Irregular grids in seismic tomography and minimum-time ray tracing

Tomographic inversion of traveltimes is often carried out by discretizing the Earth as a grid of regular pixels. This choice simplifies the related ray-tracing algorithms, but contributes significantly to the non-uniqueness of the estimated velocity distribution. A singular value decomposition of the tomographic matrix enables one to recognize the causes of this mathematical ambiguity in the model space. This is more intuitive than introducing arbitrary damping factors and spatial filters, and allows one to control the non-uniqueness of solutions by modifying the pixel distribution or the acquisition geometry. This approach lends itself to the adoption of irregular grids and to the definition of a new ray-tracing algorithm, based on Fermat's principle of minimum time, which is able to simulate transmitted, reflected, refracted and diffracted waves. The joint tomographic inversion of these different types of waves potentially provides an additional improvement to the quality and reliability of the estimated velocities.