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SUMMARY The frictional properties of large faults are expected to vary in space. However, fault models often assume that properties are homogeneous, or nearly so. We investigate the conditions under which the details of variations may be neglected and properties homogenized. We do so by examining the behaviour of nonlinear solutions for unstably accelerating fault slip under frictional heterogeneity. We consider a rate- and state-dependent fault friction in which the characteristic wavelength for the property variations is a problem parameter. We find that homogenization is permissible only when that wavelength shows scale separation from an elasto-frictional length scale. However, fault models also often include property transitions that occur over distances comparable to the elasto-frictional length. We show that under such comparable variations, the dynamics of earthquake-nucleating instabilities is controlled by the properties’ spatial distribution.
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This content will become publicly available on December 1, 2025
Adjoint-based inversion for stress and frictional parameters in earthquake modeling
We present an adjoint-based optimization method to invert for stress and frictional parameters used in earthquake modeling. The forward problem is linear elastodynamics with nonlinear rate-and-state frictional faults. The misfit functional quantifies the difference between simulated and measured particle displacements or velocities at receiver locations. The misfit may include windowing or filtering operators. We derive the corresponding adjoint problem, which is linear elasticity with linearized rate-and-state friction and, for forward problems involving fault normal stress changes, nonzero fault opening, with time-dependent coefficients derived from the forward solution. The gradient of the misfit is efficiently computed by convolving forward and adjoint variables on the fault. The method thus extends the framework of full-waveform inversion to include frictional faults with rate-and-state friction. In addition, we present a space-time dual-consistent discretization of a dynamic rupture problem with a rough fault in antiplane shear, using high-order accurate summation-by-parts finite differences in combination with explicit Runge–Kutta time integration. The dual consistency of the discretization ensures that the discrete adjoint-based gradient is the exact gradient of the discrete misfit functional as well as a consistent approximation of the continuous gradient. Our theoretical results are corroborated by inversions with synthetic data. We anticipate that adjoint-based inversion of seismic and/or geodetic data will be a powerful tool for studying earthquake source processes; it can also be used to interpret laboratory friction experiments.
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- Award ID(s):
- 1947448
- PAR ID:
- 10553403
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of Computational Physics
- Volume:
- 519
- Issue:
- C
- ISSN:
- 0021-9991
- Page Range / eLocation ID:
- 113447
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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