# Double Difference Earthquake Location with Graph Neural Networks

arXiv: https://arxiv.org/abs/2410.19323 · HTML: https://mlsanity.com/paper/2410.19323/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 69 references that are in the map.
- First posted on arXiv 25 Oct 2024.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Understanding and Extending Subgraph GNNs by Rethinking Their Symmetries](https://mlsanity.com/paper/2206.11140/) (2022)
- [Expander Graph Propagation](https://mlsanity.com/paper/2210.02997/) (2022)
- [Subgraph Neural Networks](https://mlsanity.com/paper/2006.10538/) (2020)
- [EikoNet: Solving the Eikonal equation with Deep Neural Networks](https://mlsanity.com/paper/2004.00361/) (2020)
- [Bayesian-Deep-Learning Estimation of Earthquake Location from Single-Station Observations](https://mlsanity.com/paper/1912.01144/) (2019)
- [PhaseLink: A Deep Learning Approach to Seismic Phase Association](https://mlsanity.com/paper/1809.02880/) (2018)
- [Earthquake Phase Association with Graph Neural Networks](https://mlsanity.com/paper/2209.07086/) (2022)
- [A Machine-Learning Approach for Earthquake Magnitude Estimation](https://mlsanity.com/paper/1911.05975/) (2019)
- [A multi-channel approach for automatic microseismic event association using RANSAC-based arrival time event clustering(RATEC)](https://mlsanity.com/paper/1702.01856/) (2017)

## Built on by (most cited first, 1 of 1)

- [HEIMDALL: a grapH-based sEIsMic Detector And Locator for microseismicity](https://mlsanity.com/paper/2507.10850/) (2025)

## Abstract (arXiv)

Double difference earthquake relocation is an essential component of many earthquake catalog development workflows. This technique produces high-resolution relative relocations between events by minimizing differential measurements of the arrival times of waves from nearby sources, which highlights the resolution of faults and improves interpretation of seismic activity. The inverse problem is typically solved iteratively using conjugate-gradient minimization, however the cost scales significantly with the total number of sources and stations considered. Here we propose a Graph Neural Network (GNN) based earthquake double-difference relocation framework, Graph Double Difference (GraphDD), that is trained to minimize the double-difference residuals of a catalog to locate earthquakes. Through batching and sampling the method can scale to arbitrarily large catalogs. Our architecture uses one graph to represent the stations, a second graph to represent the sources, and creates the Cartesian product graph between the two graphs to capture the relationships between the stations and sources (e.g., the residuals and travel time partial derivatives). This key feature allows a natural architecture that can be used to minimize the double-difference residuals. We implement our model on several distinct test cases including seismicity from northern California, Turkiye, and northern Chile, which have highly variable data quality, and station and source distributions. We obtain high resolution relocations in these tests, and our model shows adaptability to variable types of loss functions and location objectives, including learning station corrections and mapping into the reference frame of a different catalog. Our results suggest that a GNN approach to double-difference relocation is a promising direction for scaling to very large catalogs and gaining new insights into the relocation problem.