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Solving the eikonal equation on a triangulated grid

Unstructured (triangulated) grids have computational advantages over rectangular ones in three common situations:

With its computational speed and unconditional stability, the fast marching method provides considerable savings in comparison with alternative, more accurate methods, such as semi-analytical ray tracing Guiziou et al. (1991); Stankovic and Albertin (1995) or the general Hamilton-Jacobi solver of Abgrall (1996).

 
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Figure 5
Traveltime contours, computed in the rough Marmousi model (left), the smoothed Marmousi (middle), and the smoothed triangulated Marmousi (right).
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Figure 5 shows a comparison between first-arrival traveltime computations in regularly gridded and triangulated Marmousi models. The two results match each other within the first-order accuracy of the fast marching method. However, the cost of the triangulated computation has been greatly reduced by constraining the number of nodes.

Computational aspects of triangular grid generation are outlined in Appendix A. A three-dimensional application would follow the same algorithmic patterns.


next up previous print clean
Next: Conclusions Up: Fomel: Fast marching Previous: Variational principles on a
Stanford Exploration Project
9/12/2000