An eikonal based formulation for traveltime perturbation with respect to the source location |

perturbation with respect to the source location

**Tariq Alkhalifah and Sergey Fomel**

Traveltime calculations amount to solving the nonlinear eikonal
equation for a given source location. We analyze the relationship
between the eikonal solution and its perturbations with respect to
the source location and develop a partial differential equation 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 formulation has
several potential applications, such that fast 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.

- Introduction
- Shift in the source location
- A linear velocity model example
- Higher-order accuracy
- Algorithm
- Examples

- Discussion
- Conclusions
- Acknowledgments
- Bibliography
- Appendix A: Higher-order expansions
- About this document ...

An eikonal based formulation for traveltime perturbation with respect to the source location |

2013-04-02