Phase association groups seismic wave arrivals according to their originating
earthquakes. It is a fundamental task in a seismic data processing pipeline,
but challenging to perform for smaller, high-rate seismic events which carry
fundamental information about earthquake dynamics, especially with a commonly
assumed inaccurate wave speed model. As a consequence, most association methods
focus on larger events that occur at a lower rate and are thus easier to
associate, even though microseismicity provides a valuable description of the
elastic medium properties in the subsurface. In this paper, we show that
association is possible at rates much higher than previously reported even when
the wave speed is unknown. We propose Harpa, a high-rate seismic phase
association method which leverages deep neural fields to build generative
models of wave speeds and associated travel times, and first solves a joint
spatio--temporal source localization and wave speed recovery problem, followed
by association. We obviate the need for associated phases by interpreting
arrival time data as probability measures and using an optimal transport loss
to enforce data fidelity. The joint recovery problem is known to admit a unique
solution under certain conditions but due to the non-convexity of the
corresponding loss a simple gradient scheme converges to poor local minima. We
show that this is effectively mitigated by stochastic gradient Langevin
dynamics (SGLD). Numerical experiments show that \harpa~efficiently associates
high-rate seismicity clouds over complex, unknown wave speeds and graciously
handles noisy and missing picks.

利用深度神经场建立波速及相应行程时间生成模型，并采用一种优化输运损失来执行高速地震相联合估计和结合。解决了波速及异源估计问题，实现了对高速地震云的有效结合，处理了嘈杂数据和缺失数据，极大地促进了地震数据处理的技术进步。