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.
Differences between 3-D numerical predictions of earthquake ground motion in the Mygdonian basin near Thessaloniki, Greece, led us to define four canonical stringent models derived from the complex realistic 3-D model of the Mygdonian basin. Sediments atop an elastic bedrock are modelled in the 1D-sharp and 1D-smooth models using three homogeneous layers and smooth velocity distribution, respectively. The 2D-sharp and 2D-smooth models are extensions of the 1-D models to an asymmetric sedimentary valley. In all cases, 3-D wavefields include strongly dispersive surface waves in the sediments. We compared simulations by the Fourier pseudo-spectral method (FPSM), the Legendre spectral-element method (SEM) and two formulations of the finite-difference method (FDM-S and FDM-C) up to 4Hz. The accuracy of individual solutions and level of agreement between solutions vary with type of seismic waves and depend on the smoothness of the velocity model. The level of accuracy is high for the body waves in all solutions. However, it strongly depends on the discrete representation of the material interfaces (at which material parameters change discontinuously) for the surface waves in the sharp models. An improper discrete representation of the interfaces can cause inaccurate numerical modelling of surface waves. For all the numerical methods considered, except SEM with mesh of elements following the interfaces, a proper implementation of interfaces requires definition of an effective medium consistent with the interface boundary conditions. An orthorhombic effective medium is shown to significantly improve accuracy and preserve the computational efficiency of modelling. The conclusions drawn from the analysis of the results of the canonical cases greatly help to explain differences between numerical predictions of ground motion in realistic models of the Mygdonian basin. We recommend that any numerical method and code that is intended for numerical prediction of earthquake ground motion should be verified through stringent models that would make it possible to test the most important aspects of accuracy.
International audienceBy means of three-dimensional (3-D) numerical simulations, including the Laboratoire Souterrain à Bas-Bruit (LSBB) topography, we carefully analyze site effects assessments yielded by two approaches: the classical site to reference spectral-ratio method (SRM) and the statistical median reference method (MRM). We show for both isotropic and double-couple point sources that a 94% reduction in the number of stations of a regularly spaced array yields MRM site-effect estimates within 5% of those obtained from the absolute regional median, and within 20% using a 98% station reduction with irregularly located sites. In contrast, the SRM yielded site-effect overestimates greater than 50% in some areas and up to 100% in specific sites, which makes the MRM much more robust than the SRM. We determined a 33% probability to exceed an amplification factor of 2, and an 8% probability to exceed a factor of 3 due to topography in the surroundings of the sharpest summit of the LSBB area
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