Multi-Layer Constrained Identification in Geophysics with Shape Optimization and Level Set Methods

Abstract

This work shows the use of multiple level set functions with constraints in order to reconstruct multiple geophysical layers from temperature measurements with shape optimization methods. Temperature is measured inside subdomains modeling the boreholes and the interface of the geophysical zones is described with level set functions. Shape optimization techniques are used to derive the adjoint equations and the gradient for the iterative process. The direct and the adjoint equations are solved with the standard finite element method.