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

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

<p>Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material.  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).</p><p>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),  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.</p><p>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).</p><p>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. </p><p>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.</p>

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

2021 ◽  
Vol 379 (2196) ◽  
pp. 20200130 ◽  
Author(s):  
A.-A. Gabriel ◽  
D. Li ◽  
S. Chiocchetti ◽  
M. Tavelli ◽  
I. Peshkov ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Scalar Fields ◽  
Fault Zones ◽  
Nonlinear Material ◽  
Diffuse Interface ◽  
Hyperbolic Model ◽  
Material Damage ◽  
First Order ◽  
Secondary Cracks ◽  
Wide Range

Earthquake fault zones are more complex, both geometrically and rheologically, than an idealized infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities and multi-physics coupling within and outside of fault zones, here we present a first-order hyperbolic and thermodynamically compatible mathematical model for 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 fault geometry and secondary cracks are described via a scalar function ξ  ∈ [0, 1] that indicates the local level of material damage. The model also permits the representation of arbitrarily complex geometries via a diffuse interface approach based on the solid volume fraction function α  ∈ [0, 1]. Neither of the two scalar fields ξ and α needs to be mesh-aligned, allowing thus faults and cracks with complex topology and the use of adaptive Cartesian meshes (AMR). The model shares common features with phase-field approaches, but substantially extends them. 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. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

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

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

<p>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.  <br>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.</p><p>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 Kaikōura event, Klinger et al. 2018), small events (e.g.,  in the San Jacinto Fault Zone, Cheng et al. 2018), and laboratory-scale experiments (e.g., in high-velocity friction experiments, Passelègue et al., 2016).</p><p>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.<br>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.  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.</p>

Modeling earthquake rupture dynamics across diffuse deforming fault zones

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

<p>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.<span> </span></p><p>While complex volumetric failure patterns of fault networks are observed from well-recorded large earthquakes (e.g., the 2016 M<sub>w</sub>7.8 Kaikōura event, <em>Klinger et al. 2018</em>) and small earthquakes (e.g., events in the San Jacinto Fault Zone, <em>Cheng et al. 2018</em>) as well as in laboratory experiments (e.g., in high-velocity friction experiments,<em> Passelègue et al., 2016</em>) 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 (<em>van Zelst et al., 2019</em>).</p><p>To understand the mechanics of slip in extended fault zones the ERC project <strong>TEAR</strong> (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<span>  </span>sing a diffuse fault representation (adapted stress-glut approach, Madariaga et al., 1998) within a <em>PETSc</em> spectral element discretisation of the seismic wave equation; (ii) Verification of modeling rupture dynamics using a novel diffuse interface approach using<em> ExaHyPE</em> (www.exahype.eu, <em>Reinarz et al. 2019</em>) that allows spontaneous, finite crack formation (<em>Tavelli et al.,</em> in prep.) and adaptive mesh refinement (AMR) zooming into the process zone at the rupture tip.</p><p>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.</p><p>References:</p><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– 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>Passelègue, F. X. et al. Frictional evolution, acoustic emissions activity, and off‐fault damage in simulated faults sheared at seismic slip rates. JGR: Solid Earth, 121(10), 7490-7513 (2016). 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, <span>124</span>, <span>11414</span>–<span>11446</span> (2019). https://doi.org/10.1029/2019JB017539</li> </ul>

scholarly journals Seismic velocity structure at the southern termination of the 2016 Kumamoto Earthquake rupture, Japan

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Yasuhira Aoyagi ◽  
Haruo Kimura ◽  
Kazuo Mizoguchi
Keyword(s):  
Fault Zone ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Earthquake Rupture ◽  
2016 Kumamoto Earthquake ◽  
Seismic Velocity Structure ◽  
Kumamoto Earthquake ◽  
Seismogenic Layer ◽  
The 2016 Kumamoto Earthquake ◽  
Tectonic Line

Abstract The earthquake rupture termination mechanism and size of the ruptured area are crucial parameters for earthquake magnitude estimations and seismic hazard assessments. The 2016 Mw 7.0 Kumamoto Earthquake, central Kyushu, Japan, ruptured a 34-km-long area along previously recognized active faults, eastern part of the Futagawa fault zone and northernmost part of the Hinagu fault zone. Many researchers have suggested that a magma chamber under Aso Volcano terminated the eastward rupture. However, the termination mechanism of the southward rupture has remained unclear. Here, we conduct a local seismic tomographic inversion using a dense temporary seismic network to detail the seismic velocity structure around the southern termination of the rupture. The compressional-wave velocity (Vp) results and compressional- to shear-wave velocity (Vp/Vs) structure indicate several E–W- and ENE–WSW-trending zonal anomalies in the upper to middle crust. These zonal anomalies may reflect regional geological structures that follow the same trends as the Oita–Kumamoto Tectonic Line and Usuki–Yatsushiro Tectonic Line. While the 2016 Kumamoto Earthquake rupture mainly propagated through a low-Vp/Vs area (1.62–1.74) along the Hinagu fault zone, the southern termination of the earthquake at the focal depth of the mainshock is adjacent to a 3-km-diameter high-Vp/Vs body. There is a rapid 5-km step in the depth of the seismogenic layer across the E–W-trending velocity boundary between the low- and high-Vp/Vs areas that corresponds well with the Rokkoku Tectonic Line; this geological boundary is the likely cause of the dislocation of the seismogenic layer because it is intruded by serpentinite veins. A possible factor in the southern rupture termination of the 2016 Kumamoto Earthquake is the existence of a high-Vp/Vs body in the direction of southern rupture propagation. The provided details of this inhomogeneous barrier, which are inferred from the seismic velocity structures, may improve future seismic hazard assessments for a complex fault system composed of multiple segments.

scholarly journals First-order formalism for twinlike models with several real scalar fields

2014 ◽  
Vol 74 (2) ◽  
Author(s):  
D. Bazeia ◽  
A. S. Lobão ◽  
L. Losano ◽  
R. Menezes
Keyword(s):  
Scalar Fields ◽  
First Order ◽  
Real Scalar

DETAIL GRAVITY PROFILE ACROSS SAN ANDREAS FAULT ZONE

Geophysics ◽  
1967 ◽  
Vol 32 (2) ◽  
pp. 297-301 ◽  
Author(s):  
S. N. Domenico
Keyword(s):  
Fault Zone ◽  
Mojave Desert ◽  
San Andreas Fault ◽  
Surface Expression ◽  
Fault Zones ◽  
Rock Masses ◽  
San Andreas ◽  
Major Fault ◽  
Reduced Density ◽  
Gravity Profile

A gravity profile was obtained from closely spaced readings along a traverse approximately nine miles in length across the San Andreas fault zone immediately south of Palmdale, California in the western Mojave Desert. Corrected gravity values show a slight but distinctive minimum associated with the fault zone which may be attributed to the reduced density of the shattered rock masses in the fault zone. The existence of this minimum suggests that major fault zones may be traced across terrain, on which surface expression of the fault does not exist, by successive profiles across the suspected position of the fault zone.

scholarly journals Rupture-dependent breakdown energy in fault models with thermo-hydro-mechanical processes

2020 ◽  
Author(s):  
Valère Lambert ◽  
Nadia Lapusta
Keyword(s):  
Material Property ◽  
Numerical Models ◽  
Slip Rate ◽  
Shear Cracks ◽  
Dynamic Rupture ◽  
Rupture Dynamics ◽  
Stress Changes ◽  
History Of ◽  
Thermal Pressurization ◽  
Pass Through

Abstract. Substantial insight into earthquake source processes has resulted from considering frictional ruptures analogous to cohesive-zone shear cracks from fracture mechanics. This analogy holds for slip-weakening representations of fault friction that encapsulate the resistance to rupture propagation in the form of breakdown energy, analogous to fracture energy, prescribed in advance as if it were a material property of the fault interface. Here, we use numerical models of earthquake sequences with enhanced weakening due to thermal pressurization of pore fluids to show how accounting for thermo-hydro-mechanical processes during dynamic shear ruptures makes breakdown energy rupture-dependent. We find that local breakdown energy is neither a constant material property nor uniquely defined by the amount of slip attained during rupture, but depends on how that slip is achieved through the history of slip rate and dynamic stress changes during the rupture process. As a consequence, the frictional breakdown energy of the same location along the fault can vary significantly in different earthquake ruptures that pass through. These results suggest the need for re-examining the assumption of pre-determined frictional breakdown energy common in dynamic rupture modeling and for better understanding of the factors that control rupture dynamics in the presence of thermo-hydro-mechanical processes.

scholarly journals Heterogeneous stresses and deformation mechanisms at shallow crustal conditions, Hungaroa Fault Zone, Hikurangi Subduction Margin, New Zealand

2020 ◽  
Author(s):  
Carolyn Boulton ◽  
Marcel Mizera ◽  
Maartje Hamers ◽  
Inigo Müller ◽  
Martin Ziegler ◽  
...  
Keyword(s):  
Friction Coefficient ◽  
Fault Zone ◽  
Mixed Mode ◽  
Fluid Pressure ◽  
Fault Zones ◽  
Deformation Mechanisms ◽  
Multiple Observations ◽  
Calcite Veins ◽  
Dynamic Recrystallisation ◽  
Clumped Isotope

<p>The Hungaroa Fault Zone (HFZ), an inactive thrust fault along the Hikurangi Subduction Margin, accommodated large displacements (~4–10 km) at the onset of subduction in the early Miocene. Within a 40 m-wide high-strain fault core, calcareous mudstones and marls display evidence for mixed-mode viscous flow and brittle fracture, including: discrete faults; extensional veins containing stretched calcite fibers; shear veins with calcite slickenfibers; calcite foliation-boudinage structures; calcite pressure fringes; dark dissolution seams; stylolites; embayed calcite grains; and an anastomosing phyllosilicate foliation.</p><p>Multiple observations indicate a heterogeneous stress state within the fault core. Detailed optical and electron backscatter diffraction-based texture analysis of syntectonic calcite veins and isoclinally folded limestone layers within the fault core reveal that calcite grains have experienced intracrystalline plasticity and interface mobility, and local subgrain development and dynamic recrystallisation. The recrystallized grain size in two calcite veins of 6.0±3.9 µm (n=1339; 1SD; HFZ-H4-5.2m_A;) and 7.2±4.2µm (n=406; 1SD; HFZ-H4-19.9m) indicate high differential stresses (~76–134 MPa). Hydrothermal friction experiments on a foliated, calcareous mudstone yield a friction coefficient of μ≈0.35. Using this friction coefficient in the Mohr-Coulomb failure criterion yields a maximum differential stress of 55 MPa at 4 km depth, assuming a minimum principal stress equal to the vertical stress, an average sediment density of 2350 kg/m<sup>3</sup>, and hydrostatic pore fluid pressure. Interestingly, calcareous microfossils within the foliated mudstone matrix are undeformed. Moreover, calcite veins are oriented both parallel to and highly oblique to the foliation, indicating spatial and/or temporal variations in the maximum principle stress azimuth.</p><p>To further constrain HFZ deformation conditions, clumped isotope geothermometry was performed on six syntectonic calcite veins, yielding formation temperatures of 79.3±19.9°C (95% confidence interval). These temperatures are well below those at which dynamic recrystallisation of calcite is anticipated and exclude shear heating and the migration of hotter fluids as an explanation for dynamic recrystallisation of calcite at shallow crustal levels (<5 km depth).</p><p>Our results indicate that: (1) stresses are spatiotemporally heterogeneous in crustal fault zones containing mixtures of competent and incompetent minerals; (2) heterogeneous deformation mechanisms, including frictional sliding, pressure solution, dynamic recrystallization, and mixed-mode fracturing accommodate slip in shallow crustal fault zones; and (3) brittle fractures play a pivotal role in fault zone deformation by providing fluid pathways that promote fluid-enhanced recovery and dynamic recrystallisation in the deforming calcite at remarkably low temperatures. Together, field geology, microscopy, and clumped isotope geothermometry provide a powerful method for constraining the multiscale slip behavior of large-displacement fault zones.</p>

scholarly journals Geomorphological reconnaissance of the Psathopyrgos and Rion-Patras Fault zones (Achaia, NW Peloponnesus).

2007 ◽  
Vol 40 (4) ◽  
pp. 1586 ◽  
Author(s):  
N. Palyvos ◽  
D. Pantosti ◽  
L. Stamatopoulos ◽  
P. M. De Martini
Keyword(s):  
Fault Zone ◽  
Fault Zones ◽  
Fault Slip ◽  
Geological Data ◽  
Slip Rates ◽  
The Holocene ◽  
Fault Slip Rates ◽  
Earthquake Ruptures ◽  
Surficial Deposits

In this communication we discuss reconnaissance geomorphological observations along the active Psathopyrgos and Rion-Patras (NE part) fault zones. These fault zones correspond to more or less complex rangefronts, the geomorphic characteristics of which provide hints on the details of the fault zone geometries, adding to the existing geological data in the bibliography. Aiming at the identification of locations suitable or potentially suitable for geomorphological and geological studies for the determination of fault slip rates in the Holocene, we describe cases of faulted Holocene landforms and associated surficial deposits. We also discuss problems involved in finding locations suitable for geological (paleoseismological) studies for the determination of the timing of recent earthquake ruptures, problems due to both man-made and natural causes.

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