** Next:** Nonlinear schemes
** Up:** Cunha: Walsh function decomposition
** Previous:** Introduction

For a medium that can be described (or approximated) by elliptically
anisotropic velocities (with vertical and horizontal symmetry axes),
the traveltime between two points separated by a vertical
distance *z* and a horizontal distance *x* is given by

| |
(1) |

where *M*^{x} and *M*^{z} are the squared horizontal and vertical slownesses.
If the medium is heterogeneous, this equation is valid either within
each cell or within each layer (if a layered description is appropriate)
of the model. The inversion problem can be formulated as the search for
the model (*M*^{x}_{j},*M*^{z}_{j}), for all layers *j*, that minimizes the
objective function
| |
(2) |

where *N* is the number of source-receiver pairs,
*t*_{i} is the measured traveltime
corresponding to source-receiver index *i*, and is the traveltime predicted by the perturbed model.

** Next:** Nonlinear schemes
** Up:** Cunha: Walsh function decomposition
** Previous:** Introduction
Stanford Exploration Project

12/18/1997