1. Ruiqing He University of Utah Feb. 2003
RAY TRACING IN MATLAB
Ruiqing He
University of Utah
Feb

2. Outline Introduction Modeling Strategy and steps
Reflection and multiple ray tracing
Examples
Conclusion

3. Introduction Role of ray tracing in geophysics Practical requirements:
accuracy, speed, ray path,
reflection, multiples, 3D, amplitude.
Matlab

4. Ray Tracing Methods Shortest path methods:
Fischer (1993), Moser (1991)
Wave-equation-based:
Sava (2001)

5. This Ray Tracer Shortest path method:
Grid of velocity is finer than or
equal to the grid of ray path.
Versatile: reflection & multiples
Accurate
Robust

6. Modeling
Block model & grid model

7. Strategy Fermat’s principle Huygen’s principle:
original source and secondary source
Data structure: V(x,z), T(x,z), Ray(x,z,1:2)
Flag(x,z): 0-unvisited; 1-visited; 2-decided

8. Steps Step 0: T(x0,z0)=0; Flag(x0,z0)=2;
Ray(x0,z0,1)=x0; Ray(x0,z0,2)=z0;
Step 1: sub-ray tracing from the original source.

9. Search Step 2: all visited nodes record:
T(x,z) and Ray(x,z,1:2), Flag(x,z)=1.
Step 3: search nodes Flag(x,z)==1 & min(T(x,z)).
Step 4: decided node = next secondary source, as
original source, repeat from step 0, until all
interested nodes are decided.

10. Selection

11. Reflections and Multiples
Step 1: do one transmission ray tracing until all nodes on the reflector are decided.
Step 2: keep these nodes and make them Flag=1, refresh all other nodes.
Step 3: jump directly into step 3 in the transmission ray tracing loop.
So, 1 reflection ray tracing = 2 transmission ray tracing;
1 first order multiple ray tracing = 4 transmission ray tracing;
1 2nd order multiple ray tracing = 6 transmission ray tracing;

12. Reflections and Multiples

13. Reflections and Multiples
Frozen exploding reflector

14. Examples Linear gradient model Travel time field Sec. 0.08 0.05 50 m
100 m
50 m
100 m

15. Comparison
0.09 s T
0.07 s
75 m
95 m
Distance

16. Ray path
50 m
100 m
50 m
100 m

17. Reflection ray tracing
50 m
100 m
50 m
100 m

18. Multiple ray tracing
50 m
100 m
50 m
100 m

19. 3D ray tracing

20. Complex model ray tracing
Salt Dome Model
ft/s
14000
6000 ft
6000
12000 ft
25000 ft
50000 ft

21. Travel Time Field
Sec. 5
6000 ft 3
12000 ft
25000 ft
50000 ft

22. Ray Path
6000 ft
12000 ft
25000 ft
50000 ft

23. Speed CPU Time on a 2.2 GHZ AMD Grid size CPU Time (Sec.) 16 10 2
10,000
40,000
90,000
Grid size

24. Conclusion Flexibility: ray path, reflections & multiples
Speed: depends on sub ray tracing length
Accuracy and robustness
Applications: tomography and migration
Extendable: C or Fortran
Available by

25. Thanks
2002 members of UTAM for financial support.