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\begin{document}

\title{Convolutional event embeddings for fast probabilistic earthquake
assessment}



\author[1]{Jannes Münchmeyer}%
\author[1]{Dino Bindi}%
\author[2]{Ulf Leser}%
\author[1]{Frederik Tilmann}%
\affil[1]{Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences}%
\affil[2]{Humboldt University of Berlin}%


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  \date{May 21, 2024}


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\begin{abstract}
Recent research showed that machine learning, in particular deep
learning, can be applied with great success to a multitude of
seismological tasks, e.g. phase picking and earthquake localization. One
reason is that neural networks can be used as feature extractors,
generating generally applicable representations of complex data. We
employ a convolutional network to condense earthquake waveforms from a
varying set of stations into a high dimensional vector, which we call
event embedding. For each event the embedding is calculated from
instrument-corrected waveforms beginning at the first P pick and updated
continuously with incoming data. We employ event embeddings for real
time magnitude estimation, earthquake localization and ground motion
prediction, which are central tasks for early warning and for guiding
rapid disaster response. We evaluate our model on the IPOC catalog for
Northern Chile, containing ~100,000 events with low uncertainty
hypocenters and magnitude estimates. We split the catalog sequentially
into a training and a test set, with the 2014 Iquique event (Mw 8.1) and
its fore- and aftershocks contained in the test set. Following
preliminary results the system achieves a test RMSE of 0.28 magnitude
units (m.u.) and 35 km hypocentral distance 1 s after the first P
arrival at the nearest station, which improves to 0.17 m.u. and 22 km
after 5 s and 0.11 m.u. and 15 km after 25 s. As applications in the
hazard domain require proper uncertainty estimates, we propose a
probabilistic model using Gaussian mixture density networks. By
analyzing the predictions in terms of their calibration, we show that
the model exhibits overconfidence i.e. overly optimistic confidence
intervals. We show that deep ensembles substantially improve
calibration. To assess the limitations of our model and elucidate the
pitfalls of machine learning for early warning in general, we conduct an
error analysis and discuss mitigation strategies. Despite the size of
our catalog, we observe issues with two kinds of data sparsity. First,
we observe increased residuals for the source parameters of the largest
events, as training data for these events is scarce. Second, similar
inaccuracies occur in areas without events of a certain size in the
training catalog. We investigate the impact of these limitations on the
Iquique fore- and aftershocks.%
\end{abstract}%



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