Regardless of how the model is described, the problem of ray theoretic traveltime tomography always reduces to the solution of a system of equations of the form:

(2) |

The model can be described in many different ways. However, in
this paper I will only focus on three of them .
The first one will be the conventional
discretization of the medium in cells of constant slowness *S*_{j} (McMechan,
1983):

(3) |

The second discretization I will consider will be the one based on natural pixels (Michelena and Harris, 1991):

(4) |

Finally, I will consider the discretization of the model in homogeneous orthogonal regions with elliptical velocity dependencies (Michelena and Muir, 1991):

(5) |

The reasons why I will perform the SVD only for these three particular parametrizations are the following:

- Compare the matrices obtained by discretizing the model in orthogonal homogeneous cells with those obtained by discretizing the model in natural pixels (for the isotropic case).
- Compare the matrices obtained by allowing the model to be either isotropic or anisotropic (when the model is discretized in orthogonal homogeneous cells).

12/18/1997