  Our understanding of regional seismicity from multi-station seismograms
relies on the ability to associate arrival phases with their originating
earthquakes. Deep-learning-based phase detection now detects small, high-rate
arrivals from seismicity clouds, even at negative magnitudes. This new data
could give important insight into earthquake dynamics, but it is presents a
challenging association task. Existing techniques relying on coarsely
approximated, fixed wave speed models fail in this unexplored dense regime
where the complexity of unknown wave speed cannot be ignored. We introduce
Harpa, a high-rate association framework built on deep generative modeling and
neural fields. Harpa incorporates wave physics by using optimal transport to
compare arrival sequences. It is thus robust to unknown wave speeds and
estimates the wave speed model as a by-product of association. Experiments with
realistic, complex synthetic models show that Harpa is the first seismic phase
association framework which is accurate in the high-rate regime, paving the way
for new avenues in exploratory Earth science and improved understanding of
seismicity.
