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

Abstract

We introduce a new methodology to predict the topographic site-effect amplification. Ground motions obtained from a large database of 3D earthquake simulations show that the curvature of the Earth's surface, defined as the second spatial derivative of the elevation map, is correlated with the topographic site amplification. The highest 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 (i.e., frequency-scaled curvature [FSC]). This implies the amplification is caused by topographic features for which horizontal dimensions are similar to half of the S wavelength. The largest ground-motion variabilities are found at sites located on slopes and on the largest summits, whereas intermediate variabilities occur over narrow ridges and a stable behavior in the bottom valleys. The FSC proxy allows the identification of topographic features with similar characteristic dimensions and probabilistic estimates of amplification values accounting on the variability of ground motions due to source-site interactions. Amplification estimates using the FSC proxy are robust and easily computed from digital elevation maps provided that reasonable values of S-wave velocities are available in the area of interest.

Characterization of site conditions (soil class, VS30, velocity profiles) for 33 stations from the French permanent accelerometric network (RAP) using surface-wave methods

“…In order to perform this evaluation, the 'frequency-scaled curvature' (FSC) proxy proposed by Maufroy et al (2015) was computed using available digital terrain models. This approach was applied on four selected stations (IRVG, OGCA, GRN and IRPV).…”

“…The topographic site effect may affect rock sites typically used as reference sites, which underlines the importance to carefully analyse the amplitude of the ground Lithological amplification is computed with 1D numerical simulation using the 33 shear wave velocity profiles for each site obtained in the present paper. Topographic amplification is predicted using the frequency-scaled curvature proxy proposed by Maufroy et al (2015) using digital terrain models (with a resolution of 1 m for IRVG, OGCA and IRPV; and 25 m for GRN-causing the evaluation limitation at high frequency) motion at those sites even if no clear peak of amplification appears, keeping in mind that the topography may smoothly amplify the ground motion over a large bandwidth. One remaining issue is the combination of both lithological and topographic site effects at the same site.…”

2D dynamic studies combined with the surface curvature analysis to predict Arias Intensity amplification

“…those with higher L and H, induce amplification at low frequencies, while smaller morphologies amplify at higher frequencies. Maufroy et al (2015) apply this link to relate the spectral amplification to the frequency-scaled curvature (FSC) which represents the values of earth's surface curvature doublesmoothed over a specific spatial extent (see a more detailed review of curvature and FSC later in the BCurvature, FSC and smoothed curvature^section). The size of smoothing extent in FSC laterally expresses the size of analysed morphology.…”

“…Moreover, the smoothing itself can be applied several times. For example, Maufroy et al (2015) apply double-smoothing of original curvature values to get the parameter termed as FSC. In this respect, given the variety of smoothing options, we prefer to treat FSC as the particular case of smoothed curvature.…”

“…That link is proven through the 2D dynamic tests with a single value of central frequency, while signals with varying spectral content are not studied. Meanwhile, Maufroy et al (2015) apply the surface curvature in a modified way to regionally predict the spectral amplification patterns. The authors performed a set of dynamic tests in the 3D domain and show that amplified frequency range can be predicted via the parameter known as the frequency-scaled curvature (FSC).…”