEs), etc. The non-stationary background rate is expressed as a linear combination of B-splines, and a method is proposed that allows for simultaneous estimation of background rate as well as other ETAS model parameters. We also present an extension to this non-stationary ETAS model where an adaptive roughness penalty function is used and consequently provides better estimates of rapidly varying background rate functions. The performance of the proposed methods is demonstrated on synthetic catalogs and an application to detect earthquake swarms (possibly associated with SSEs) in Hikurangi margin (North Island, New Zealand) is presented.
Highlights
Earthquakes are generated by a complex system—the Earth
To see if slow slip earthquakes are associated with increased seismicity that manifests as peaks in the estimated background activity, we look at continuous global positioning system (cGPS) data recorded at the nearby cGPS stations LEYL, WAHU, MAHI, MAKO and ANAU
(b) L-curve method for choosing optimal smoothness parameter. This procedure allows for simultaneous estimation of both background rate function and the other epidemic-type aftershock sequence (ETAS) model parameters
Summary
Earthquakes are generated by a complex system—the Earth. Lithospheric plates gliding past one another causes stress buildup in the crustal rocks which is released in short, sudden bursts causing earthquakes. . ., M} corresponding to background activity, and other model parameters = {K , α, c, p} related to aftershock activity Estimating these unknowns and plugging them in the above expression would give us the non-stationary ETAS model that best describes the observed earthquake sequence. In situations where the background rate function has significant non-uniform roughness over its time domain, use of a global smoothness parameter as indicated in the proposed method could be insufficient to model the earthquake sequence effectively. For all the non-stationary ETAS models tested in this study, we employ 100 linear B-splines to represent background rate and a roughness penalty on the first-order derivatives (m = 1). We estimated optimal τ by computing L-curve only for
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