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1. Reply to “Comment on ‘Two Foreshock Sequences Post Gulia and Wiemer (2019)’ by Kelian Dascher-Cousineau, Thorne Lay, and Emily E. Brodsky” by Laura Gulia and Stefan Wiemer

   https://doi.org/10.1785/0220210059  

   Dascher-Cousineau, Kelian ; Lay, Thorne ; Brodsky, Emily E. ( July 2021 , Seismological Research Letters)

   Abstract Gulia and Wiemer (2019; hereafter, GW2019) proposed a near-real-time monitoring system to discriminate between foreshocks and aftershocks. Our analysis (Dascher-Cousineau et al., 2020; hereinater, DC2020) tested the sensitivity of the proposed Foreshock Traffic-Light System output to parameter choices left to expert judgment for the 2019 Ridgecrest Mw 7.1 and 2020 Puerto Rico Mw 6.4 earthquake sequences. In the accompanying comment, Gulia and Wiemer (2021) suggest that at least six different methodological deviations lead to different pseudoprospective warning levels, particularly for the Ridgecrest aftershock sequence which they had separately evaluated. Here, we show that for four of the six claimed deviations, we conformed to the criteria outlined in GW2019. Two true deviations from the defined procedure are clarified and justified here. We conclude as we did originally, by emphasizing the influence of expert judgment on the outcome in the analysis.
2. A deep Gaussian process model for seismicity background rates

   https://doi.org/10.1093/gji/ggad074  

   Muir, Jack B. ; Ross, Zachary E. ( February 2023 , Geophysical Journal International)

   The spatio-temporal properties of seismicity give us incisive insight into the stress state evolution and fault structures of the crust. Empirical models based on self-exciting point processes continue to provide an important tool for analysing seismicity, given the epistemic uncertainty associated with physical models. In particular, the epidemic-type aftershock sequence (ETAS) model acts as a reference model for studying seismicity catalogues. The traditional ETAS model uses simple parametric definitions for the background rate of triggering-independent seismicity. This reduces the effectiveness of the basic ETAS model in modelling the temporally complex seismicity patterns seen in seismic swarms that are dominated by aseismic tectonic processes such as fluid injection rather than aftershock triggering. In order to robustly capture time-varying seismicity rates, we introduce a deep Gaussian process (GP) formulation for the background rate as an extension to ETAS. GPs are a robust non-parametric model for function spaces with covariance structure. By conditioning the length-scale structure of a GP with another GP, we have a deep-GP: a probabilistic, hierarchical model that automatically tunes its structure to match data constraints. We show how the deep-GP-ETAS model can be efficiently sampled by making use of a Metropolis-within-Gibbs scheme, taking advantage of the branching processmore »formulation of ETAS and a stochastic partial differential equation (SPDE) approximation for Matérn GPs. We illustrate our method using synthetic examples, and show that the deep-GP-ETAS model successfully captures multiscale temporal behaviour in the background forcing rate of seismicity. We then apply the results to two real-data catalogues: the Ridgecrest, CA 2019 July 5 Mw 7.1 event catalogue, showing that deep-GP-ETAS can successfully characterize a classical aftershock sequence; and the 2016–2019 Cahuilla, CA earthquake swarm, which shows two distinct phases of aseismic forcing concordant with a fluid injection-driven initial sequence, arrest of the fluid along a physical barrier and release following the largest Mw 4.4 event of the sequence.

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3. Rupture Process of the 2019 Ridgecrest, California Mw 6.4 Foreshock and Mw 7.1 Earthquake Constrained by Seismic and Geodetic Data

   https://doi.org/10.1785/0120200108  

   Wang, Kang ; Dreger, Douglas S. ; Tinti, Elisa ; Bürgmann, Roland ; Taira, Taka’aki ( July 2020 , Bulletin of the Seismological Society of America)

   ABSTRACT The 2019 Ridgecrest earthquake sequence culminated in the largest seismic event in California since the 1999 Mw 7.1 Hector Mine earthquake. Here, we combine geodetic and seismic data to study the rupture process of both the 4 July Mw 6.4 foreshock and the 6 July Mw 7.1 mainshock. The results show that the Mw 6.4 foreshock rupture started on a northwest-striking right-lateral fault, and then continued on a southwest-striking fault with mainly left-lateral slip. Although most moment release during the Mw 6.4 foreshock was along the southwest-striking fault, slip on the northwest-striking fault seems to have played a more important role in triggering the Mw 7.1 mainshock that happened ∼34  hr later. Rupture of the Mw 7.1 mainshock was characterized by dominantly right-lateral slip on a series of overall northwest-striking fault strands, including the one that had already been activated during the nucleation of the Mw 6.4 foreshock. The maximum slip of the 2019 Ridgecrest earthquake was ∼5  m, located at a depth range of 3–8 km near the Mw 7.1 epicenter, corresponding to a shallow slip deficit of ∼20%–30%. Both the foreshock and mainshock had a relatively low-rupture velocity of ∼2  km/s, which is possibly related to the geometric complexity and immaturity of the eastern California shear zone faults. The 2019more »Ridgecrest earthquake produced significant stress perturbations on nearby fault networks, especially along the Garlock fault segment immediately southwest of the 2019 Ridgecrest rupture, in which the coulomb stress increase was up to ∼0.5  MPa. Despite the good coverage of both geodetic and seismic observations, published coseismic slip models of the 2019 Ridgecrest earthquake sequence show large variations, which highlight the uncertainty of routinely performed earthquake rupture inversions and their interpretation for underlying rupture processes.« less
4. Characterization of Swarm and Mainshock–Aftershock Behavior in Puerto Rico

   https://doi.org/10.1785/0220210329  

   Ventura-Valentín, Wilnelly ; Brudzinski, Michael R. ( February 2022 , Seismological Research Letters)

   Abstract The recent Indios, Puerto Rico earthquake sequence has drawn attention, as the increased seismicity rate in this area was unprecedented. The sequence began on 28 December 2019, caused a 6.4 magnitude earthquake on 7 January 2020, and remained active over a year later. This sequence fits the nominal definition of an earthquake swarm in that it had an abrupt onset, a sustained high rate of seismicity without a clear triggering mainshock or evidence for Omori decay, and a lack of adherence to Bath’s law. However, the sequence also had several prominent mainshock–aftershock (MS–AS) sequences embedded within it. We applied three-station waveform cross correlation to the early part of this sequence using the Puerto Rico Seismic Network (PRSN) catalog as templates, which confirmed the mixture of swarm and MS–AS patterns. In an effort to place this intriguing sequence in the context of the previous seismicity in Puerto Rico, we investigated the existence of swarms and MS–AS sequences recorded by the PRSN since 1987 by identifying sequences with increased seismicity rate when compared to the background rate. About 59 sequences were manually verified and characterized into swarms or MS–AS. We found that 58% of the sequences follow traditional swarm patterns andmore »14% adhere to traditional MS–AS behavior, whereas 29% of the sequences have a mixture of both swarm and MS–AS behaviors. These findings suggest that it is not unusual for the Indios sequence to have a mixture of both the characteristics. In addition, the detection of many swarms distributed over a broad area of the subduction interface indicates stress heterogeneity and low-coupling consistent with prior studies indicating that the potential for a magnitude ∼8 megathrust earthquake along the Puerto Rico trench is unlikely.« less
5. Cross Validation of Stress Drop Estimates and Interpretations for the 2011 Prague, OK, Earthquake Sequence Using Multiple Methods

   https://doi.org/10.1029/2020JB020888  

   Pennington, Colin N. ; Chen, Xiaowei ; Abercrombie, Rachel E. ; Wu, Qimin ( March 2021 , Journal of Geophysical Research: Solid Earth)

   We compare source parameter estimates for earthquakes in the 2011 Prague Mw 5.7, Oklahoma, sequence to investigate random uncertainty and systematic bias, and resolve reliable relative variations in stress drop. Source parameters provide insight into the earthquake rupture processes but large variations between studies occur. The Prague earthquake sequence is a prime example of this, with different studies reaching contrasting interpretations of the effects of injection on source parameters. We examine the Prague earthquake sequence using a single coherent catalog for all the events detected by the Oklahoma Geological Survey (OGS) and McMahon et al. (2017). We use three principal approaches to estimate stress drop in order to understand the biases of each: a spectral decomposition method based on stacking, individual event spectral modeling, and a spectral ratio method based on highly correlated events. We also compare our results with previous studies for the Prague sequences aftershocks, as well as past results for the Mw 4.8 foreshock and Mw 4.8 aftershock and Mw 5.7 mainshock. The absolute values of stress drop vary significantly between methods, but the relative patterns remain consistent, except when low quality or low bandwidth data are included. The consistent relative patterns reveal that the stress drops ofmore »aftershocks are dependent on the fault orientation and the proximity of the events to the mainshocks slip. These results indicate that fault structure as well as past events play an important role in stress drop patterns.

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