The State of Pore Fluid Pressure and 3-D Megathrust Earthquake Dynamics

We study the effects of pore fluid pressure (P-f) on the pre-earthquake, near-fault stress state, and 3-D earthquake rupture dynamics through six scenarios utilizing a structural model based on the 2004 M-w 9.1 Sumatra-Andaman earthquake. As pre-earthquake P-f magnitude increases, effective normal stress and fault shear strength decrease. As a result, magnitude, slip, peak slip rate, stress drop, and rupture velocity of the scenario earthquakes decrease. Comparison of results with observations of the 2004 earthquake support that pre-earthquake P-f averages near 97% of lithostatic pressure, leading to pre-earthquake average shear and effective normal tractions of 4-5 and 22 MPa. The megathrust in these scenarios is weak, in terms of low mean shear traction at static failure and low dynamic friction coefficient during rupture. Apparent co-seismic principal stress rotations and absolute post-seismic stresses in these scenarios are consistent with the variety of observed aftershock focal mechanisms. In all scenarios, the mean apparent stress rotations are larger above than below the megathrust. Scenarios with larger P-f magnitudes exhibit lower mean apparent principal stress rotations. We further evaluate pre-earthquake P-f depth distribution. If P-f follows a sublithostatic gradient, pre-earthquake effective normal stress increases with depth. If P-f follows the lithostatic gradient exactly, then this normal stress is constant, shifting peak slip and peak slip rate updip. This renders constraints on near-trench strength and constitutive behavior crucial for mitigating hazard. These scenarios provide opportunity for future calibration with site-specific measurements to constrain dynamically plausible megathrust strength and P-f gradients

An introduction to semiparametric function-on-scalar regression

Function-on-scalar regression models feature a function over some domain as the response while the regressors are scalars. Collections of time series as well as 2D or 3D images can be considered as functional responses. We provide a hands-on introduction for a flexible semiparametric approach for function-on-scalar regression, using spatially referenced time series of ground velocity measurements from large-scale simulated earthquake data as a running example. We discuss important practical considerations and challenges in the modelling process and outline best practices. The outline of our approach is complemented by comprehensive R code, freely available in the online appendix. This text is aimed at analysts with a working knowledge of generalized regression models and penalized splines

Modeling and Quantifying Parameter Uncertainty of Co‐Seismic Non‐Classical Nonlinearity in Rocks

Dynamic perturbations reveal unconventional nonlinear behavior in rocks, as evidenced by field and laboratory studies. During the passage of seismic waves, rocks exhibit a decrease in elastic moduli, slowly recovering after. Yet, comprehensive physical models describing these moduli alterations remain sparse and insufficiently validated against observations. Here, we demonstrate the applicability of two physical damage models—the internal variable model (IVM) and the continuum damage model (CDM)—to provide quantitative descriptions of nonlinear co-seismic elastic wave propagation observations. While the IVM uses one internal variable to describe the evolution of elastic material moduli, the CDM damage variable is a mathematical representation of microscopic defects. We recast the IVM and CDM models as nonlinear hyperbolic partial differential equations and implement 1D and 2D numerical simulations using an arbitrary high-order discontinuous Galerkin method. We verify the modeling results with co-propagating acousto-elastic experimental measurements. Subsequently, we infer the parameters for these nonlinear models from laboratory experiments using probabilistic Bayesian inversion and 2D simulations. By adopting the Adaptive Metropolis Markov chain Monte Carlo method, we quantify the uncertainties of inferred parameters for both physical models, investigating their interplay in 70,000 simulations. We find that the damage variables can trade off with the stress-strain nonlinearity in discernible ways. We discuss physical interpretations of both damage models and that our CDM quantitatively captures an observed damage increase with perturbation frequency. Our results contribute to a more holistic understanding of co-seismic damage and post-seismic recovery after earthquakes bridging the worlds of theoretical analysis and laboratory findings

A stable discontinuous Galerkin method for the perfectly matched layer for elastodynamics in first order form

We present a stable discontinuous Galerkin (DG) method with a perfectly matched layer (PML) for three and two space dimensional linear elastodynamics, in velocity-stress formulation, subject to well-posed linear boundary conditions. First, we consider the elastodynamics equation, in a cuboidal domain, and derive an unsplit PML truncating the domain using complex coordinate stretching. Leveraging the hyperbolic structure of the underlying system, we construct continuous energy estimates, in the time domain for the elastic wave equation, and in the Laplace space for a sequence of PML model problems, with variations in one, two and three space dimensions, respectively. They correspond to PMLs normal to boundary faces, along edges and in corners. Second, we develop a DG numerical method for the linear elastodynamics equation using physically motivated numerical flux and penalty parameters, which are compatible with all well-posed, internal and external, boundary conditions. When the PML damping vanishes, by construction, our choice of penalty parameters yield an upwind scheme and a discrete energy estimate analogous to the continuous energy estimate. Third, to ensure numerical stability of the discretization when PML damping is present, it is necessary to extend the numerical DG fluxes, and the numerical inter-element and boundary procedures, to the PML auxiliary differential equations. This is crucial for deriving discrete energy estimates analogous to the continuous energy estimates. By combining the DG spatial approximation with the high order ADER time stepping scheme and the accuracy of the PML we obtain an arbitrarily accurate wave propagation solver in the time domain. Numerical experiments are presented in two and three space dimensions corroborating the theoretical results

Dynamic Rupture Models, Fault Interaction and Ground Motion Simulations for the Segmented Húsavík‐Flatey Fault Zone, Northern Iceland

The Húsavík-Flatey Fault Zone (HFFZ) is the largest strike-slip fault in Iceland and poses a high seismic risk to coastal communities. To investigate physics-based constraints on earthquake hazards, we construct three fault system models of varying geometric complexity and model 79 3-D multi-fault dynamic rupture scenarios in the HFFZ. By assuming a simple regional prestress and varying hypocenter locations, we analyze the rupture dynamics, fault interactions, and the associated ground motions up to 2.5 Hz. All models account for regional seismotectonics, topo-bathymetry, 3-D subsurface velocity, viscoelastic attenuation, and off-fault plasticity, and we explore the effect of fault roughness. The rupture scenarios obey earthquake scaling relations and predict magnitudes comparable to those of historical events. We show how fault system geometry and segmentation, hypocenter location, and prestress can affect the potential for rupture cascading, leading to varying slip distributions across different portions of the fault system. Our earthquake scenarios yield spatially heterogeneous near-field ground motions modulated by geometric complexities, topography, and rupture directivity, particularly in the near-field. The average ground motion attenuation characteristics of dynamic rupture scenarios of comparable magnitudes and mean stress drop are independent of variations in source complexity, magnitude-consistent and in good agreement with the latest regional empirical ground motion models. However, physics-based ground motion variability changes considerably with fault-distance and increases for unilateral compared to bilateral ruptures. Systematic variations in physics-based near-fault ground motions provide important insights into the mechanics and potential earthquake hazard of large strike-slip fault systems, such as the HFFZ

Rapid 3D dynamic rupture modeling of the February 6, 2023, Kahramanmara\c{s}, Turkey, MWM_W7.8 and MWM_W7.7 earthquake doublet

The 2023 Turkey Earthquake sequence involved unexpected ruptures across numerous fault segments, challenging data interpretation efforts. We present rapid, 3D dynamic rupture simulations to illuminate the complexities of the $M_W$7.8 and $M_W$7.7 earthquake doublet. Constrained by observations available within days of the sequence, our models deliver timely, mechanically consistent explanations for the unforeseen rupture paths, diverse rupture speeds, multiple slip episodes, locally strong shaking, and fault system interactions. We reconcile regional seismo-tectonics, rupture dynamics, and ground motions of a fault system represented by ten curved dipping segments and a heterogeneous stress field. Our simulations link both events matching geodetic and seismic observations. The $M_W$7.8 earthquake features delayed backward branching from a steeply intersecting splay fault, not requiring supershear speeds. The asymmetrical dynamics of the distinct, bilateral $M_W$7.7 event is explained by heterogeneous fault strength, prestress orientation, fracture energy, and static stress changes from the previous event. Our models explain the northward deviation of its western rupture and the minimal slip observed on the S\"urg\"u fault. Rapidly developed 3D dynamic rupture scenarios can elucidate unexpected observations shortly after major earthquakes, providing timely insights for data-driven analysis and hazard assessment toward a comprehensive, physically consistent understanding of the mechanics of multi-fault systems