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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. • New boundary and interface treatments for anisotropic elastic wave equations. • Proofs of energy stability and discrete self-adjointness. • Application problems in elastodynamic cloaking and seismic imaging. [ABSTRACT FROM AUTHOR]

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. • An inversion method for parameters in earthquake modeling is presented. • Adjoint equations to linear elasticity with rate-state frictional faults are derived. • Efficient misfit gradient evaluation by solving the forward and adjoint equations. • Dual-consistent discretization of dynamic rupture problem in antiplane shear. • Inversion experiments in dynamic rupture corroborate theoretical results. [ABSTRACT FROM AUTHOR]

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 SATs by applying them to acoustic wave propagation problems inspired by marine seismic exploration and infrasound monitoring of volcanoes. • We derive new boundary and interface treatments for the Laplacian on curved grids. • We demonstrate reduced CPU times compared to the state-of-the-art method. • We apply the method to seismic exploration and infrasound monitoring of volcanoes. [ABSTRACT FROM AUTHOR]

Fault bends are known to act as barriers to rupture propagation in many earthquakes. A recent compilation of the surface rupture traces of paleo earthquakes quantifies the probability of rupture termination as a function of the bend angle. To understand the physical basis of these unique statistics, we carry out 2D quasi-dynamic earthquake sequence simulations on a fault with either a restraining or releasing (double-) bend. The fault is loaded by steady sliding from an adjacent creeping region, rather than with backslip, together with a stress relaxation method to avoid unphysical stress buildup due to the curvature of faults. This relaxation is a proxy for unmodeled off-fault secondary faulting. This ensures the existence of a long-term steady earthquake cycle and stress field, the latter of which is determined by the balance between the slip-induced stress changes and relaxation terms. We quantify the influence of the bend on rupture propagation by computing passing ratio (i.e., the fraction of ruptures that propagate through the bend). Our simulations approximately reproduce the Biasi-Wesnousky empirical law for a wide range of parameters (e.g., bend width, stress relaxation time, background stress). Also, we reproduce geologic observations that the long-term slip rate of a fault has local minima at restraining bends, without assuming spatially varying loading rates using the backslip approach. Additionally, we find that restraining and releasing bends have different earthquake cycles. For restraining bends, many ruptures are arrested before reaching the center of the bend, and the passing ratio decreases with increasing the bend angle. For releasing bends, ruptures stop after passing the center of the bend, and the passing ratio abruptly drops from near unity to zero at around 20 ∘. This difference can be qualitatively explained by an energy balance approach. Our model has a potential to understand the seismogenesis of nonplanar faults and we can readily extend our model into 3D specific fault systems for hazard assessment. • We perform earthquake cycle simulations on a fault with either restraining or releasing bend. • We quantify how often a rupture propagates through the bend. • The simulation result is consistent with empirical law from natural earthquakes that passing ratio decreases with bend angle. [ABSTRACT FROM AUTHOR]

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity. [ABSTRACT FROM AUTHOR]

We introduce an energy stable, high-order-accurate finite difference approximation of the dynamic, pure bending Kirchhoff plate equations for complex geometries and spatially variable properties. We utilize the summation-by-parts (SBP) framework to discretize the biharmonic operator with variable coefficients, with attention given to free and clamped boundary conditions and corner conditions. Energy conservation is established by combining SBP boundary closures with weak enforcement of the boundary and interface conditions using a penalty (simultaneous approximation term, SAT) technique. Then we couple the plate equations to the shallow water equations to study flexural-gravity wave propagation, and prove that the semi-discrete system of equations is self-adjoint. We demonstrate the stability and accuracy properties of the method on curvilinear multiblock grids using the method of manufactured solutions. The method, which we provide in an open-source code, is then used to model ocean wave interactions with the Thwaites Glacier and Pine Island Ice Shelf in the Amundsen Sea off the coast of West Antarctica. • Finite difference discretization of variable coefficient biharmonic operator with boundary treatment. • Proof of energy stability and semi-discrete self-adjointness. • Application problems in ocean wave-ice shelf interactions off the coast of West Antarctica. [ABSTRACT FROM AUTHOR]

Induced seismicity (earthquakes caused by injection or extraction of fluids in Earth’s subsurface) is a major, new hazard in the USA, the Netherlands, and other countries, with vast economic consequences if not properly managed. Addressing this problem requires development of predictive simulations of how fluid-saturated solids containing frictional faults respond to fluid injection/extraction. Here, we present a finite difference method for 2D linear poroelasticity with rate-and-state friction faults, accounting for spatially variable properties. Semi-discrete stability and accuracy are proven using the summation-by-parts, simultaneous-approximation-term (SBP-SAT) framework for discretization and boundary condition enforcement. Convergence rates are verified using the method of manufactured solutions and comparison to the analytical solution to Mandel’s problem. The method is then applied to study fault slip triggered by fluid injection and diffusion through high-permeability fault damage zones. We demonstrate that in response to the same, gradual forcing, fault slip can occur in either an unstable manner, as short-duration earthquakes that radiate seismic waves, or as stable, aseismic, slow slip that accumulates over much longer time scales. Finally, we use these simulation results to discuss the role of frictional and elastic properties in determining the stability and nature of slip. [ABSTRACT FROM AUTHOR]

Injection-induced seismicity and aseismic slip often involve the reactivation of long-dormant faults, which may have extremely low permeability prior to slip. In contrast, most previous models of fluid-driven aseismic slip have assumed linear pressure diffusion in a fault zone of constant permeability and porosity. Slip occurs within a frictional shear crack whose edge can either lag or lead pressure diffusion, depending on the dimensionless stress-injection parameter that quantifies the prestress and injection conditions. Here, we extend this foundational work by accounting for permeability enhancement and dilatancy, assumed to occur instantaneously upon the onset of slip. The fault zone ahead of the crack is assumed to be impermeable, so fluid flow and pressure diffusion are confined to the interior, slipped part of the crack. The confinement of flow increases the pressurization rate and reduction of fault strength, facilitating crack growth even for severely understressed faults. Suctions from dilatancy slow crack growth, preventing propagation beyond the hydraulic diffusion length. Our new two-dimensional and three-dimensional solutions can facilitate the interpretation of induced seismicity data sets. They are especially relevant for faults in initially low permeability formations, such as shale layers serving as caprock seals for geologic carbon storage, or for hydraulic stimulation of geothermal reservoirs.This article is part of the theme issue 'Induced seismicity in coupled subsurface systems'.

There is a growing recognition that subsurface fluid injection can produce not only earthquakes, but also aseismic slip on faults. A major challenge in understanding interactions between injection-related aseismic and seismic slip on faults is identifying aseismic slip on the field scale, given that most monitored fields are only equipped with seismic arrays. We present a modeling workflow for evaluating the possibility of aseismic slip, given observational constraints on the spatial-temporal distribution of microseismicity, injection rate, and wellhead pressure. Our numerical model simultaneously simulates discrete off-fault microseismic events and aseismic slip on a main fault during fluid injection. We apply the workflow to the 2012 Enhanced Geothermal System injection episode at Cooper Basin, Australia, which aimed to stimulate a water-saturated granitic reservoir containing a highly permeable ([Formula: see text] [Formula: see text]) fault zone. We find that aseismic slip likely contributed to half of the total moment release. In addition, fault weakening from pore pressure changes, not elastic stress transfer from aseismic slip, induces the majority of observed microseismic events, given the inferred stress state. We derive a theoretical model to better estimate the time-dependent spatial extent of seismicity triggered by increases in pore pressure. To our knowledge, this is the first time injection-induced aseismic slip in a granitic reservoir has been inferred, suggesting that aseismic slip could be widespread across a range of lithologies., (© 2022. The Author(s).)