On the complexity of seismic waves trapped in irregular topographies

Documented observations from strong seismic events have repeatedly shown that the ground surface topography significantly affects the characteristics of seismic waves (amplitude, frequency and duration) travelling from the deeper layers of the crust compared to what the ground motion would have been on the surface of a flat homogeneous linear elastic half-space. Although numerous theoretical studies have qualitatively corroborated these observations, they systematically underestimate the absolute level of topographic amplification up to an order of magnitude or more in some cases. In this paper, we try to bridge the quantitative gap between previous theoretical studies and observations by systematically studying the role of geometry, stratigraphy, and ground motion characteristics through a series of elaborate numerical analyses. We show a collection of examples that highlight the effects of topography on seismic ground shaking, and we point out what these results suggest in the context of the current state of earthquake engineering practice. Examples range from semi-analytical solutions of wave propagation in infinite wedges to three-dimensional numerical simulations of topography effects using digital elevation map-generated models and layered geologic features. We conclude by demonstrating that topography effects vary strongly with the stratigraphy and material properties of the underlying geologic materials, and thus it cannot be accurately predicted by studying the effects of ground surface geometry alone. •Topographic amplification by infinite wedges is frequency-independent (no characteristic length).•Slope of infinite wedge determines how the incident and geometrically reflected and refracted wave, the surface waves generated at the slopes, and the tip diffracted wavefields interact with each other.•Finite height topographies and layered media introduce constraints on the wave interference pattern of infinite wedges by adding characteristic lengths.•Topographic amplification is maximized for frequencies of wavelengths comparable to the characteristic length of the layered topographic feature.•Topographic amplification is caused by nonlinear coupling effects of geometry and underlying soil stratigraphy.