The i-FSC proxy for predicting inter-event and spatial variation of topographic site effects

Abstract Our study focuses on predicting topographic amplification of ground motion in the near-source region, where seismic rays reach the free-surface at varying incidence angles. We rely on data from previous 3D numerical simulations conducted on a topographic relief with a homogeneous medium. First, using neural networks, we identify which key parameters, describing the geometric characteristics of the relief relative to the seismic source position, control ground motion amplification. Then, we determine the functional form that relates these parameters to the simulated amplifications. Subsequently, we conduct a regression study to develop a model of topographic amplification, referred to as the i-FSC proxy (Illuminated Frequency-Scaled Curvature). Our estimator depends on the frequency-scaled (1) curvature, a parameter that accounts for the occurrence of amplifications over convex topographies and de-amplification over concave ones; (2) normalized illumination angle, a newly defined parameter that quantifies the slope exposure to the incoming wavefield, accounting for high amplification on slopes oriented opposite to the seismic source. The illumination parameter reduces the uncertainties of the proxy by a factor of 2 compared to estimators that rely solely on curvature. The proxy does not require high computational resources. It uses a digital elevation map and a seismic source position to predict amplification factors (without lithological effects) for an S -wave at any site on the surface topography. It allows exploration of variations in topographic amplification near seismic sources, representing a significant breakthrough as areas closest to the fault typically sustain the highest damages. A MATLAB script performing the i-FSC calculations is provided.