On the noninvasive determination of material parameters from a knowledge of elastic displacements: Theory and numerical simulation

In this paper, we present a formulation and numerical simulation for the noninvasive determination of the material parameter ratios (i.e., the Lame parameters divided by density) of an isotropic, inhomogenous elastic medium subject to time harmonic vibration. Given a knowledge of the displacements throughout the medium, a novel implementation of a variational formulation is used to determine the ratios lambda/rho and mu/rho. A theoretical formulation is presented and validated using numerical data obtained from a finite element method. The results indicate that the method may be applied locally within an inhomogenous medium, and that the corresponding material parameters can be recovered to a high degree of accuracy. In addition, the method does not appear to be subject to the typical wavelength constraints of previous methods.