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

Alkhalifah, Tariq Ali; Fomel, Sergey

Type

Article

Authors

Alkhalifah, Tariq Ali

Fomel, Sergey

Date

2010-11

Permanent link to this record

http://hdl.handle.net/10754/597520

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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. © 2010 Society of Exploration Geophysicists.

Citation

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