## 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 |

## ASJC Scopus subject areas

- Geochemistry and Petrology