SPIDER: Scalable Probabilistic Inference for Differential Earthquake Relocation

Seismicity catalogs are larger than ever due to an explosion of techniques for enhanced earthquake detection and an abundance of high‐quality data sets. Bayesian inference is an appealing framework for locating earthquakes due to its ability to propagate and quantify uncertainty into the inversion results, but traditional methods do not scale well to high‐dimensional parameter spaces, making them unsuitable for double‐difference relocation where the number of parameters can reach the millions. Here we introduce SPIDER, a scalable Bayesian inference framework for double‐difference hypocenter relocation. SPIDER uses a physics‐informed neural network Eikonal solver together with a highly efficient sampler called Stochastic Gradient Langevin Dynamics to generate posterior samples jointly for entire seismicity catalogs. We show that traditional double‐difference relocation formulations neglect residual correlation between observations with common events, which biases uncertainty estimates. Our formulation is designed to whiten this residual correlation, and is readily parallelized over multiple GPUs for enhanced computational efficiency. We demonstrate the capabilities of SPIDER on a rigorous synthetic seismicity catalog and three real data catalogs from California and Japan. We introduce several ways to analyze high‐dimensional posterior distributions to aid in scientific interpretation and evaluation.