Dynamic rupture on an interface between a compliant fault zone layer and a stiffer surrounding solid

Yehuda Ben-Zion

doi:10.1029/2001jb000254

Off-fault deformations and shallow slip deficit from dynamic rupture simulations with fault zone plasticity

Geophysical Research Letters ◽

10.1002/2017gl074323 ◽

2017 ◽

Vol 44 (15) ◽

pp. 7733-7742 ◽

Cited By ~ 25

Author(s):

D. Roten ◽

K. B. Olsen ◽

S. M. Day

Keyword(s):

Fault Zone ◽

Dynamic Rupture ◽

Slip Deficit

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Modeling earthquake rupture dynamics across diffuse deforming fault zones

10.5194/egusphere-egu2020-20600 ◽

2020 ◽

Author(s):

Jorge Nicolas Hayek Valencia ◽

Duo Li ◽

Dave A. May ◽

Alice-Agnes Gabriel

Keyword(s):

Solid Earth ◽

Fault Zone ◽

Fault Zones ◽

Displacement Discontinuity ◽

Diffuse Interface ◽

Dynamic Rupture ◽

San Jacinto Fault ◽

Rupture Dynamics ◽

San Jacinto Fault Zone ◽

Plastic Materials

Earthquakes are a multi-scale, multi-physics problem. For the last decades, earthquakes have been modeled as a sudden displacement discontinuity across a simplified (potentially heterogeneous) surface of infinitesimal thickness in the framework of linear elastodynamics. Thus, earthquake models are commonly forced to distinguish artificially between on-fault frictional failure and the off-fault response of rock.&#160;While complex volumetric failure patterns of fault networks are observed from well-recorded large earthquakes (e.g., the 2016 Mw7.8 Kaik&#333;ura event, Klinger et al. 2018) and small earthquakes (e.g., events in the San Jacinto Fault Zone, Cheng et al. 2018) as well as in laboratory experiments (e.g., in high-velocity friction experiments, Passel&#232;gue&#160;et al., 2016) inelastic deformation within a larger volume around the fault is generally neglected when studying kinematics, dynamics and the energy budget of earthquakes. Fault behaviour is then dominantly controlled by lab-derived friction on a surface. Recent 2D collapsing of material properties, stresses, geometry, and strength conditions from seismo-thermo-mechanical models to elastodynamic frictional interfaces illustrated resulting earthquake complexity and modeling challenges (van Zelst et al., 2019).To understand the mechanics of slip in extended fault zones the ERC project&#160;TEAR&#160;(https://www.tear-erc.eu) aims to solve the governing equations of earthquake sources based on the conservation of mass, momentum and energy and rheological models for generalized visco-elasto-plastic materials. We here present (i) 2D numerical experiments of rupture dynamics and displacement decoupling under loading for varying fault zone properties resembling observations from the San Jacinto Fault Zone in a weak discontinuity approach&#160; sing a diffuse fault representation (adapted stress-glut approach, Madariaga et al., 1998) within a PETSc spectral element discretisation of the seismic wave equation; (ii) Verification of modeling rupture dynamics using a novel diffuse interface approach using ExaHyPE (www.exahype.eu, Reinarz et al. 2019) that allows spontaneous, finite crack formation (Tavelli et al., in prep.) and adaptive mesh refinement (AMR) zooming into the process zone at the rupture tip.By this means, we start exploring scalable software for modelling shear rupture across extended, spontaneously developing fault systems for testing the hypothesis, that earthquake dynamics in fault zones can be jointly captured based on the theory of generalized visco-elasto-plastic materials.References:<ul><li>Cheng, Y. et al. Diverse volumetric faulting patterns in the San Jacinto fault zone. JGR: Solid Earth, 123.6, 5068-5081 (2018). https://doi.org/10.1029/2017JB015408</li> <li>Klinger, Y. et al. Earthquake damage patterns resolve complex rupture processes. GRL, 45, 10,279&#8211; 10,287 (2018). https://doi.org/10.1029/2018GL078842</li> <li>Madariaga, R. et al. Modeling dynamic rupture in a 3D earthquake fault model. BSSA, 88.5 (1998): 1182-1197.</li> <li>Passel&#232;gue, F. X. et al. Frictional evolution, acoustic emissions activity, and off&#8208;fault damage in simulated faults sheared at seismic slip rates. JGR: Solid Earth, 121(10), 7490-7513 (2016).&#160;doi:10.1002/2016JB012988</li> <li>Reinarz, A. et al. ExaHyPE: An Engine for Parallel Dynamically Adaptive Simulations of Wave Problems. arXiv preprint (2019), arXiv:1905.07987.</li> <li>Tavelli, M. et al. Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure, in prep.</li> <li>Van Zelst, I. et al. Modeling Megathrust Earthquakes Across Scales: One-way Coupling From Geodynamics and Seismic Cycles to Dynamic Rupture. JGR: Solid Earth,&#160;124, 11414&#8211;11446 (2019). https://doi.org/10.1029/2019JB017539</li> </ul>

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Modeling dynamic rupture in a 3D earthquake fault model

Bulletin of the Seismological Society of America ◽

10.1785/bssa0880051182 ◽

1998 ◽

Vol 88 (5) ◽

pp. 1182-1197 ◽

Cited By ~ 8

Author(s):

R. Madariaga ◽

K. Olsen ◽

R. Archuleta

Keyword(s):

Boundary Conditions ◽

Fault Zone ◽

Spontaneous Rupture ◽

Grid Method ◽

Three Dimensions ◽

Initial Stresses ◽

Staggered Grid ◽

Dynamic Rupture ◽

Plane Shear ◽

Frictional Instability

Abstract We propose a fourth-order staggered-grid finite-difference method to study dynamic faulting in three dimensions. The method uses an implementation of the boundary conditions on the fault that allows the use of general friction models including slip weakening and rate dependence. Because the staggered-grid method defines stresses and particle velocities at different grid points, we preserve symmetry by implementing a two-grid-row “thick” fault zone. Slip is computed between points located at the borders of the fault zone, while the two components of shear traction on the fault are forced to be symmetric inside the fault zone. We study the properties of the numerical method comparing our simulations with well-known properties of seismic ruptures in 3D. Among the properties that are well modeled by our method are full elastic-wave interactions, frictional instability, rupture initiation from a finite initial patch, spontaneous rupture growth at subsonic and supersonic speeds, as well as healing by either stopping phases or rate-dependent friction. We use this method for simulating spontaneous rupture propagation along an arbitrarily loaded planar fault starting from a localized asperity on circular and rectangular faults. The shape of the rupture front is close to elliptical and is systematically elongated in the inplane direction of traction drop. This elongation is due to the presence of a strong shear stress peak that moves ahead of the rupture in the in-plane direction. At high initial stresses the rupture front becomes unstable and jumps to super-shear speeds in the direction of in-plane shear. Another interesting effect is the development of relatively narrow rupture fronts due to the presence of rate-weakening friction. The solutions for the “thick fault” boundary conditions scale with the slip-weakening distance (D0) and are stable and reproducible for D0 greater than about 4 in terms of 2Tu/μ × Δx. Finally, a comparison of scalar and vector boundary conditions for the friction shows that slip is dominant along the direction of the prestress, with the largest deviations in slip-rate direction occurring near the rupture front and the edges of the fault.

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Physics-based constraints for probabilistic seismic hazard assessment in Húsavík–Flatey fault zone, Northern Iceland

10.5194/egusphere-egu2020-19007 ◽

2020 ◽

Author(s):

Bo Li ◽

Alice-Agnes Gabriel ◽

Sara A. Wirp ◽

Thomas Chartier ◽

Thomas Ulrich ◽

...

Keyword(s):

Seismic Hazard ◽

Ground Motion ◽

Fault Zone ◽

Hazard Assessment ◽

Seismic Hazard Assessment ◽

Strike Slip ◽

Probabilistic Seismic Hazard Assessment ◽

Probabilistic Seismic Hazard ◽

Dynamic Rupture ◽

Complex Fault

Probabilistic seismic hazard assessment (PSHA) is widely used to generate national seismic hazard maps, design building codes for earthquake resilient structures, determine earthquake insurance rates, and in general for the management of seismic risk. However, standard PSHA is generally based on empirical, time-independent assumptions that are simplified and not based on earthquake physics. Physics-based numerical models such as dynamic rupture simulations account for the non-linear coupling of source, path and site effects, which can be significant in their respective contributions depending on the generally complex geological environment (e.g., Wollherr et al., 2019), and could potentially complement standard PSHA. In this study we demonstrate the benefits of such an approach by modeling various rupture scenarios in the complex Hu&#769;savi&#769;k&#8211;Flatey fault zone (HFFZ), Northern Iceland. The HFFZ consists of multiple right-lateral strike slip segments distributed across ~100 km. The moment accumulated on the HFF since the last major earthquake in 1872 can result in an earthquake of magnitude 6.8 to 7 (Metzger and Jonsson, 2014) posing a high risk to Hu&#769;savi&#769;k&#8217;s community, flourishing tourism and heavy industry.We perform high-resolution 3D dynamic rupture simulations using the open-source software SeisSol (www.seissol.org), which can efficiently model spontaneous earthquake rupture across complex fault networks and seismic wave propagation with high order accuracy in space and time. Our models incorporate regional topography, bathymetry, 3D subsurface structure and varying models of the complex fault network while accounting for off-fault damage.Synthetic ground motions suggest highly heterogenous radiation patterns and intense localization of shaking in the vicinity of geometric complexities, such as fault bends or rupture transition between segments. In our models, the hypocenter location does not affect the plausible moment magnitude of large events. However, changes in rupture directivity affect the spatial distribution of ground motion significantly. &#160;We run hundreds of dynamic rupture scenarios to generate a physics-based dynamic earthquake catalog of mechanically plausible events. Based on this, we identify a possible maximum magnitude earthquake and generate model-based ground motion prediction equations to complement standard empirical ground motion models. In addition, we use the open-source python code SHERIFs (Chartier et al., 2019) to estimate the likelihood of each rupture event, which is mainly constrained by the fault slip rate estimated and fault-to-fault (f2f) rupture scenarios that are determined by the dynamic simulations. Finally, combining the fault seismic rates and the f2f probabilities with dynamic rupture scenarios and the OpenQuake framework allows us to perform physics-based PSHA for the HFFZ, the largest strike-slip fault in Iceland.

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A unified first order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones

10.5194/egusphere-egu21-15237 ◽

2021 ◽

Author(s):

Alice-Agnes Gabriel ◽

Duo Li ◽

Simone Chiocchetti ◽

Maurizio Tavelli ◽

Ilya Peshkov ◽

...

Keyword(s):

Fault Zone ◽

Scalar Fields ◽

Fault Zones ◽

Diffuse Interface ◽

Material Damage ◽

Earthquake Rupture ◽

Shear Cracks ◽

Dynamic Rupture ◽

First Order ◽

Cartesian Meshes

Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material. &#160;Field and laboratory measurements reveal complex fault zone structure involving tensile and shear fractures spanning a wide spectrum of length scales (e.g., Mitchell & Faulkner, 2009), dense seismic and geodetic recording of small and large earthquakes show hierarchical volumetric faulting patterns (e.g., Cheng et al., 2018, Ross et al., 2019) and 2D numerical models explicitly accounting for off-fault fractures demonstrate important feedback with rupture dynamics and ground motions (e.g., Thomas & Bhat 2018, Okubo et al., 2019).Here (Gabriel et al., 2021) we adopt a diffuse crack representation to incorporate finite strain nonlinear material behaviour, natural complexities and multi-physics coupling within and outside of fault zones into dynamic earthquake rupture modeling. We use a first-order hyperbolic and thermodynamically compatible mathematical model, namely the GPR model (Godunov & Romenski, 1972; Romenski, 1988), &#160;to describe a continuum in a gravitational field which provides a unified description of nonlinear elasto-plasticity, material damage and of viscous Newtonian flows with phase transition between solid and liquid phases.The model shares common features with phase-field approaches but substantially extends them. Pre-damaged faults as well as dynamically induced secondary cracks are therein described via a scalar function indicating the local level of material damage (Tavelli et al., 2020); arbitrarily complex geometries are represented via a diffuse interface approach based on a solid volume fraction function (Tavelli et al., 2019). Neither of the two scalar fields needs to be mesh-aligned, allowing thus faults and cracks with complex topology and the use of adaptive Cartesian meshes (AMR). High-order accuracy and adaptive Cartesian meshes are enabled in 2D and 3D by using the extreme scale hyperbolic PDE solver ExaHyPE (Reinarz et al., 2019).We show a wide range of numerical applications that are relevant for dynamic earthquake rupture in fault zones, including the co-seismic generation of secondary off-fault shear cracks, tensile rock fracture in the Brazilian disc test, as well as a natural convection problem in molten rock-like material. We compare diffuse interface fault models of kinematic cracks, spontaneous dynamic rupture and dynamically generated off-fault shear cracks to sharp interface reference models. To this end, we calibrate the GPR model to resemble empirical tensile and shear crack formation and friction laws. We find that the continuum model can resemble and extend classical solutions, while introducing dynamic differences (i) on the scale of pre-damaged/low-rigidity fault zone, such as out-of- plane rupture rotation; and (ii) on the scale of the intact host rock, such as conjugate shear cracking in tensile lobes.&#160;Our approach is part of the TEAR ERC project (www.tear-erc.eu) and will potentially allow to fully model volumetric fault zone shearing during earthquake rupture, which includes spontaneous partition of fault slip into intensely localized shear deformation within weaker (possibly cohesionless/ultracataclastic) fault-core gouge and more distributed damage within fault rocks and foliated gouges.

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Studying stress state and fault zone properties of source regions of induced seismicity using dynamic rupture models

10.1190/segam2019-3216344.1 ◽

2019 ◽

Author(s):

Dawid Szafranski ◽

Benchun Duan

Keyword(s):

Stress State ◽

Fault Zone ◽

Induced Seismicity ◽

Dynamic Rupture ◽

Source Regions

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Non-planar dynamic rupture modelling across diffuse, deforming fault zones using a spectral finite element method with a non-mesh aligned embedded diffuse discontinuity

10.5194/egusphere-egu21-15686 ◽

2021 ◽

Author(s):

Jorge Nicolas Hayek Valencia ◽

Dave A. May ◽

Alice-Agnes Gabriel

Keyword(s):

Finite Element ◽

Galerkin Method ◽

Fault Zone ◽

Fault Zones ◽

Diffuse Interface ◽

Earthquake Rupture ◽

Dynamic Rupture ◽

Failure Patterns ◽

Continuous Galerkin ◽

Spectral Finite Element

Faults in earthquake rupture dynamic simulations are typically treated as infinitesimally thin planes with distinct on- versus off-fault rheologies. These faults are prescribed and can be explicitly accounted for with hexahedral or unstructured tetrahedral meshing approaches.&#160;&#160; We present a diffuse interface alternative to dynamic rupture modelling on non-mesh aligned faults and, by design, permits modelling of non-planar faults and time-dependent fault geometries. We use se2dr, a spectral finite element (continuous Galerkin) method with a non-mesh aligned embedded diffuse discontinuity for dynamic rupture simulations.Natural fault systems are characterised by fault zone complexity, e.g. the frictional strength and spatio-temporal slip localisation may change drastically from the outer damage zone to the fault core. Complex volumetric failure patterns are observed in well-recorded large complex earthquakes (e.g., the 2016 Mw7.8 Kaik&#333;ura event, Klinger et al. 2018), small events (e.g.,&#160; in the San Jacinto Fault Zone, Cheng et al. 2018), and laboratory-scale experiments (e.g., in high-velocity friction experiments, Passel&#232;gue et al., 2016).We develop a diffuse description of fault slip to better understand complex volumetric failure patterns and the mechanics of slip in diffuse fault zones. The fault is defined via a signed distance function (s(x)), which is in turn used to define a fault indicator function with compact support H. If s(x) > H the material behaves as a pure elastic solid - otherwise the tangential stress is governed by a frictional sliding law. Our approach is implemented on a structured hexahedral mesh using a spectral finite element (continuous Galerkin) method for wave propagation using PETSc. Our diffuse fault SEM method is inspired by the stress-glut method of Andrews, 1999.&#160; A non-mesh aligned embedded diffusive discontinuity allows for complex dynamic rupture simulations. We present 2D numerical experiments of kinematically driven rupture and spontaneous dynamic rupture on non-planar and non-mesh aligned complex fault geometries. The method can be used to model earthquake rupture dynamics on specifically complex and evolving fault faults such as the San Jacinto, CA, fault, or shallowly dipping megathrusts and splay faulting structures in subduction zones.

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