PERTURBATION-BASED APPROACH FOR SIMULATING SEISMIC MOTION IN LINEAR ELASTIC HALF-SPACE WITH 1-D NON-PLANAR TOPOGRAPHY

Abstract

The seismic motion of a point on the ground is a result of the complex interactions between the incident waves and the surface topography. It is therefore crucial to properly take into account the non-planar topography of the ground, whenever this exists, while simulating the seismic motion (especially at locations close to the topographic irregularities and in cases when the dominant wavelengths of the incident wavefield are of the same order as the size of the irregularity). For planar topography, while accurate, simple and computationally efficient analytical or semi-analytical solutions exist, computationally intensive numerical approaches (e.g., finite element method) are typically used to solve for the ground motion. If one were interested in simulating the seismic motion for an ensemble of non-planar topographies using FEM (finite element model), one would need to run a fresh simulation for each non-planar topography model. To address this computational challenge, current research focuses on formulating a straightforward and flexible semi-analytical technique known as the perturbation technique. This method is recognized for its analytical simplicity and potential computational efficiency. In this method, the aforementioned simulation problem is simplified to calculating the response of the medium with flat topography but exposed to surface tractions that mathematically represent the non-planar irregularities. As the dynamic response of the medium with flat surface is easier and faster to synthesize, the perturbation-based approach can be easily applied and is expected to be computationally less demanding compared to alternative numerical techniques.