## Abstract

Traveltime calculations amount to solving the nonlinear eikonal equation for a given source location. The relationship between the eikonal solution and its perturbations is analyzed with respect to the source location and a partial differential equation is developed that relates the traveltime field for one source location to that for a nearby source. This linear first-order equation in one form depends on lateral changes in velocity and in another form is independent of the velocity field and relies on second-order derivatives of the original traveltime field. For stable finite-difference calculations, this requires the velocity field to be smooth in a sense similar to ray-tracing requirements. Our formulation for traveltime perturbation has several potential applications, such that as traveltime calculation by source-location perturbation, velocity-independent interpolation including datuming, and velocity estimation. Additionally, higher-order expansions provide parameters necessary for Gaussian-beam computations.

Original language | English (US) |
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Pages (from-to) | T175-T183 |

Journal | Geophysics |

Volume | 75 |

Issue number | 6 |

DOIs | |

State | Published - Nov 2010 |

### Bibliographical note

KAUST Repository Item: Exported on 2023-03-31Acknowledgements: The first author thanks KACST and KAUST for their support of this research. We also thank the associate editor and the reviewers for their fine review of the paper.

This publication acknowledges KAUST support, but has no KAUST affiliated authors.

## ASJC Scopus subject areas

- Geochemistry and Petrology