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Accounting for prediction uncertainty when inferring subsurface fault slip

Duputel, Zacharie and Agram, Piyush S. and Simons, Mark and Minson, Sarah E. and Beck, James L. (2014) Accounting for prediction uncertainty when inferring subsurface fault slip. Geophysical Journal International, 197 (1). pp. 464-482. ISSN 0956-540X. https://resolver.caltech.edu/CaltechAUTHORS:20140515-083746685

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Abstract

This study lays the groundwork for a new generation of earthquake source models based on a general formalism that rigorously quantifies and incorporates the impact of uncertainties in fault slip inverse problems. We distinguish two sources of uncertainty when considering the discrepancy between data and forward model predictions. The first class of error is induced by imperfect measurements and is often referred to as observational error. The second source of uncertainty is generally neglected and corresponds to the prediction error, that is the uncertainty due to imperfect forward modelling. Yet the prediction error can be shown to scale approximately with the size of earthquakes and thus can dwarf the observational error, particularly for large events. Both sources of uncertainty can be formulated using the misfit covariance matrix, C_χ, which combines a covariance matrix for observation errors, C_d and a covariance matrix for prediction errors, C_p, associated with inaccurate model predictions. We develop a physically based stochastic forward model to treat the model prediction uncertainty and show how C_p can be constructed to explicitly account for some of the inaccuracies in the earth model. Based on a first-order perturbation approach, our formalism relates C_p to uncertainties on the elastic parameters of different regions (e.g. crust, mantle, etc.). We demonstrate the importance of including C_p using a simple example of an infinite strike-slip fault in the quasi-static approximation. In this toy model, we treat only uncertainties in the 1-D depth distribution of the shear modulus. We discuss how this can be extended to general 3-D cases and applied to other parameters (e.g. fault geometry) using our formalism for C_p. The improved modelling of C_p is expected to lead to more reliable images of the earthquake rupture, that are more resistant to overfitting of data and include more realistic estimates of uncertainty on inferred model parameters.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1093/gji/ggt517 DOIArticle
http://gji.oxfordjournals.org/content/197/1/464PublisherArticle
http://gji.oxfordjournals.org/content/197/1/464/suppl/DC1PublisherSupporting Information
ORCID:
AuthorORCID
Simons, Mark0000-0003-1412-6395
Minson, Sarah E.0000-0001-5869-3477
Additional Information:© 2014 The Authors. Published by Oxford University Press on behalf of The Royal Astronomical Society. Accepted 2013 December 20. Received 2013 December 20; in original form 2013 August 1. First published online: January 24, 2014. We thank Bernard Valette and Yukitoshi Fukahata for their helpful reviews. We have benefited from discussions with Jean-Paul Ampuero, Jean Virieux, Romain Brossier, Victor Tsai, Romain Jolivet and Luis Rivera. MS acknowledges sabbatical support from the Univ. Joseph Fourier (Grenoble, France) during which this project started. PSA was supported by the Keck Institute of Space Studies Postdoctoral Fellowship. Our Bayesian sampling algorithm is based on the ALTAR implementation of CATMIP developed by Michael Aivasis and Hailiang Zhang. This work made use of the Matplotlib python library created by John D. Hunter. P. Agram was supported by the Keck Institute of Space Studies Postdoctoral Fellowship. This research was supported by the Southern California Earthquake Center. SCEC is funded by NSF Cooperative Agreement EAR-0529922 and USGS Cooperative Agreement 07HQAG0008. The SCEC contribution number for this paper is 1791. This work was partially supported by the National Science Foundation under Grant No. EAR-0941374.
Group:Keck Institute for Space Studies
Funders:
Funding AgencyGrant Number
Keck Institute for Space Studies (KISS)UNSPECIFIED
Southern California Earthquake Center (SCEC)UNSPECIFIED
NSFEAR-0529922
USGS07HQAG0008
NSFEAR-0941374
Subject Keywords:Inverse theory; Probability distributions; Earthquake source observations
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Southern California Earthquake Center1791
Issue or Number:1
Record Number:CaltechAUTHORS:20140515-083746685
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140515-083746685
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:45757
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:15 May 2014 16:07
Last Modified:13 Dec 2019 03:10

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