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SUMMARY 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. 

SUMMARY Distributed acoustic sensing (DAS) networks promise to revolutionize observational seismology by providing cost-effective, highly dense spatial sampling of the seismic wavefield, especially by utilizing pre-deployed telecomm fibre in urban settings for which dense seismic network deployments are difficult to construct. However, each DAS channel is sensitive only to one projection of the horizontal strain tensor and therefore gives an incomplete picture of the horizontal seismic wavefield, limiting our ability to make a holistic analysis of instrument response. This analysis has therefore been largely restricted to pointwise comparisons where a fortuitious coincidence of reference three-component seismometers and colocated DAS cable allows. We evaluate DAS instrument response by comparing DAS measurements from the PoroTomo experiment with strain-rate wavefield reconstructed from the nodal seismic array deployed in the same experiment, allowing us to treat the entire DAS array in a systematic fashion irrespective of cable geometry relative to the location of nodes. We found that, while the phase differences are in general small, the amplitude differences between predicted and observed DAS strain rates average a factor of 2 across the array and correlate with near-surface geology, suggesting that careful assessment of DAS deployments is essential for applications that require reliable assessments of amplitude. We further discuss strategies for empirical gain corrections and optimal placement of point sensor deployments to generate the best combined sensitivity with an already deployed DAS cable, from a wavefield reconstruction perspective. 

SUMMARY The proliferation of large seismic arrays have opened many new avenues of geophysical research; however, most techniques still fundamentally treat regional and global scale seismic networks as a collection of individual time-series rather than as a single unified data product. Wavefield reconstruction allows us to turn a collection of individual records into a single structured form that treats the seismic wavefield as a coherent 3-D or 4-D entity. We propose a split processing scheme based on a wavelet transform in time and pre-conditioned curvelet-based compressive sensing in space to create a sparse representation of the continuous seismic wavefield with smooth second-order derivatives. Using this representation, we illustrate several applications, including surface wave gradiometry, Helmholtz–Hodge decomposition of the wavefield into irrotational and solenoidal components, and compression and denoising of seismic records. 

SUMMARY We introduce a scheme for probabilistic hypocentre inversion with Stein variational inference. Our approach uses a differentiable forward model in the form of a physics informed neural network, which we train to solve the Eikonal equation. This allows for rapid approximation of the posterior by iteratively optimizing a collection of particles against a kernelized Stein discrepancy. We show that the method is well-equipped to handle highly multimodal posterior distributions, which are common in hypocentral inverse problems. A suite of experiments is performed to examine the influence of the various hyperparameters. Once trained, the method is valid for any seismic network geometry within the study area without the need to build traveltime tables. We show that the computational demands scale efficiently with the number of differential times, making it ideal for large-N sensing technologies like Distributed Acoustic Sensing. The techniques outlined in this manuscript have considerable implications beyond just ray tracing procedures, with the work flow applicable to other fields with computationally expensive inversion procedures such as full waveform inversion. 

Abstract The proliferation of dense arrays promises to improve our ability to image geological structures at the scales necessary for accurate assessment of seismic hazard. However, combining the resulting local high‐resolution tomography with existing regional models presents an ongoing challenge. We developed a framework based on the level‐set method that infers where local data provide meaningful constraints beyond those found in regional models ‐ for example the Community Velocity Models (CVMs) of southern California. This technique defines a volume within which updates are made to a reference CVM, with the boundary of the volume being part of the inversion rather than explicitly defined. By penalizing the complexity of the boundary, a minimal update that sufficiently explains the data is achieved. To test this framework, we use data from the Community Seismic Network, a dense permanent urban deployment. We inverted Love wave dispersion and amplification data, from the Mw 6.4 and 7.1 2019 Ridgecrest earthquakes. We invert for an update to CVM‐S4.26 using the Tikhonov Ensemble Sampling scheme, a highly efficient derivative‐free approximate Bayesian method. We find the data are best explained by a deepening of the Los Angeles Basin with its deepest part south of downtown Los Angeles, along with a steeper northeastern basin wall. This result offers new progress toward the parsimonious incorporation of detailed local basin models within regional reference models utilizing an objective framework and highlights the importance of accurate basin models when accounting for the amplification of surface waves in the high‐rise building response band.