Seismic Wave Simulation for Complex Rheologies on Unstructured Meshes

The possibility of using accurate numerical methods to simulate seismic wavefields on unstructured meshes for complex rheologies is explored. In particular, the Discontinuous Galerkin (DG) finite element method for seismic wave propagation is extended to the rheological types of viscoelasticity, anisotropy and poroelasticity. First is presented the DG method for the elastic isotropic case on tetrahedral unstructured meshes. Then an extension to viscoelastic wave propagation based upon a Generalized Maxwell Body formulation is introduced which allows for quasi-constant attenuation through the whole frequency range. In the following anisotropy is incorporated in the scheme for the most general triclinic case, including an approach to couple its effects with those of viscoelasticity. Finally, poroelasticity is incorporated for both the propagatory high-frequency range and for the diffusive low-frequency range. For all rheology types, high-order convergence is achieved simultaneously in space and time for three-dimensional setups. Applications and convergence tests verify the proper accuracy of the approach. Due to the local character of the DG method and the use of tetrahedral meshes, the presented schemes are ready to be applied for large scale problems of forward wave propagation modeling of seismic waves in setups highly complex both geometrically and physically

Flexible Modellerweiterung und Optimierung von Erdbebensimulationen

Simulations of realistic earthquake scenarios require scalable software and extensive supercomputing resources. With increasing fidelity in simulations, advanced rheological and source models need to be incorporated. I introduce a domain-specific language in order to handle the model flexibility in combination with the high efficiency requirements. The contributions in this thesis enabled the to date largest and longest dynamic rupture simulation of the 2004 Sumatra earthquake.Realistische Erdbebensimulationen benötigen skalierbare Software und beträchtliche Rechenressourcen. Mit zunehmender Genauigkeit der Simulationen müssen fortschrittliche rheologische und Quellmodelle integriert werden. Ich führe eine domänenspezifische Sprache ein, um die Modelflexibilität in Kombination mit den hohen Effizienzanforderungen zu beherrschen. Die Beiträge in dieser Arbeit haben die bisher größte und längste dynamische Bruchsimulation des Sumatra-Erdbebens von 2004 ermöglicht

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

Coupled, Physics-Based Modeling Reveals Earthquake Displacements are Critical to the 2018 Palu, Sulawesi Tsunami

The September 2018, Mw 7.5 Sulawesi earthquake occurring on the Palu-Koro strike-slip fault system was followed by an unexpected localized tsunami. We show that direct earthquake-induced uplift and subsidence could have sourced the observed tsunami within Palu Bay. To this end, we use a physics-based, coupled earthquake–tsunami modeling framework tightly constrained by observations. The model combines rupture dynamics, seismic wave propagation, tsunami propagation and inundation. The earthquake scenario, featuring sustained supershear rupture propagation, matches key observed earthquake characteristics, including the moment magnitude, rupture duration, fault plane solution, teleseismic waveforms and inferred horizontal ground displacements. The remote stress regime reflecting regional transtension applied in the model produces a combination of up to 6 m left-lateral slip and up to 2 m normal slip on the straight fault segment dipping 65∘ East beneath Palu Bay. The time-dependent, 3D seafloor displacements are translated into bathymetry perturbations with a mean vertical offset of 1.5 m across the submarine fault segment. This sources a tsunami with wave amplitudes and periods that match those measured at the Pantoloan wave gauge and inundation that reproduces observations from field surveys. We conclude that a source related to earthquake displacements is probable and that landsliding may not have been the primary source of the tsunami. These results have important implications for submarine strike-slip fault systems worldwide. Physics-based modeling offers rapid response specifically in tectonic settings that are currently underrepresented in operational tsunami hazard assessment

Multiscale Method for Elastic Wave Propagation in the Heterogeneous, Anisotropic Media

Seismic wave simulation in realistic Earth media with full wavefield methods is a fundamental task in geophysical studies. Conventional approaches such as the finite-difference method and the finite-element method solve the wave equation in geological models represented with discrete grids and elements. When the Earth model includes complex heterogeneities at multiple spatial scales, the simulation requires fine discretization and therefore a system with many degrees of freedom, which often exceeds current computational abilities. In this dissertation, I address this problem by proposing new multiscale methods for simulating elastic wave propagation based on previously developed algorithms for solving the elliptic partial differential equations and the acoustic wave equation. The fundamental motivation for developing the multiscale method is that it can solve the wave equation on a coarsely discretized mesh by incorporating the effects of fine-scale medium properties using so-called multiscale basis functions. This can greatly reduce computation time and degrees of freedom compared with conventional methods. I first derive a numerical homogenization method for arbitrarily heterogeneous, anisotropic media that utilizes the multiscale basis functions determined from a local linear elasticity equation to compute effective, anisotropic properties, and these equivalent elastic medium parameters can be used directly in existing elastic modeling algorithms. Then I extend the approach by constructing multiple basis functions using two types of appropriately defined local spectral linear elasticity problems. Given the eigenfunctions determined from local spectral problems, I develop a generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media in both continuous Galerkin (CG) and discontinuous Galerkin (DG) formulations. The advantage of the multiscale basis functions is they are model-dependent, unlike the predefined polynomial basis functions applied in conventional finite-element methods. For this reason, the GMsFEM can effectively capture the influence of fine-scale variation of the media. I present results for several numerical experiments to verify the effectiveness of both the numerical homogenization method and GMsFEM. These tests show that the effectiveness of the multiscale method relies on the appropriate choice of boundary conditions that are applied for the local problem in numerical homogenization method and on the selection of basis functions from a large set of eigenfunctions contained in local spectral problems in GMsFEM. I develop methods for solving both these problems, and the results confirm that the multiscale method can be powerful tool for providing accurate full wavefield solutions in heterogeneous, anisotropic media, yet with reduced computation time and degrees of freedom compared with conventional full wavefield modeling methods. Specially, I applied the DG-GMsFEM to the Marmousi-2 elastic model, and find that DG-GMsFEM can greatly reduce the computation time compared with continuous Galerkin (CG) FEM

Simulation de la propagation d'ondes électromagnétiques en nano-optique par une méthode Galerkine discontinue d'ordre élevé

The goal of this thesis is to develop a discontinuous Galerkin time-domain method to be able to handle realistic nanophotonics computations. During the last decades, the evolution of lithography techniques allowed the creation of geometrical structures at the nanometer scale, thus unveiling a variety of new phenomena arising from light-matter interactions at such levels. These effects usually occur when the device is of comparable size or (much) smaller than the wavelength of the incident field. This work relies on the development and implementation of appropriate models for dispersive materials (mostly metals), as well as on a large panel of classical computational techniques. Two major methodological developments are presented and studied in details: (i) curvilinear elements, and (ii) local order of approximation. This work is complemented with several physical studies of real-life nanophotonics applications.L’objectif de cette thèse est de développer une méthode Galerkine discontinue d’ordre élevé capable de prendre en considération des simulations réalistes liées à la nanophotonique. Au cours des dernières décennies, l’évolution des techniques de lithographie a permis la création de structure géométriques de tailles nanométriques, révélant ainsi une large gamme de phénomènes nouveaux nés de l’interaction lumière-matière à ces échelles. Ces effets apparaissent généralement pour des objets de taille égale ou (très) inférieure à la longueur d’onde du champ incident. Ce travail repose sur le développement et l’implémentation de modèles de dispersion appropriés (principalement pour les métaux), ainsi que sur un large éventail de méthodes computationnelles classiques. Deux développements méthodologiques majeurs sont présentés et étudiés en détails: (i) les éléments courbes, et (ii) l’ordre d’approximation local. Ces études sont accompagnées de plusieurs cas-tests réalistes tirés de la nanophotonique