Fast 3D two-point ray tracing for travel-time tomography

Fabrice Jurado; Patrick Lailly; Andreas Ehinger

doi:10.1117/12.323296

1 October 1998 Fast 3D two-point ray tracing for travel-time tomography

Fabrice Jurado, Patrick Lailly, Andreas Ehinger

Proceedings Volume 3453, Mathematical Methods in Geophysical Imaging V; (1998) https://doi.org/10.1117/12.323296
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

The determination of a correct subsurface velocity model is of strategic importance for seismic imaging of complex geologies by use of 3D prestack depth migration. To accomplish this task we have developed a 3D reflection tomography software (called jerry) that is designed to handle methods of realistic complexity and that is fast enough to allow practical 3D applications. We use a blocky representation of the subsurface with a B-Spline parametrization for interface geometries and for velocity distributions within layers. The forward problem of reflection tomography is formulated as a two-point ray tracing problem and is solved by a bending method based on Fermat's principle with an approximation of the actual ray geometry within a layer by a straight line. The C² property of the model parametrization allows to calculate exact derivatives of the traveltime function with respect to the model and thus to calculate rays (trajectories that satisfy Fermat's principle) from initial trial trajectories. The trajectory initialization is based on Snell's law for transmission/reflection at interfaces and uses an iterative method to calculate the intersection point between straight rays and interfaces. The introduction of non-physical ghost interfaces allows to improve the ray path approximation and thus the accuracy of the calculated traveltimes.

Citation Download Citation

Fabrice Jurado, Patrick Lailly, and Andreas Ehinger "Fast 3D two-point ray tracing for travel-time tomography", Proc. SPIE 3453, Mathematical Methods in Geophysical Imaging V, (1 October 1998); https://doi.org/10.1117/12.323296

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