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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 process 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.

 

The spatial geometry of seismicity encodes information about loading and failure processes, as well as properties of the underlying fault structure. Traditional approaches to characterizing geometrical attributes of seismicity rely on assumed locations and geometry of fault surfaces, particularly at depth, where resolution is overall quite poor. In this study, we develop an alternative approach to quantifying geometrical properties of seismicity using techniques from anisotropic point process theory. Our approach does not require prior knowledge about the underlying fault properties. We characterize the geometrical attributes of 32 distinct seismicity regions in California and introduce a simple four class classification scheme that covers the range of geometrical properties observed. Most of the regions classified as having localized seismicity are within northern California, while nearly all of the regions classified as having distributed seismicity are within southern California. In addition, we find that roughly 1 out of 4 regions exhibit orthogonal seismicity structures. The results of this study provide a foundation for future analyses of geometrical properties of seismicity and new observables to compare with numerical modelling studies.

 

Interacting magmatic sills at about 40-kilometer depth under the island of Hawai‘i feed into multiple different volcanoes. 

Earthquake swarms are ubiquitous in volcanic systems, being manifestations of underlying nontectonic processes such as magma intrusions or volatile fluid transport. The Long Valley caldera, California, is one such setting where episodic earthquake swarms and persistent uplift suggest the presence of active magmatism. We quantify the long-term spatial and temporal characteristics of seismicity in the region using cluster analysis on a 25-year high-resolution earthquake catalog derived using leading-edge deep-learning algorithms. Our results show that earthquake swarms beneath the caldera exhibit enlarged families with statistically significant tendency for upward migration patterns. The ascending swarms tend to nucleate at the base of the seismogenic zone with a spatial footprint that is laterally constrained by the southern rim of the caldera. We suggest that these swarms are driven by the transport of volatile-rich fluids released from deep volcanic processes. The observations highlight the potential for extreme spatial segmentation of earthquake triggering processes in magmatic systems.