A tomographic scheme

Since we had a single profile of data, we would not be able to do more than estimate the mean elastic properties of the material between the two boreholes. However, Reinaldo Michelena had been working on a 1-component, multiple profile dataset, and this would be useful for testing out ideas on anisotropic tomographic inversion methods.

This work is incomplete, but we have developed some ideas for a practical scheme:

• Replace the conventional isotropic scheme with one based on elliptic dispersion relations with vertical symmetry axes. This only doubles the degrees of freedom for each wavetype, but is sufficient to arrive at reasonable estimates of the elastic moduli of the material.
• Begin by estimating the best homogeneous model, and then, by a divide-and-conquer technique, arrive at increasingly finely layered models.
• If it proves necessary, use the final, finely layered output as the input to a vertical divide-and-conquer scheme.