Geodesic
Numerical simulation of recovery of the velocity parameters of elastic inhomogeneities by diffraction tomography method
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 28, Tome 257 (1999), pp. 101-115

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For the solution of direct problem the finite difference method is used, that allows to take into account the diffraction phenomenon on not weak-contrast local inhomogeneities with a simple and complex geometry. The inverse problem is solved by diffraction tomography method with the use of the Born approximation. The examples of recovery of inhomogeneities with the use of wave field (2-D $P$-$SV$ problem) produced in uniform space by a source of a type of center of pressure at three locations of a source and three observation points with their location on a linear profile are demonstrated. An opportunity to recover of elastic parameters $(\lambda,\mu)$ and mass density $\rho$ separately allows to find the velocity perturbations as well as ratio of shear wave velocity to compressional wave velocity. 
@article{ZNSL_1999_257_a6,
     author = {Yu. V. Kiselev and V. N. Troyan},
     title = {Numerical simulation of recovery of the velocity parameters of elastic inhomogeneities by diffraction tomography method},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {101--115},
     publisher = {mathdoc},
     volume = {257},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_257_a6/}
}
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Yu. V. Kiselev; V. N. Troyan. Numerical simulation of recovery of the velocity parameters of elastic inhomogeneities by diffraction tomography method. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 28, Tome 257 (1999), pp. 101-115. http://geodesic.mathdoc.fr/item/ZNSL_1999_257_a6/