High-Rate Phase Association with Travel Time Neural Fields

TL;DR

HARPA introduces a novel framework for high-rate seismic phase association that treats arrivals at each station as probability distributions and matches them to generative travel-time models via Wasserstein-2 distance. It jointly infers earthquake spatiotemporal parameters and a latent wave-speed model using a travel-time neural field and an autoencoder, with optimization guided by stochastic gradient Langevin dynamics to navigate a nonconvex landscape. Across real-field (Chile and Ridgecrest) and synthetic high-rate scenarios, HARPA outperforms state-of-the-art methods, especially when wave speeds are unknown or highly complex, and demonstrates robust wave-speed recovery with practical accuracy. By reframing phase association as distribution matching and leveraging implicit neural representations, HARPA paves the way for scalable microseismic monitoring and potential enhancements in seismic tomography, while remaining accessible as open-source software.

Abstract

Earthquake science and seismology rely on the ability to associate seismic waves with their originating earthquakes. Earthquake detection algorithms based on deep learning have progressed rapidly and now routinely detect microearthquakes with unprecedented clarity, providing information about fault dynamics on increasingly finer spatiotemporal scales. However, this densification of detections can overwhelm existing techniques for phase association which rely on fixed wave speed models and associate events one by one. These methods fail when the event rates become high or where the 4D complexity of elastic wave speeds cannot be ignored. Here, we introduce HARPA, a deep learning solution to this problem. HARPA is a high-rate association framework which incorporates wave physics by leveraging deep generative models and travel time neural fields. Instead of associating events one by one, it lifts arrival sequences to probability distributions and compares them using an optimal transport metric. The generative travel time neural fields are used to estimate the wave speed simultaneously with association. HARPA outperforms state-of-the-art association methods for both real seismic data and complex synthetic models and paves the way for improved understanding of seismicity while establishing a new seismic data analysis paradigm.

Figures (6)

• Figure 1: Phase arrivals at different event frequencies. Each row of Panels a-c shows data for a given seismometer location (latitude at right) as a function of time. Event rates are (a) 0.3, (b) 3, and (c) 30 per minute. Panel (b) shows real seismic data from the 2019 Ridgecrest earthquake, while (a) and (c) are generated by shifting arrivals and events from (b) to produce a range of event rates for phase association testing. (d) and (e) show performance comparison of Harpa with other algorithms across different frequencies of events. Note that Harpa outperforms all associators for high event rates. $\mathsf{CF}$ is the confusion factor representing the degree of arrival complexity based on phase overlap and ranges from 0 (easy) to 1 (difficult) as detailed in the SI.
• Figure 2: Workflow for travel time neural field implementation with optimal transport. (a) Diagram of Harpa's association pipeline. Note connections between discrete measurements, latent code and optimal association. (b) Diagram of the wave speed autoencoder and travel time neural field with encoder/decoder stages. QAP, LSAP, and SGLD refer to the Quadratic Assignment Problem, the Linear Sum Assignment Problem, and Stochastic Gradient Langevin Dynamics, respectively.
• Figure 3: Association for four wave speed models (top) and event frequencies of 3 and 30 per minute. The histograms illustrate the accuracy of various algorithms, with 0D and 1D denoting constant and one-dimensional wave speed models, respectively. IND and OOD represent in-distribution and out-of-distribution wave speed models used for testing against the trained generative model for Harpa. In the scatter plots, the top row shows the relationship between station-event distance and arrival time, while the bottom row presents x-coordinates versus arrival time. Note that Harpa associates with high accuracy even when event rates are high in areas with complex wave speed models.
• Figure 4: Performance of Harpa and other algorithms on data for the 2014 $M_w$ 8.2 Iquique Chile earthquake. Triangles are seismic stations and dots are earthquake epicenters color coded by depth. Note that the event rates vary from about 0.1 to 0.4 per minute. For these low to moderate event rates performance is about the same for each model.
• Figure 5: Performance of Harpa and other algorithms for the 2019 $M_w$ 7.1 Ridgecrest earthquake sequence. For the map views, each row show results for one model (Harpa, GaMMA, PyOcto) and each column is a different phase pick density for the association task. We adjusted the threshold in PhaseNet to obtain a range of event densities. The number of phase picks is given above each row of map views; number in each map is the number of events detected. Plot at left shows comparison of the events associated as a function of phase picks. Harpa performs as well or better than the other models.