US Patent 7675818 Method for tomographic inversion by matrix transformation

Method for reducing instability and increasing computational efficiency in tomographic inversion for velocity model building. A system of tomographic equations is developed for a uniform grid. A non-uniform parameterization is found for which a linear mapping exists between the space of the uniform grid and the space of the non-uniform grid. The matrix that relates velocity to the tomographic data in the non-uniform representation is then given by the matrix product of the corresponding matrix in the uniform grid representation and the mapping matrix. Inversion can then be performed for the non-uniform parameterization on a smaller, more stable matrix.