First-break traveltime tomography with the double-square-root eikonal equation |

To derive the Frechét derivative, we start from equations 13 and
14. Applying
to both sides of equation 13 results in

Analogously

Inserting equations B-1 and B-2 into 14 and regrouping the terms, we prove equation 15

where

and

At the singularity of DSR eikonal equation, the operators , and take simpler forms and can be derived directly from equation 3.

First-break traveltime tomography with the double-square-root eikonal equation |

2013-10-16