Topographic amplification of seismic motion
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Seismic hazard assessment relies increasingly on the numerical simulation of ground motion, since recent advances in numerical methods and computer architectures have made it ever more practical to obtain the surface response to idealized or realistic seismic events. The key motivation stems from the need to assess the performance of sensitive components of the civil infrastructure (nuclear power plants, bridges, lifelines, etc.), when subjected to realistic scenarios of seismic events. To date, most simulation tools rely on a flat-earth assumption, which ignores topography and its effects on seismic motion amplification. In an attempt to narrow the gap between modeling and physical reality, in this dissertation we study systematically the effects topographic features have on the surface motion when compared against motion obtained using a at-surface assumption. To this end, we discuss first an integrated approach that deploys best-practice tools for simulating seismic events in arbitrarily heterogeneous formations, while also accounting for topography. Specifically, we describe an explicit forward wave solver based on a hybrid formulation that couples a single-field formulation for the computational domain with an unsplit mixed-field formulation for Perfectly-Matched-Layers (PMLs or M-PMLs) used to limit the computational domain. We use spectral elements for spatial discretization, and an efficient Runge-Kutta explicit solver for time integration. Due to the material heterogeneity and the contrasting discretization needs it imposes, we also use an adaptive Runge-Kutta-Fehlberg time-marching scheme to optimally adjust the time step so that the local truncation error rests below a predefined tolerance. To account for the seismic load, we use the Domain- Reduction-Method to introduce the incoming seismic motion in the computational domain whenever the introduction of the actual seismic source would make the computational domain unnecessarily large. Lastly, we couple the DRM with the PMLs to complete the seismic motion simulation engine. Using the developed toolchain, we then report results of parametric studies involving idealized topographic features, which show motion amplification that depends, as expected, on the relation between the topographic features' characteristics and the dominant wavelength. More interestingly, we also report motion de-amplification patterns. Given the prevalence of lower dimensionality models for seismic risk assessment, we also report on the effects model dimensionality has in the presence of heterogeneity and topography. The results reported herein, support the thesis that, for purposes of seismic risk assessment, topography and heterogeneity are best treated when fully accounted for in three-dimensional models. Even this is only a first and necessary step towards higher fidelity modeling of seismic motion effects.
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