Traveltimes are a line integral of the slowness along the ray path expressed as

(23) |

(24) |

This nonlinear problem can be linearized by subtracting a reference problem and expressing the forward problem of the traveltime deviations from the reference model as follows:

(25) |

In order to solve the original nonlinear problem (),
the above linearized inversion is applied iteratively
with the updated back projection operator *L*_{i},
which is obtained by ray tracing through the new reference slowness model

(26) |

Therefore, traveltime tomography can be summarized as an iterative two-step process. First, traveltime deviations are measured by comparing picked traveltimes with expected traveltimes obtained through an assumed velocity model. Then the differences are projected back over the traced ray paths through the assumed velocity model to update the model.

In contrast to transmission traveltime tomography,
in which computation of the operator *L* only
requires a slowness model to trace rays,
reflection traveltime tomography requires
additional information about reflectors, such as the dip and location.
Therefore, an image space after prestack migration
that can provide both the reflector information and the traveltime
deviation is a good choice for picking.

2/5/2001