arXiv subjects

Eric M. Dunham

Publications and source records attributed to Eric M. Dunham.

6 recordsLinked to original sources

arXiv2024

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.

math.NA↗

arXiv2021

3D Acoustic-Elastic Coupling with Gravity: The Dynamics of the 2018 Palu, Sulawesi Earthquake and Tsunami

We present a highly scalable 3D fully-coupled Earth & ocean model of earthquake rupture and tsunami generation. We model seismic, acoustic and surface gravity wave propagation in elastic (Earth) and acoustic (ocean) materials sourced by physics-based non-linear earthquake dynamic rupture. Complicated geometries, including high-resolution bathymetry, coastlines and segmented earthquake faults are discretized by adaptive unstructured tetrahedral meshes. A Discontinuous Galerkin discretization with ADER local time-stepping (ADER-DG) yields petascale computational efficiency and high-order accuracy in time and space. We compare the 3D fully-coupled approach to a benchmark problem for 3D-2D linked models that use 2D shallow-water modeling. We present a large-scale fully-coupled model of the 2018 Sulawesi events that links the dynamics from supershear earthquake faulting to elastic and acoustic waves in Earth and ocean to tsunami gravity wave propagation in the narrow Palu Bay. And we demonstrate scalability and performance of the MPI+OpenMP parallelization on three petascale supercomputers.

physics.comp-ph↗

arXiv2020

Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions

Summation-by-parts (SBP) finite difference methods have several desirable properties for second-order wave equations. They combine the computational efficiency of narrow-stencil finite difference operators with provable stability on curvilinear multiblock grids. While several techniques for boundary and interface conditions exist, weak imposition via simultaneous approximation terms (SATs) is perhaps the most flexible one. Although SBP methods have been applied to elastic wave equations many times, an SBP-SAT method for general anisotropic elastic wave equations has not yet been presented in the literature. We fill this gap by deriving energy-stable self-adjoint SBP-SAT methods for general anisotropic materials on curvilinear multiblock grids. The methods are based on fully compatible SBP operators. Although this paper focuses on classical SBP finite difference operators, the presented boundary and interface treatments are general and apply to a range of methods that satisfy an SBP property. We demonstrate the stability and accuracy properties of a particular set of fully compatible SBP-SAT schemes using the method of manufactured solutions. We also demonstrate the utility of the new method in elastodynamic cloaking and seismic imaging in mountainous regions.

math.NA↗

arXiv2020

Fault Valving and Pore Pressure Evolution in Simulations of Earthquake Sequences and Aseismic Slip

Fault-zone fluids control effective normal stress and fault strength. While most earthquake models assume a fixed pore fluid pressure distribution, geologists have documented fault valving behavior, that is, cyclic changes in pressure and unsteady fluid migration along faults. Here we quantify fault valving through 2-D antiplane shear simulations of earthquake sequences on a strike-slip fault with rate-and-state friction, upward Darcy flow along a permeable fault zone, and permeability evolution. Fluid overpressure develops during the interseismic period, when healing/sealing reduces fault permeability, and is released after earthquakes enhance permeability. Coupling between fluid flow, permeability and pressure evolution, and slip produces fluid-driven aseismic slip near the base of the seismogenic zone and earthquake swarms within the seismogenic zone, as ascending fluids pressurize and weaken the fault. This model might help explain observations of late interseismic fault unlocking, slow slip and creep transients, swarm seismicity, and rapid pressure/stress transmission in induced seismicity sequences.

physics.geo-ph↗

arXiv2020

Spring-Slider and Finite Element Modeling of Microseismic Events and Fault Slip during Hydraulic Fracturing

Hydraulic fracturing increases reservoir permeability by opening fractures and triggering slip on natural fractures and faults. While seismic slip of small faults or fault patches is detectable as microseismic events, the role of aseismic slip is poorly understood. From a modeling standpoint, geomechanical analysis using the Coulomb criterion can determine if faults slip but not whether slip is seismic or aseismic. Here we propose a computational methodology to predict fault slip, and whether slip is seismic or aseismic, using rate-and-state friction. To avoid computational costs associated with resolving small faults, we use the spring-slider idealization that treats faults as points. Interaction between faults is neglected. The method is applied to study fault slip from a hydraulic fracture that grows past a fault, without intersecting it. We represent the hydraulic fracture stressing using an asymptotic expansion of stresses around the tip of a tensile crack. We investigate the effect of fault length, orientation, and distance from the hydraulic fracture. For velocity-weakening faults with stiffness smaller than a critical stiffness, slip is seismic, whereas faults with stiffness greater than the critical stiffness slip aseismically. Furthermore, we compare the spring-slider idealization with a finite element analysis that resolves spatially variable slip. The spring-slider idealization provides reasonably accurate predictions of moment and even moment-rate history, especially for faults having stiffness close to or larger than the critical stiffness. Differences appear for large faults where rupture propagation is important, though differences might still be negligible for many applications.

physics.geo-ph↗

arXiv2019

Non-stiff narrow-stencil finite difference approximations of the Laplacian on curvilinear multiblock grids

The Laplacian appears in several partial differential equations used to model wave propagation. Summation-by-parts--simultaneous approximation term (SBP-SAT) finite difference methods are often used for such equations, as they combine computational efficiency with provable stability on curvilinear multiblock grids. However, the existing SBP-SAT discretization of the Laplacian quickly becomes prohibitively stiff as grid skewness increases. The stiffness stems from the SATs that impose inter-block couplings and Dirichlet boundary conditions. We resolve this issue by deriving stable SATs whose stiffness is almost insensitive to grid skewness. The new discretization thus allows for large time steps in explicit time integrators, even on very skewed grids. It also applies to the variable-coefficient generalization of the Laplacian. We demonstrate the efficacy and versatility of the new method by applying it to acoustic wave propagation problems inspired by marine seismic exploration and infrasound monitoring of volcanoes.

math.NA↗