REFERENCES

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Beydoun, W. B., and Keho, T. H., 1987, The paraxial ray method: Geophysics, 52, no. 12, 1639-1653.

Cervený, V., 1987, Ray tracing algorithms in three-dimensional laterally varying layered structures in Nolet, G., Ed., Seismic Tomography:: Riedel Publishing Co., 99-134.

Fomel, S., 1997, A variational formulation of the fast marching eikonal solver: SEP-95, 127-147.

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A In this Appendix, we present a description of the steps taken during the interpolation process as described in this paper.

Figure 10 is a 3-D representation of the rays shot on the Gaussian velocity anomaly model. Note that the rays are heavily bent, which makes it very difficult to interpolate in a consistent way, especially in the central part where the velocity anomaly is located.

Figure 11 is a representation of the same rays expanded in the ray parameter direction. The correct succession of rays becomes more obvious.

Figure 12 shows the rays expanded in the take-off angle direction and the triangles built on them.

Figure 13 shows the surface built on the rays when collapsed in the 2-D plane. It is practically not possible to see the features of the surface.

 

1
Figure 10 A 3-D view of the rays shot in the 2-D plane. Compare this figure with Figure 4.

 

2
Figure 11 A 3-D view of the rays expanded in the take-off angle direction.

 

3
Figure 12 A 3-D view of the triangles built on the rays expanded in the take-off angle direction.

 

4
Figure 13 The same surface as in Figure 12 collapsed back into the 2-D plane, when the take-off angle is not used.