Using simplex for 3-D two point ray tracing on very complex surfaces

Philippe Nobili and Jean-Laurent Mallet and Yungao Huang. ( 1990 )
in: SEG Technical Program Expanded Abstracts, pages 1020--1023

Abstract

In the frame of the GOCAD project, we have proposed (See [9], [8]) to model very complex geological surfaces with triangles. This choice of triangular facets was governed by the fact that any surface can always be decomposed into flat or curvilinear triangles and we will show in this paper that this decomposition can also be used to solve the two point ray tracing problem very efficiently. The determination of the ray path is based on Fermat's principle consisting of minimizing the travel time on each ray for a given shot point, a given receiver and a given reflector; the minimization is performed iteratively by a simplex method using the triangular decomposition of the surfaces. The initial rays may be provided by a shooting algorithm a ray migration algorithm or a bending algorithm. Moreover, the geometrical data base of the GOCAD software allows to account for dynamic signatures; for that purpose, we define homogeneous domains of the 3D space by boundary surfaces and we have developed a new algorithm based on a finite states automata for determining the domain corresponding to any given point in the 3D space. Some examples of applications are presented.

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BibTeX Reference

@INPROCEEDINGS{nobili:1020,
    author = { Nobili, Philippe and Mallet, Jean-Laurent and Huang, Yungao },
     title = { Using simplex for 3-D two point ray tracing on very complex surfaces },
 booktitle = { SEG Technical Program Expanded Abstracts },
    volume = { 9 },
    number = { 1 },
   chapter = { 0 },
      year = { 1990 },
     pages = { 1020--1023 },
       doi = { 10.1190/1.1889896 },
  abstract = { In the frame of the GOCAD project, we have proposed (See [9], [8]) to model very complex geological surfaces with triangles. This choice of triangular facets was governed by the fact that any surface can always be decomposed into flat or curvilinear triangles and we will show in this paper that this decomposition can also be used to solve the two point ray tracing problem very efficiently. The determination of the ray path is based on Fermat's principle consisting of minimizing the travel time on each ray for a given shot point, a given receiver and a given reflector; the minimization is performed iteratively by a simplex method using the triangular decomposition of the surfaces. The initial rays may be provided by a shooting algorithm a ray migration algorithm or a bending algorithm. Moreover, the geometrical data base of the GOCAD software allows to account for dynamic signatures; for that purpose, we define homogeneous domains of the 3D space by boundary surfaces and we have developed a new algorithm based on a finite states automata for determining the domain corresponding to any given point in the 3D space. Some examples of applications are presented. }
}