A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

Puel, S.; Khattatov, E.; Villa, U.; Liu, D.; Ghattas, O.; Becker, T. W.

doi:10.1093/gji/ggac050

Title: A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

Journal Article · Tue Feb 08 00:00:00 EST 2022 · Geophysical Journal International

DOI:https://doi.org/10.1093/gji/ggac050· OSTI ID:1862887

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SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

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Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

Grant/Contract Number:: SC0019303; EAR-2121666; EAR-2045292; 19214743; 1927216; ACI-1550593

OSTI ID:: 1862887

Alternate ID(s):: OSTI ID: 1979491

Journal Information:: Geophysical Journal International, Journal Name: Geophysical Journal International Vol. 230 Journal Issue: 2; ISSN 0956-540X

Publisher:: Oxford University PressCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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