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An EPIC Tikhonov Regularization: Application to Quasi-Static Fault Slip Inversion

Ortega-Culaciati, F. and Simons, M. and Ruiz, J. and Rivera, L. and Diaz-Salazar, N. (2021) An EPIC Tikhonov Regularization: Application to Quasi-Static Fault Slip Inversion. Journal of Geophysical Research. Solid Earth, 126 (7). Art. No. e2020JB021141. ISSN 2169-9313.

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Imaging subsurface fault slip from surface observations is essential to improving our understanding of the physics of earthquakes and tsunamis. As the estimation of subsurface fault slip is inherently ill-posed, common inversion methods usually require a regularization term to counteract instabilities. Such regularization introduces biases in inferred slip estimates. Here, we discuss the effects that prior information, implied by a given regularization scheme, can have on fault slip estimates. We propose a novel Equal Posterior Information Condition (EPIC)—based Tikhonov regularization that generalizes the concept of prior information. The EPIC determines variances of prior information based on a chosen form of the structure of the posterior covariance matrix. In the context of subduction zone earthquakes, use of the EPIC counterbalances the spatial heterogeneity of observational constraints on fault slip, improving stability, quality and interpretability of fault slip estimates. We investigate the efficiency of the EPIC in the context of various synthetic fault slip distributions. We also demonstrate the methodology by inferring co-seismic slip from geodetic data for the 2011 (M_w 9.0) Tohoku-Oki, Japan, earthquake, obtaining robust slip estimates that are similar to those inferred using a unregularized fully Bayesian approach.

Item Type:Article
Related URLs:
URLURL TypeDescription ItemData/Code
Ortega-Culaciati, F.0000-0002-2983-8646
Simons, M.0000-0003-1412-6395
Rivera, L.0000-0002-0726-5445
Diaz-Salazar, N.0000-0002-9711-7402
Additional Information:© 2021 American Geophysical Union. Issue Online: 28 June 2021; Version of Record online: 28 June 2021; Accepted manuscript online: 04 June 2021; Manuscript accepted: 02 June 2021; Manuscript revised: 20 May 2021; Manuscript received: 08 October 2020. F. Ortega-Culaciati acknowledges support from Proyecto Fondecyt 11140904 and 1181479, as well as from ANID PIA ACT 192169. J. Ruiz acknowledges support from Proyecto Fondecyt 1200679, and CONICYT PIA grant ACT172002. Powered@NLHPC: This research was partially supported by the supercomputing infrastructure of the NLHPC (ECM-02). We thank the editors and anonymous reviewers for providing insightful comments that helped to improve the clarity and quality of this manuscript. Data Availability Statement: Data sets for this research are included in this paper (and its supplementary information files): Minson et al. (2014). Python codes to solve the general linear least squares inversion problem using EPIC Tikhonov are available at, as well as in
Group:Seismological Laboratory
Funding AgencyGrant Number
Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT)11140904
Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT)1181479
Comisión Nacional de Investigación Científica y Tecnológica (CONICYT)ACT192169
Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT)1200679
Comisión Nacional de Investigación Científica y Tecnológica (CONICYT)ACT172002
Subject Keywords:regularization; prior information; EPIC Tikhonov; inverse methods; least squares; slip inversion
Issue or Number:7
Record Number:CaltechAUTHORS:20210607-115053217
Persistent URL:
Official Citation:Ortega-Culaciati, F., Simons, M., Ruiz, J., Rivera, L., & Díaz-Salazar, N. (2021). An EPIC Tikhonov regularization: Application to quasi-static fault slip inversion. Journal of Geophysical Research: Solid Earth, 126, e2020JB021141.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109413
Deposited By: George Porter
Deposited On:07 Jun 2021 21:55
Last Modified:16 Jul 2021 18:20

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