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Several regularly recurring moderate-size earthquakes motivated dense instrumentation of the Parkfield section of the San Andreas fault, providing an invaluable near-fault observatory. We present a seismo-geodetic dynamic inversion of the 2004 Parkfield earthquake, which illuminates the interlinked complexity of faulting across time scales. Using fast-velocity-weakening rate-and-state friction, we jointly model 3D coseismic dynamic rupture and the 90-day evolution of postseismic slip. We utilize a parallel tempering Markov chain Monte Carlo approach to solve this non-linear high-dimensional inverse problem, constraining spatially varying prestress and fault friction parameters by 30 strong motion and 12 GPS stations. From visiting >2 million models, we discern complex coseismic rupture dynamics that transition from a strongly radiating pulse-like phase to a mildly radiating crack-like phase. Both coseismic phases are separated by a shallow strength barrier that nearly arrests rupture and leads to a gap in the afterslip. Coseismic rupture termination involves distinct arrest mechanisms that imprint on afterslip kinematics. A backward propagating afterslip front may drive delayed aftershock activity above the hypocenter. Analysis of the 10,500 best-fitting models uncovers local correlations between prestress levels and the reference friction coefficient, alongside an anticorrelation between prestress and rate-state parameters b−a. We find that a complex, fault-local interplay of dynamic parameters determines the nucleation, propagation, and arrest of both, co- and postseismic faulting. This study demonstrates the potential of inverse physics-based modeling to reveal novel insights and detailed characterizations of well-recorded earthquakes.
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Ensemble Kalman inversion for spatially varying rheological parameters in a stress-driven model of post-seismic deformation
SUMMARY Geodetic observations of post-seismic deformation due to afterslip and viscoelastic relaxation can be used to infer fault and lithosphere rheologies by combining the observations with mechanical models of post-seismic processes. However, estimating the spatial distributions of rheological parameters remains challenging because it requires solving a nonlinear inverse problem with a high-dimensional parameter space and potentially computationally expensive forward model. Here we introduce an inversion method to estimate spatially varying fault and lithospheric rheological parameters in a mechanical model of post-seismic deformation using geodetic time series. The forward model combines afterslip and viscoelastic relaxation governed by a velocity-strengthening frictional rheology and a power-law Burgers rheology, respectively, and incorporates the mechanical coupling between coseismic slip, afterslip and viscoelastic relaxation. The inversion method estimates spatially varying fault frictional parameters, viscoelastic constitutive parameters and coseismic stress change. We formulate the inverse problem in a Bayesian framework to quantify the uncertainties of the estimated parameters. To solve this problem with reasonable computational costs, we develop an algorithm to estimate the mean and covariance matrix of the posterior probability distribution based on an ensemble Kalman filter. We validate our method through numerical tests using a 2-D forward model and synthetic post-seismic GNSS time-series. The test results suggest that our method can estimate the spatially varying rheological parameters and their uncertainties reasonably well with tolerable computational costs. Our method can also recover spatially and temporally varying afterslip, viscous strain and effective viscosities and can distinguish the contributions of afterslip and viscoelastic relaxation to observed post-seismic deformation.
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- Award ID(s):
- 1848192
- PAR ID:
- 10609504
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Geophysical Journal International
- Volume:
- 242
- Issue:
- 2
- ISSN:
- 0956-540X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Several regularly recurring moderate‐size earthquakes motivated dense instrumentation of the Parkfield section of the San Andreas fault (SAF), providing an invaluable near‐fault observatory. We present a seismo‐geodetic dynamic inversion of the 2004 Parkfield earthquake, which illuminates the interlinked complexity of faulting across time scales. Using fast‐velocity‐weakening rate‐and‐state friction, we jointly model coseismic dynamic rupture and the 90‐day evolution of postseismic slip in a 3D domain. We utilize a parallel tempering Markov chain Monte Carlo approach to solve this non‐linear high‐dimensional inverse problem, constraining spatially varying prestress and fault friction parameters by 30 strong motion and 12 GPS stations. From visiting 2 million models, we discern complex coseismic rupture dynamics that transition from a strongly radiating pulse‐like phase to a mildly radiating crack‐like phase. Both coseismic phases are separated by a shallow strength barrier that nearly arrests rupture and leads to a gap in the afterslip, reflecting the geologic heterogeneity along this segment of the SAF. Coseismic rupture termination involves distinct arrest mechanisms that imprint on afterslip kinematics. A backward propagating afterslip front may drive delayed aftershock activity above the hypocenter. Trade‐off analysis of the 10,500 best‐fitting models uncovers local correlations between prestress levels and the reference friction coefficient, alongside an anticorrelation between prestress and rate‐state parameters . We find that a complex, fault‐local interplay of dynamic parameters determines the nucleation, propagation, and arrest of both, co‐ and postseismic faulting. This study demonstrates the potential of inverse physics‐based modeling to reveal novel insights and detailed characterizations of well‐recorded earthquakes.more » « less
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Abstract Following large earthquakes, viscoelastic stress relaxation may contribute to postseismic deformation observed at Earth's surface. Mechanical representations of viscoelastic deformation require a constitutive relationship for the lower crust/upper mantle material where stresses are diffused and, for non‐linear rheologies, knowledge of absolute stress level. Here, we describe a kinematic approach to representing geodetically observed postseismic motions that does not require an assumed viscoelastic rheology. The core idea is to use observed surface motions to constrain time‐dependent displacement boundary conditions applied at the base of the elastic upper crust by viscoelastic motions in the lower crust/upper mantle, approximating these displacements as slip on a set of dislocation elements. Using three‐dimensional forward models of viscoelastically modulated postseismic deformation in a thrust fault setting, we show how this approach can accurately represent surface motions and recover predicted displacements at the base of the elastic layer. Applied to the 1999 Chi‐Chi (Taiwan) earthquake, this kinematic approach can reproduce geodetically observed displacements and estimates of the partitioning between correlated postseismic deformation mechanisms. Specifically, we simultaneously estimate afterslip on the earthquake source fault that is similar to previous estimates, along with slip on dislocations at the base of the elastic layer that mimic predictions from viscous stress dissipation models in which viscosity is inferred to vary three‐dimensionally. A use case for the dislocation approach to modeling viscoelastic deformation is the estimation of spatiotemporally variable fault slip processes, including across sequential interseismic phases of the earthquake cycle, without assuming a lower crust/upper mantle rheology.more » « less
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