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Directivity Modes of Earthquake Populations with Unsupervised Learning

Ross, Zachary E. and Trugman, Daniel T. and Azizzadenesheli, Kamyar and Anandkumar, Anima (2020) Directivity Modes of Earthquake Populations with Unsupervised Learning. Journal of Geophysical Research. Solid Earth, 125 (2). Art. No. e2019JB018299. ISSN 2169-9313. doi:10.1029/2019JB018299.

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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, each with compact clusters of several thousand earthquakes with comparable slip mechanisms. 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 63–73% of the time on average. The results provide important observational constraints on the physics of earthquakes and faults.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Ross, Zachary E.0000-0002-6343-8400
Trugman, Daniel T.0000-0002-9296-4223
Azizzadenesheli, Kamyar0000-0001-8507-1868
Anandkumar, Anima0000-0002-6974-6797
Additional Information:© 2020 American Geophysical Union. Received 1 JUL 2019; Accepted 31 JAN 2020; Accepted article online 5 FEB 2020. We thank Valère Lambert for helpful discussions. The waveform and catalog data used in this study are publicly available from the Southern California Earthquake Data Center ( and the Northern California Earthquake Data Center ( D. Trugman acknowledges institutional support from the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory under project number 20180700PRD1. A. Anandkumar is supported in part by Bren endowed chair, Darpa PAI, Raytheon, and Microsoft, Google, and Adobe faculty fellowships. K. Azizzadenesheli is supported in part by NSF Career Award CCF‐1254106 and AFOSR YIPFA9550‐15‐1‐0221.
Group:Seismological Laboratory, Division of Geological and Planetary Sciences
Funding AgencyGrant Number
Los Alamos National Laboratory20180700PRD1
Bren Professor of Computing and Mathematical SciencesUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Microsoft Faculty FellowshipUNSPECIFIED
Google Faculty Research AwardUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)YIPFA9550‐15‐1‐0221
Subject Keywords:rupture directivity; earthquake source properties; machine learning; unsupervised learning
Issue or Number:2
Record Number:CaltechAUTHORS:20190905-154247884
Persistent URL:
Official Citation:Ross, Z. E., Trugman, D. T., Azizzadenesheli, K., & Anandkumar, A. (2020). Directivity modes of earthquake populations with unsupervised learning. Journal of Geophysical Research: Solid Earth, 125, e2019JB018299.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98453
Deposited By: George Porter
Deposited On:05 Sep 2019 23:21
Last Modified:23 Dec 2022 18:50

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