# Directivity Modes of Earthquake Populations with Unsupervised Learning

## TL;DR

This paper introduces an unsupervised learning method using Gaussian mixture models to identify rupture directivity modes in earthquake populations, revealing distinct rupture directions and fault planes in large datasets.

## Contribution

It presents a novel spectral decomposition and clustering approach to determine earthquake rupture modes without fitting kinematic models, improving understanding of rupture directions.

## Key findings

- Earthquake datasets decompose into distinct rupture modes
- Fault planes are unambiguously identified for all cases
- Small earthquakes exhibit unilateral ruptures 53-74% of the time

## Abstract

We present a novel approach for resolving modes of rupture directivity in large populations of earthquakes. A seismic spectral decomposition technique is used to first produce relative measurements of radiated energy for earthquakes in a spatially-compact cluster. The azimuthal distribution of energy for each earthquake is then assumed to result from one of several distinct modes of rupture propagation. Rather than fitting a kinematic rupture model to determine the most likely mode of rupture propagation, we instead treat the modes as latent variables and learn them with a Gaussian mixture model. The mixture model simultaneously determines the number of events that best identify with each mode. The technique is demonstrated on four datasets in California with several thousand earthquakes. We show that the datasets naturally decompose into distinct rupture propagation modes that correspond to different rupture directions, and the fault plane is unambiguously identified for all cases. We find that these small earthquakes exhibit unilateral ruptures 53-74% of the time on average. The results provide important observational constraints on the physics of earthquakes and faults.