A 2-D hybrid technique to model the effect of topography on coseismic displacements. Application to the Umbria-Marche (central Italy) 1997 earthquake sequence

We face the problem of modelling the influence of the irregular topography of the Earth's crust on coseismic displacements. The modelling technique we propose is valid for a homogeneous elastic 2-D domain and is based on a two-step approach that uses (1) the traditional analytical results valid for elastic spaces and elastic half-spaces with a flat with free surface (FFS) and (2) a finite-element (FE) numerical code to compute the disturbance induced by the local topography. Attention is particularly focused on: (1) the comparison between the results obtained through our method and the analytical formulae valid for FFS geometries, which are used extensively today in both forward and inverse modelling even in the presence of irregular topography and (2) the advantages of our hybrid approach over pure FE models. After discussing the theoretical experiment of a Gaussian topography, we present an application to modelling the displacement fields induced by selected events of the earthquake sequence that hit the Umbria-Marche region in the central Apennines (Italy) in 1997, devoting major attention to the effect of the Apennines chain topography in the source region. In all cases the topography is found to play an important role and to introduce non-negligible corrections to the coseismic surface displacement components computed through the FFS approximation. The main effect is that topography not only affects the magnitude of the surface signal, but it may also lead to highfrequency disturbances that tend to grow with the shallowness of the fault.