Ground motions from earthquakes are known to be affected by earth's surface topography. Topographic effects are a result of several physical phenomena such as the focusing or defocusing of seismic waves reflected from a topographic feature and the interference between direct and diffracted seismic waves. This typically causes an amplification of ground motion on convex features such as hills and ridges and a de-amplification on concave features such as valleys and canyons. Topographic effects are known to be frequency dependent and the spectral accelerations can sometimes reach high values causing significant damages to the structures located on the feature. Topographically correlated damage pattern have been observed in several earthquakes and topographic amplifications have also been observed in several recorded ground motions. This phenomenon has also been extensively studied through numerical analyses. Even though different studies agree on the nature of topographic effects, quantifying these effects have been challenging. The current literature has no consensus on how to predict topographic effects at a site. With population centers growing around regions of high seismicity and prominent topographic relief, such as California, and Japan, the quantitative estimation of the effects have become very important. In this dissertation, we address this shortcoming by developing empirical models that predict topographic effects at a site. These models are developed through an extensive empirical study of recorded ground motions from two large strong-motion datasets namely the California small to medium magnitude earthquake dataset and the global NGA-West2 datasets, and propose topographic modification factors that quantify expected amplification or deamplification at a site.

To develop these models, we required a parameterization of topography. We developed two types of topographic parameters at each recording stations. The first type of parameter is developed using the elevation data around the stations, and comprise of parameters such as smoothed slope, smoothed curvature, and relative elevation. The second type of parameter is developed using a series of simplistic 2D numerical analysis. These numerical analyses compute an estimate of expected 2D topographic amplification of a simple wave at a site in several different directions. These 2D amplifications are used to develop a family of parameters at each site. We study the trends in the ground motion model residuals with respect to these topographic parameters to determine if the parameters can capture topographic effects in the recorded data. We use statistical tests to determine if the trends are significant, and perform mixed effects regression on the residuals to develop functional forms that can be used to predict topographic effect at a site. Finally, we compare the two types of parameters, and their topographic predictive power.