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Classical point process models, such as the epidemic-type aftershock sequence (ETAS) model, have been widely used for forecasting the event times and locations of earthquakes for decades. Recent advances have led to Neural Point Processes (NPPs), which promise greater flexibility and improvements over classical models. However, the currently-used benchmark dataset for NPPs does not represent an up-to-date challenge in the seismological community since it lacks a key earthquake sequence from the region and improperly splits training and testing data. Furthermore, initial earthquake forecast benchmarking lacks a comparison to state-of-the-art earthquake forecasting models typically used by the seismological community. To address these gaps, we introduce EarthquakeNPP: a collection of benchmark datasets to facilitate testing of NPPs on earthquake data, accompanied by a credible implementation of the ETAS model. The datasets cover a range of small to large target regions within California, dating from 1971 to 2021, and include different methodologies for dataset generation. In a benchmarking experiment, we compare three spatio-temporal NPPs against ETAS and find that none outperform ETAS in either spatial or temporal log-likelihood. These results indicate that current NPP implementations are not yet suitable for practical earthquake forecasting. However, EarthquakeNPP will serve as a platform for collaboration between the seismology and machine learning communities with the goal of improving earthquake predictability.

Performing Bayesian inference for the Epidemic-Type Aftershock Sequence (ETAS) model of earthquakes typically requires MCMC sampling using the likelihood function or estimating the latent branching structure. These tasks have computational complexity $O(n^2)$ with the number of earthquakes and therefore do not scale well with new enhanced catalogs, which can now contain an order of $10^6$ events. On the other hand, simulation from the ETAS model can be done more quickly $O(n \log n )$. We present SB-ETAS: simulation-based inference for the ETAS model. This is an approximate Bayesian method which uses Sequential Neural Posterior Estimation (SNPE), a machine learning based algorithm for learning posterior distributions from simulations. SB-ETAS can successfully approximate ETAS posterior distributions on shorter catalogues where it is computationally feasible to compare with MCMC sampling. Furthermore, the scaling of SB-ETAS makes it feasible to fit to very large earthquake catalogs, such as one for Southern California dating back to 1932. SB-ETAS can find Bayesian estimates of ETAS parameters for this catalog in less than 10 hours on a standard laptop, which would have taken over 2 weeks using MCMC. Looking beyond the standard ETAS model, this simulation based framework would allow earthquake modellers to define and infer parameters for much more complex models that have intractable likelihood functions.

This article presents a weakly supervised machine learning method, which we call DAS-N2N, for suppressing strong random noise in distributed acoustic sensing (DAS) recordings. DAS-N2N requires no manually produced labels (i.e., pre-determined examples of clean event signals or sections of noise) for training and aims to map random noise processes to a chosen summary statistic, such as the distribution mean, median or mode, whilst retaining the true underlying signal. This is achieved by splicing (joining together) two fibres hosted within a single optical cable, recording two noisy copies of the same underlying signal corrupted by different independent realizations of random observational noise. A deep learning model can then be trained using only these two noisy copies of the data to produce a near fully-denoised copy. Once the model is trained, only noisy data from a single fibre is required. Using a dataset from a DAS array deployed on the surface of the Rutford Ice Stream in Antarctica, we demonstrate that DAS-N2N greatly suppresses incoherent noise and enhances the signal-to-noise ratios (SNR) of natural microseismic icequake events. We further show that this approach is inherently more efficient and effective than standard stop/pass band and white noise (e.g., Wiener) filtering routines, as well as a comparable self-supervised learning method based on masking individual DAS channels. Our preferred model for this task is lightweight, processing 30 seconds of data recorded at a sampling frequency of 1000 Hz over 985 channels (approx. 1 km of fiber) in $<$1 s. Due to the high noise levels in DAS recordings, efficient data-driven denoising methods, such as DAS-N2N, will prove essential to time-critical DAS earthquake detection, particularly in the case of microseismic monitoring., Comment: Submitted for publication to Geophysical Journal International. For the purpose of open access, the author(s) has applied a Creative Commons Attribution (CC BY) licence to the Author Accepted Manuscript version arising from this submission

Point processes have been dominant in modeling the evolution of seismicity for decades, with the Epidemic Type Aftershock Sequence (ETAS) model being most popular. Recent advances in machine learning have constructed highly flexible point process models using neural networks to improve upon existing parametric models. We investigate whether these flexible point process models can be applied to short-term seismicity forecasting by extending an existing temporal neural model to the magnitude domain and we show how this model can forecast earthquakes above a target magnitude threshold. We first demonstrate that the neural model can fit synthetic ETAS data, however, requiring less computational time because it is not dependent on the full history of the sequence. By artificially emulating short-term aftershock incompleteness in the synthetic dataset, we find that the neural model outperforms ETAS. Using a new enhanced catalog from the 2016-2017 Central Apennines earthquake sequence, we investigate the predictive skill of ETAS and the neural model with respect to the lowest input magnitude. Constructing multiple forecasting experiments using the Visso, Norcia and Campotosto earthquakes to partition training and testing data, we target M3+ events. We find both models perform similarly at previously explored thresholds (e.g., above M3), but lowering the threshold to M1.2 reduces the performance of ETAS unlike the neural model. We argue that some of these gains are due to the neural model's ability to handle incomplete data. The robustness to missing data and speed to train the neural model present it as an encouraging competitor in earthquake forecasting.

Operational earthquake forecasting for risk management and communication during seismic sequences depends on our ability to select an optimal forecasting model. To do this, we need to compare the performance of competing models with each other in prospective forecasting mode, and to rank their performance using a fair, reproducible and reliable method. The Collaboratory for the Study of Earthquake Predictability (CSEP) conducts such prospective earthquake forecasting experiments around the globe. One metric that has been proposed to rank competing models is the Parimutuel Gambling score, which has the advantage of allowing alarm-based (categorical) forecasts to be compared with probabilistic ones. Here we examine the suitability of this score for ranking competing earthquake forecasts. First, we prove analytically that this score is in general improper, meaning that, on average, it does not prefer the model that generated the data. Even in the special case where it is proper, we show it can still be used in an improper way. Then, we compare its performance with two commonly-used proper scores (the Brier and logarithmic scores), taking into account the uncertainty around the observed average score. We estimate the confidence intervals for the expected score difference which allows us to define if and when a model can be preferred. Our findings suggest the Parimutuel Gambling score should not be used to distinguishing between multiple competing forecasts. They also enable a more rigorous approach to distinguish between the predictive skills of candidate forecasts in addition to their rankings., Comment: 29 pages, 14 figures. Work presented at vEGU21 as vPico presentation

Recent studies have shown that many results published in peer-reviewed scientific journals are not reproducible. This raises the following question: why is it so easy to fool myself into believing that a result is reliable when in fact it is not? Using Brownian motion as a toy model, we show how this can happen if ergodicity is assumed where it is unwarranted. A measured value can appear stable when judged over time, although it is not stable across the ensemble: a different result will be obtained each time the experiment is run., Comment: 11 pages, 4 figures