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- Erickson, Brittany A., et al.
(author)
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Incorporating Full Elastodynamic Effects and Dipping Fault Geometries in Community Code Verification Exercises for Simulations of Earthquake Sequences and Aseismic Slip (SEAS)
- 2023
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In: Bulletin of The Seismological Society of America (BSSA). - : SEISMOLOGICAL SOC AMER. - 0037-1106 .- 1943-3573. ; 113:2, s. 499-523
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Journal article (peer-reviewed)abstract
- Numerical modeling of earthquake dynamics and derived insight for seismic hazard relies on credible, reproducible model results. The sequences of earthquakes and aseismic slip (SEAS) initiative has set out to facilitate community code comparisons, and verify and advance the next generation of physics-based earthquake models that reproduce all phases of the seis-mic cycle. With the goal of advancing SEAS models to robustly incorporate physical and geo-metrical complexities, here we present code comparison results from two new benchmark problems: BP1-FD considers full elastodynamic effects, and BP3-QD considers dipping fault geometries. Seven and eight modeling groups participated in BP1-FD and BP3-QD, respectively, allowing us to explore these physical ingredients across multiple codes and better understand associated numerical considerations. With new comparison metrics, we find that numerical resolution and computational domain size are critical parameters to obtain matching results. Codes for BP1-FD implement different criteria for switching between quasi-static and dynamic solvers, which require tuning to obtain matching results. In BP3-QD, proper remote boundary conditions consistent with specified rigid body translation are required to obtain matching surface displacements. With these numerical and mathematical issues resolved, we obtain excellent quantitative agreements among codes in earthquake interevent times, event moments, and coseismic slip, with reasonable agreements made in peak slip rates and rupture arrival time. We find that including full inertial effects generates events with larger slip rates and rupture speeds compared to the quasi-dynamic counterpart. For BP3-QD, both dip angle and sense of motion (thrust versus normal faulting) alter ground motion on the hanging and foot walls, and influence event patterns, with some sequences exhibiting similar-size character-istic earthquakes, and others exhibiting different-size events. These findings underscore the importance of considering full elastodynamics and nonvertical dip angles in SEAS models, as both influence short-and long-term earthquake behavior and are relevant to seismic hazard.
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| 4. |
- Kozdon, Jeremy E., et al.
(author)
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Interaction of waves with frictional interfaces using summation-by-parts difference operators : Weak enforcement of nonlinear boundary conditions
- 2011
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Reports (peer-reviewed)abstract
- We present a high-order difference method for problems in elastodynamics involving the interaction of waves with highly nonlinear frictional interfaces. We restrict our attention to two-dimensional antiplane problems involving deformation in only one direction. Jump conditions that relate tractions on the interface, or fault, to the relative sliding velocity across it are of a form closely related to those used in earthquake rupture models and other frictional sliding problems. By using summation-by-parts (SBP) finite difference operators and weak enforcement of boundary and interface conditions, a strictly stable method is developed. Furthermore, it is shown that unless the nonlinear interface conditions are formulated in terms of characteristic variables, as opposed to the physical variables in terms of which they are more naturally stated, the semi-discretized system of equations can become extremely stiff, preventing efficient solution using explicit time integrators. The use of SBP operators also provides a rigorously defined energy balance for the discretized problem that, as the mesh is refined, approaches the exact energy balance in the continuous problem. This enables one to investigate earthquake energetics, for example the efficiency with which elastic strain energy released during rupture is converted to radiated energy carried by seismic waves, rather than dissipated by frictional sliding of the fault. These theoretical results are confirmed by several numerical tests in both one and two dimensions demonstrating the computational efficiency, the high-order convergence rate of the method, the benefits of using strictly stable numerical methods for long time integration, and the accuracy of the energy balance.
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| 6. |
- Kozdon, Jeremy E., et al.
(author)
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Interaction of waves with frictional interfaces using summation-by-parts difference operators I : Weak enforcement of nonlinear boundary conditions
- 2010
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Reports (other academic/artistic)abstract
- In this work we develop a high-order method for problems in scalar elastodynamics with nonlinear boundary conditions in a form closely related to those seen in earthquake rupture modeling and other frictional sliding problems. By using summation-by-parts finite difference operators and weak enforcement of boundary conditions with the simultaneous approximation term method, a strictly stable method is developed that dissipates energy at a slightly faster rate than the continuous solution (with the difference in energy dissipation rates vanishing as the mesh is refined). Furthermore, it is shown that unless boundary conditions are formulated in terms of characteristic variables, as opposed to the physical variables in terms of which boundary conditions are more naturally stated, the semi-discretized system of equations can become extremely stiff, preventing efficient solution using explicit time integrators.These theoretical results are confirmed by several numerical tests demonstrating the high-order convergence rate of the method and the benefits of using strictly stable numerical methods for long time integration.
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| 7. |
- Kozdon, Jeremy E., et al.
(author)
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Interaction of waves with frictional interfaces using summation-by-parts difference operators II : Extension to full elastodynamics
- 2010
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Reports (other academic/artistic)abstract
- Problems in elastodynamics with nonlinear boundary conditions, such as those arising when modeling earthquake rupture propagation along internal interfaces (faults) governed by nonlinear friction laws, are inherently boundary driven. For such problems, stable and accurate enforcement of boundary conditions is essential for obtaining globally accurate numerical solutions (and predictions of ground motion in earthquake simulations). High-order finite difference methods are a natural choice for problems like these involving wave propagation, but enforcement of boundary conditions is complicated by the fact that the stencil must transition to one-sided near the boundary.In this work we develop a high-order method for tensor elasticity with faults whose strength is a nonlinear function of sliding velocity and a set of internal state variables obeying differential evolution equations (a mathematical framework known as rate-and-state friction). The method is based on summation-by-parts finite difference operators and weak enforcement of boundary conditions using the simultaneous approximation term method. We prove that the method is strictly stable and dissipates energy at a slightly faster rate than the continuous solution (with the difference in energy dissipation rates vanishing as the mesh is refined)
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| 8. |
- Kozdon, Jeremy E., et al.
(author)
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Interaction of Waves with Frictional Interfaces Using Summation-by-Parts Difference Operators: Weak Enforcement of Nonlinear Boundary Conditions
- 2012
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In: Journal of Scientific Computing. - : Springer. - 0885-7474 .- 1573-7691. ; 50:2, s. 341-367
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Journal article (peer-reviewed)abstract
- We present a high-order difference method for problems in elastodynamics involving the interaction of waves with highly nonlinear frictional interfaces. We restrict our attention to two-dimensional antiplane problems involving deformation in only one direction. Jump conditions that relate tractions on the interface, or fault, to the relative sliding velocity across it are of a form closely related to those used in earthquake rupture models and other frictional sliding problems. By using summation-by-parts (SBP) finite difference operators and weak enforcement of boundary and interface conditions, a strictly stable method is developed. Furthermore, it is shown that unless the nonlinear interface conditions are formulated in terms of characteristic variables, as opposed to the physical variables in terms of which they are more naturally stated, the semi-discretized system of equations can become extremely stiff, preventing efficient solution using explicit time integrators. The use of SBP operators also provides a rigorously defined energy balance for the discretized problem that, as the mesh is refined, approaches the exact energy balance in the continuous problem. This enables one to investigate earthquake energetics, for example the efficiency with which elastic strain energy released during rupture is converted to radiated energy carried by seismic waves, rather than dissipated by frictional sliding of the fault. These theoretical results are confirmed by several numerical tests in both one and two dimensions demonstrating the computational efficiency, the high-order convergence rate of the method, the benefits of using strictly stable numerical methods for long time integration, and the accuracy of the energy balance.
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| 9. |
- Kozdon, Jeremy E., et al.
(author)
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Simulation of Dynamic Earthquake Ruptures in Complex Geometries Using High-Order Finite Difference Methods
- 2012
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Reports (other academic/artistic)abstract
- We develop a stable and high-order accurate finite difference method for problems in earthquake rupture dynamics capable of handling complex geometries and multiple faults. The bulk material is an isotropic elastic solid cut by preexisting fault interfaces. The fields across the interfaces are related through friction laws which depend on the sliding velocity, tractions acting on the interface, and state variables which evolve according to ordinary differential equations involving local fields. The method is based on summation-by-parts finite difference operators with irregular geometries handled through coordinate transforms and multi-block meshes. Boundary conditions as well as block interface conditions (whether frictional or otherwise) are enforced weakly through the simultaneous approximation term method, resulting in a provably stable discretization. The theoretical accuracy and stability results are confirmed with the method of manufactured solutions. The practical benefits of the new methodology are illustrated in a simulation of a subduction zone megathrust earthquake, a challenging application problem involving complex free-surface topography, nonplanar faults, and varying material properties.
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| 10. |
- Kozdon, Jeremy E., et al.
(author)
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Simulation of Dynamic Earthquake Ruptures in Complex Geometries Using High-Order Finite Difference Methods
- 2013
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In: Journal of Scientific Computing. - : Springer. - 0885-7474 .- 1573-7691. ; 55:1, s. 92-124
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Journal article (peer-reviewed)abstract
- We develop a stable and high-order accurate finite difference method for problems in earthquake rupture dynamics in complex geometries with multiple faults. The bulk material is an isotropic elastic solid cut by pre-existing fault interfaces that accommodate relative motion of the material on the two sides. The fields across the interfaces are related through friction laws which depend on the sliding velocity, tractions acting on the interface, and state variables which evolve according to ordinary differential equations involving local fields. The method is based on summation-by-parts finite difference operators with irregular geometries handled through coordinate transforms and multi-block meshes. Boundary conditions as well as block interface conditions (whether frictional or otherwise) are enforced weakly through the simultaneous approximation term method, resulting in a provably stable discretization. The theoretical accuracy and stability results are confirmed with the method of manufactured solutions. The practical benefits of the new methodology are illustrated in a simulation of a subduction zone megathrust earthquake, a challenging application problem involving complex free-surface topography, nonplanar faults, and varying material properties.
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