## Abstract

Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for integral imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial at each computational step. Using perturbation theory, we approximate the first-order discretized form of the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for the anisotropic Marmousi model, with complex distribution of velocity and anellipticity anisotropy parameter. The formulation allows tremendous cost reduction compared to using the exact TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy of the proposed approximation, without any addition to the computational cost.

Original language | English (US) |
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Title of host publication | 75th European Association of Geoscientists and Engineers Conference and Exhibition 2013 Incorporating SPE EUROPEC 2013 |

Subtitle of host publication | Changing Frontiers |

Publisher | European Association of Geoscientists and Engineers, EAGE |

Pages | 5644-5648 |

Number of pages | 5 |

ISBN (Electronic) | 9781629937915 |

State | Published - 2013 |

Event | 75th European Association of Geoscientists and Engineers Conference and Exhibition 2013 Incorporating SPE EUROPEC 2013: Changing Frontiers - London, United Kingdom Duration: Jun 10 2013 → Jun 13 2013 |

### Other

Other | 75th European Association of Geoscientists and Engineers Conference and Exhibition 2013 Incorporating SPE EUROPEC 2013: Changing Frontiers |
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Country | United Kingdom |

City | London |

Period | 06/10/13 → 06/13/13 |

## ASJC Scopus subject areas

- Geotechnical Engineering and Engineering Geology
- Geochemistry and Petrology