Speaker: Samuel Bignardi

Visiting Ph.D. Student, University of Ferrara, Italy

Title: Surface Wave Dispersion in Laterally Heterogeneous Media

Date and Time: Wednesday, September 9 at 1:00 pm

Location: SEB 122


Abstract: Consider a soil layer surrounding a piecewise homogenous half-space their separation surface. The depth η(x) of the upper soil layer is not uniform in space, and x is the direction of wave propagation. We are interested in the following inverse problem: given measurements of the spatial variation of the phase velocity c(x) of Love/Rayleigh waves at the free surface, determine the spatial variation of the depth s(x) of the interface between the two soil layers and their associated mechanical properties. To do so, we define an error functional as the mismatch between the given phase velocity data and the theoretical phase velocity c(x) computed by the ‘forward model’ which solves the wave dynamics. The forward model may be solved only if both the interface and the soil properties are known in advance or estimated. This, however, is exactly what is not known and what one wants to reconstruct via the inverse problem above. This is typically solved by making an initial guess for the unknown variables, solving the forward model, and then comparing the resulting modeled data with the actual measured data. The assumed piece-wise homogeneous nature of the soil is ideally suited for a class of geometric evolution techniques known as Active Surfaces which have become one of the more promising recent computational and mathematical methods in biomedical imaging. Active surfaces in combination with Adjoint Methods can be exploited to determine how the interface s(x) should be evolved during the iterations until the best match is achieved. In this talk, I will give an overview of the inverse problem above and then I will present some recent results on the theoretical formulation of the forward model for the Love wave dynamics. Using calculus of variations, such model stems from a Lagrangian appropriate to Love waves in the form of a system of coupled second order linear ODEs. These are solved numerically using Chebycheff spectral methods. Applications are finally presented.