Wave Modeling for Inverse Problems with Acoustic, Electromagnetic, and Elastic Waves

Abstract

Applied inverse problems comprise radar remote sensing, geophysical exploration, medical diagnostics, nondestructive testing a.s.o., and as such, acoustic, electromagnetic, and elastic waves are under concern. Therefore, appropriate models have to be found to solve the inverse scattering problem for these types of waves algorithmically. Essentially, the linearization of the direct as well as the inverse scattering problem is most often required, and the underlying model is either the weak scattering (Born) approximation, or the physical optics (Kirchhoff) approximation. This allows a unified treatment of the scalar — acoustic — as well as the vector inverse scattering problem for electromagnetic and elastic waves, thus yielding full Polarimetric backpropagation inversion schemes. In order to check the validity of the linearization and the influence of insufficient experimental data due to aperture or frequency bandwidth limitations, simulations are required utilizing appropriate numerical codes. Here, we essentially present results for acoustic and elastic wave scattering obtained with our AFIT and EFIT Finite Difference codes.