Forward-Inverse Modeling of Earthquake Cycle Deformation

Simone Puel, Thorsten W. Becker, Umberto Villa, Omar Ghattas, Dunyu Liu, & Eldar Khattatov

Published August 16, 2021, SCEC Contribution #11494, 2021 SCEC Annual Meeting Poster #025 (PDF)

Analysis of coseismic and postseismic surface displacements can help to constrain the Earth's structure and physics of deformation mechanisms occurring at depth. Here, we propose a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting including adjoint approaches. Based on two advanced open-source 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 stress-accurate implementation in a mixed FE elastic formulation, which exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches.
To demonstrate the potential of this new computational framework, two examples are shown. Synthetic surface geodetic data are used to infer the coseismic slip distribution during megathrust earthquakes (linear inversion) and the crust and mantle Poisson's ratio (non-linear). While the estimation of the fault slip is crucial to understand seismic source processes and mitigate seismic and tsunamigenic hazards, the Poisson's ratio has been used as a proxy of presence of fluids and postseismic poroelastic effects.
For the linear inversion, we compare our results with the standard linear approach where fault slip is inferred using elastic Green’s functions. Such approaches require numerous forward computations, and do not allow resolving structure. These limitations may be overcome by adjoint-based optimization methods, which efficiently minimize the gradient of the cost functional. In this case, the computational time is independent of the number of model parameters. We compare eigenvalues and eigenfunctions of both approaches to gain insights on performance for the linear problem, and then explore the non-linear problem.
Our inversion represents a novel technique to infer 3-D properties such as Poisson's ratio, often used as a proxy for fluid flow, in the crust and mantle wedge. Our approach has promise to explore more general inverse questions, such as to the best constitutive behavior, and might be helpful in future optimal experimental design and parametric sensitivity studies.

Key Words
Inverse problems, finite-element, elastic deformation, non-linear inversion, adjoint method

Citation
Puel, S., Becker, T. W., Villa, U., Ghattas, O., Liu, D., & Khattatov, E. (2021, 08). Forward-Inverse Modeling of Earthquake Cycle Deformation. Poster Presentation at 2021 SCEC Annual Meeting.

Related Projects & Working Groups
Computational Science (CS)