The i-FSC Proxy for Predicting Spatial and Inter-Event Variations of Topographic Site Effects



This study focuses on predicting how surface topography amplifies ground motion near earthquake sources, where seismic waves reach the surface at varying angles of incidence. The work relies on results from 3D numerical simulations carried out over a homogeneous topographic model.

Comparison between ground motion amplification estimated using (a) 3D numerical simulations on supercomputers (tens of thousands of computing hours) and (b) the i-FSC proxy (a few minutes on a laptop).


The research was conducted in several stages. First, neural networks were used to identify key parameters describing the geometry of the terrain relative to the seismic source, those that effectively control ground motion amplification. Next, the team analysed how these parameters relate to the amplification patterns observed in the simulations. Finally, these relationships were formalized through a regression-based amplification model.

The outcome is a new parameter called i-FSC (Illuminated Frequency-Scaled Curvature). This proxy depends on two main components :

1. Frequency-scaled curvature, which explains strong shaking on convex features and reduced shaking on concave ones.

2. A normalized illumination angle, a newly introduced parameter measuring how exposed a slope is to the incoming wavefield, capturing the tendency for significant amplification on slopes facing away from the source.


Including this illumination term cuts uncertainty by a factor of two compared with traditional approaches based only on curvature.


Another strength of the proxy is its practicality : it requires no intensive computing. Using only a digital elevation model and the position of an earthquake source, it estimates S-wave amplification factors (excluding lithological effects) at any point on the surface.


This capability allows researchers to investigate how amplification varies close to seismic sources, a critical advance, since areas near the fault are typically those that suffer the most severe damage.

The full study is published in : SPRINGER NATURE Link

References :

Bou Nassif, A., Maufroy, E., Lacroix, P., Chaljub, E., Causse, M., Bard, P.-Y., 2025.
The i-FSC proxy for predicting inter-event and spatial variation of topographic site effects
Bulletin of Earthquake Engineering, 23, 2, 671–692.

Scientific contacts :

  • A. Bou-Nassif – Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, Université Gustave Eiffel, ISTerre
  • E. Maufroy – Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, Université Gustave Eiffel, ISTerre
  • P. Lacroix – Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, Université Gustave Eiffel, ISTerre
  • E. Chaljub – Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, Université Gustave Eiffel, ISTerre
  • M. Causse – Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, Université Gustave Eiffel, ISTerre
  • P.-Y. Bard – Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, Université Gustave Eiffel, ISTerre