Inversion of conic projections with applications to inverse scattering for elastic media

Multidimensional inverse scattering problems of elastics are formulated as generalized tomographic problems. The 2-D elastic problem for wideband plane P-wave illumination is considered with emphasis on the inversion of the PS mode. Using the Born approximation and filtering the observed scattered field, generalized elliptic projections of the perturbations to the Lame parameters and density are obtained. The resulting integral geometric problem is solved in the frequency domain, deriving the projection slice theorem associated with this problem. The reconstructed image is a linear combination of the unknown parameter perturbations, where the coefficients depend on the angle of incidence of the probing wave