Simulations of Ground Motion in the Los Angeles Basin Based upon the Spectral-Element Method

We use the spectral-element method to simulate ground motion generated by two recent and well-recorded small earthquakes in the Los Angeles basin. Simulations are performed using a new sedimentary basin model that is constrained by hundreds of petroleum-industry well logs and more than 20,000 km of seismic reflection profiles. The numerical simulations account for 3D variations of seismic-wave speeds and density, topography and bathymetry, and attenuation. Simulations for the 9 September 2001 M_w 4.2 Hollywood earthquake and the 3 September 2002 M_w 4.2 Yorba Linda earthquake demonstrate that the combination of a detailed sedimentary basin model and an accurate numerical technique facilitates the simulation of ground motion at periods of 2 sec and longer inside the basin model and 6 sec and longer in the regional model. Peak ground displacement, velocity, and acceleration maps illustrate that significant amplification occurs in the basin

Numerical Simulations of Earthquake Scenarios in the Lower Rhine Embayment Area

The choice of the Lower Rhine Embayment as study area for strong ground motion modeling may be puzzling at first glance. This region in the northwest of the European continent is characterized by active tectonics on a complex system of fault-zones with relatively low deformation rates. Consequently, the area has shown low to moderate seismicity in the time frame covered by observational seismology. However, historical and geological evidence proves that the fault systems of the Lower Rhine Embayment have the potential of producing large earthquakes with magnitudes 6 and above accompanied by surface rupture. The presence of large sediment deposits in this region leads to local amplification of ground motion with large lateral variations. Dense population and an agglomeration of industry results in an elevated seismic risk. Assessment of seismic hazard in regions characterized by low recent seismicity is afflicted with large uncertainties. This is mainly due to the dearth of observational data on strong ground motions associated with large earthquakes. Numerical simulations of earthquake scenarios can account for estimates on peak ground motion and waveforms and therefore help closing this gap. Naturally the first step consists in accurate reproduction of the few observed events. An additional crucial quantity is the range of variations of the simulation results within the uncertainty margins associated with input parameters. Knowledge about this behavior enlarges the significance of numerical simulation results. Four historical and recent earthquake scenarios are modeled using a finite difference approach. Results are analyzed with special emphasis given to their intrinsic variability with model complexity and simulation settings. The choice of investigated parameters is adopted to the differing scope of observational data available for the individual events. In general encouraging similarity between synthetic and observed ground motions is found, even when a simplified model is used. However, detailed investigation carried out for the most recent earthquake scenario - the magnitude 4.9 July 22 2002 Alsdorf event - strongly suggests the significance of an appropriate source description and the modeling of anelastic behavior on simulation results. Finally a web-based application for storage and visualization of synthetic ground motion data is presented

Influences of Poroelasticity on Wave Propagation: A Time Stepping Boundary Element Formulation

Wave propagation phenomena in poroelastic continua are modeled with a Boundary Element (BE) formulation based on Biots theory. The Convolution Quadrature Method (CQM) makes it possible to use the available Laplace domain fundamental solutions in a time domain BE formulation. Support for 2-d problems has been added to the existing 3-d implementation. Further, a formulation for incompressible constituents and mixed elements have been implemented and tested. In a two-phase material not only each constituent, the solid and the fluid, may be compressible on the microscopic level but also the skeleton itself possesses a structural compressibility. If the compression modulus of a constituent is much larger than the compression modulus of the bulk material, this constituent is assumed to be materially incompressible. The fundamental solutions for incompressible poroelasticity in both 2-d and 3-d are derived using the method of Hörmander. Numerical experiments show that there are no noticeable differences for some materials (e.g., soil), and then the incompressible model can be recommended to obtain a speedup of about 20 percent. In the conventional BEM implementation, the same shape functions are applied to all state variables. Motivated by the improvements due to mixed elements in FEM, i.e. the shape function for the pressure is chosen one degree lower than for the displacement, such elements have been added to the BEM implementation. A study about the influence of the mixed shape functions to the quality of numerical results and the stability of the time-stepping scheme shows that the mixed elements can only be recommended in special cases in BEM. The proposed formulation is validated by comparison to a 1-d analytical solution. A poroelastic halfspace is modeled in both 2-d and 3-d numerical experiments to study wave propagation with emphasis on surface waves. The influence of material incompressibility on various wave types is also examined.Zur Simulation von Wellenausbreitungsvorgängen in poroelastischen Kontinua wird in dieser Arbeit die Randelementmethode (BEM) benutzt. Mit den von Lubich entwickelten Faltungsquadraturverfahren kann ein Zeitschrittalgorithmus aufbauend auf den laplacetransformierten Fundamentallösungen formuliert werden. Die bestehende drei-dimensionale Formulierung wurde auf zwei-dimensionale Problemstellungen erweitert und eine Formulierung für inkompressible Konstituierende entwickelt. Weiterhin wurden gemischte Elemente implementiert und getestet. Zweiphasenmaterialien weisen neben der Kompressibilität der Konstituierenden noch eine Strukturkompressibilität auf. Ist die Kompressibilität einer Komponente vernachlässigbar klein im Vergleich zur Strukturkompressibilität, kann die Komponente inkompressibel modelliert werden. Für den Fall, dass sowohl das Fluid als auch das Festkörpermaterial inkompressibel modelliert werden kann, wurden zwei- und drei-dimensionale Fundamentallösungen mit der Methode von Hörmander hergeleitet und implementiert. Die numerischen Ergebnisse bestätigen, dass bei manchen Materialien (z.B. Boden) die inkompressible Modellierung zulässig ist, und dazu noch eine Ersparnis an Rechenzeit (um 20%) bringen kann. In den bisher publizierten poroelastischen BEM Formulierungen werden die gleichen Ansatzfunktionen für alle Unbekannte verwendet. In der FEM hingegen wird die Ansatzfunktion für den Porendruck um einen Grad niedriger als die der Verschiebung gewählt. Dies hat die Implementierung gemischter Elemente in die BEM motiviert. Die anschließend durchgeführte Studie zeigt jedoch, dass diese Elemente bei der BEM nur in Spezialfällen empfohlen werden können. Die Validierung des entwickelten Programms wurde mit einer analytischen ein-dimensionalen Lösung durchgeführt. Nachfolgend wurden mit Blick auf Oberflächenwellen Wellenausbreitungsprobleme im poroelastischen Halbraum modelliert und diskutiert