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## Exploding Reflector Modeling

The subsurface model is used to trace rays up to the surface from points on the reflectors of interest at finely-sampled opening (polar) and azimuth angles. The number and location of the reflecting points on the reflectors of interest, as well as the number of rays shot from each such point, is a matter of design. The important point is that they represent our ideal subsurface illumination response. Departures from this ideal will be penalized in the optimization process. For this paper I used the Integra software to do the ray tracing. I used Gocad to compute a stratigraphic grid draped over the target reflector (Figure ) and used the grid centers as the starting points for the rays. The grid is 25 x 25 m and 20 rays were shot from each point. The range of azimuths was from 0 to 135 degrees in intervals of 45 and the range of opening angles was from 0 to 60 degrees in intervals of 15 degrees. Figure  shows ray cones emanating from a few selected points on the target horizon's surface.

rays1
Figure 6
Exploding reflector rays. Rays from a few of the reflecting points on the target horizon. There are several thousand such reflecting points, so the resulting density of rays is very large.

Integra ray tracing program computes, for each ray, its travel time and the coordinates of the emerging point at the surface. The program also records the coordinates of the normal to the reflector at the starting point, as well as the opening and azimuth angle of the corresponding ray. In the present example I used this information to separate the rays originating at different depths in the target reflector.

Next: Geometry Optimization Up: The Proposed Approach Previous: Building of the Model
Stanford Exploration Project
7/8/2003