The material-geometry nexus: Understanding topographic effects on wave propagation

Qianli Chen, & Ahmed E. Elbanna

Published August 15, 2017, SCEC Contribution #7740, 2017 SCEC Annual Meeting Poster #172

Topographic effects are associated with the presence of strong topographic relief (hills, ridges, canyons, cliffs, and slopes), complicated subsurface topography (sedimentary basins, alluvial valleys), and geological lateral discontinuities (e.g., ancient faults, debris zones). These features have been shown to significantly affect the intensity and frequency content of ground shaking during earthquakes. Observational evidence from past earthquakes indicates that damage concentrations occur where steep slopes or complicated topography is present; buildings located on the tops of hills, ridges, and canyons, suffer more intense damage than those located at the base during earthquakes. A prominent example is the extraordinary ground motion (PGA=1.82g) recorded at the hilltop Tarzana strong motion station during the 1994 Northridge Earthquake.

Experimental evidence and theoretical results suggest that the observed or computed amplification is first-order related to the “sharpness” of the topography: the steeper the average slope, the higher the peak amplification and that the stronger amplification effects correspond to wavelengths comparable to the horizontal dimension of the topographic feature.

Here, we present a new and simple interpretation for the influence of surface topography on wave propagation and more generally for wave interactions with curvilinear boundaries. Our approach implements a coordinate transformation technique to rewrite the elastodynamic equations in a mapped domain with a flat boundary. We show that under this transformation, the equations of motion preserve their mathematical structure and are satisfied with the same displacement field as in the reference configuration. However, the elastic tensor and material density transform into modified quantities. It then becomes possible to make correspondences between curvilinear geometry in the reference configuration and variation in impedance and wave speed in the mapped configuration revealing domains of possible amplification and suppression. In particular, we show that if the topographical feature is steep enough, a region of effective locally lower impedance emerges at the hill top. We demonstrate our findings through several examples and discuss the implications of the proposed technique for understanding a wide range of elastodynamic problems from non-planar faults to metamaterials.

Citation
Chen, Q., & Elbanna, A. E. (2017, 08). The material-geometry nexus: Understanding topographic effects on wave propagation. Poster Presentation at 2017 SCEC Annual Meeting.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)