Frequency-Scaled Curvature as a Proxy for Topographic Site-Effect Amplification and Ground-Motion Variability

Abstract:

The seismic waves propagating in mountainous areas are highly disrupted by the intricate surface geometry. As a consequence of that effect, the topography produces large ground-motion amplifications in the vicinity of summits, possibly causing damages during large earthquakes. Another consequence is the strong variability of the ground motion occurring on steep slopes, where the amplification patterns are complex and event-dependent. We introduce a new methodology to forecast the topographic site-effect amplification. Ground motions are obtained from a large database of 3-D earthquake simulations with numerical accuracy achieved up to 4 Hz and including the topography surrounding the inter-Disciplinary Underground Science and Technology laboratory (i-DUST/LSBB), Rustrel, France. Those ground motions show that the Earth’s surface curvature, defined as the second spatial-derivative of the elevation map, is correlated with the topographic site amplification. The highest linear correlation between the frequency-dependent topographic amplification and the topographic curvature is reached when the curvature is smoothed over a characteristic length equal to the S-wavelength divided by two, implying that the amplification is caused by topographic features whose horizontal dimensions are similar to half of the S-wavelength. The largest single-station variabilities are found at sites located on slopes and on the largest summits, while intermediate variabilities occur over narrow ridges and a stable behavior in the bottom valleys. The Frequency-Scaled Curvature (FSC) proxy allows the determination of topographic features with similar characteristic dimensions and probabilistic estimates of amplification values accounting on the phenomenon variability. Amplification estimates using the FSC proxy are robust and easily computed from digital elevation maps provided reasonable values of S-velocities in the area of interest.