SPIDER: Scalable Probabilistic Inference for Differential Earthquake Relocation

TL;DR

SPIDER addresses the challenge of scalable, uncertainty-aware differential earthquake relocation for massive seismic catalogs by merging a physics-informed Eikonal forward model with Stochastic Gradient Langevin Dynamics to sample full posteriors over millions of parameters. It explicitly accounts for residual correlation among observations sharing common events, enabling calibrated uncertainty estimates and richer posterior diagnostics. Validated on a synthetic Ridgecrest catalog and three real data sets from California and Japan, SPIDER achieves location accuracy comparable to or better than existing double-difference methods while providing robust, interpretable uncertainty quantification. The framework supports GPU-parallel computation and is adaptable to future forward models and inference methods, offering a practical tool for large-scale seismology and hazard analysis.

Abstract

Seismicity catalogs are larger than ever due to an explosion of techniques for enhanced earthquake detection and an abundance of high-quality datasets. 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.

Figures (8)

• Figure 1: Location errors and uncertainties for the synthetic Ridgecrest catalog. Upper row contains absolute errors for the posterior mean compared with GrowClust best-fit. Middle row shows marginal posterior calibration plots for uncertainty quantification (see definition in main text). Lower row shows signed posterior width error vs central mass percentile. Negative values indicate the posterior is too narrow, whereas positive values indicate the posterior is too wide.
• Figure 2: Comprehensive analysis of the Cahuilla Swarm. Top: Comparison of relocation methods, with GrowClust on left and SPIDER on right. Bottom: Posterior density and cross-sections C1-C3.
• Figure 3: Cahuilla swarm catalog-wide posterior densities stacked over all events. Upper row shows 1D marginal posteriors for X, Y, and Z, whereas lower row shows 2D joint posteriors. These diagrams give a snapshot of the uncertainties and correlations (if present) that persist over the entire catalog.
• Figure 4: Ridgecrest real-data catalog relocation results. Upper left: GrowClust baseline. Upper right: SPIDER. Insets: closer view of locations within the black box. Lower left: stacked posterior densities for the R1-R1' section in map view, highlighting fault strand details. Lower right: stacked posterior densities for R1-R1' in depth view, highlighting the separation and dip of individual fault strands.
• Figure 5: Ridgecrest (real data) catalog-wide posterior densities stacked over all events. Upper row shows 1D marginal posteriors for X, Y, and Z, whereas lower row shows 2D joint posteriors with contours. These diagrams give a snapshot of the uncertainties and correlations that persist over the entire catalog.

Theorems & Definitions (2)

• Proposition 1
• proof