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

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Presentation on theme: "RAY TRACING IN MATLAB Ruiqing He University of Utah Feb. 2003."— Presentation transcript:


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

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

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

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

6 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

7 Modeling Block model & grid model

8 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

9 Steps Step 0: T( x 0, z 0 )=0; Flag( x 0, z 0 )=2; Ray( x 0,z 0,1)= x 0 ; Ray( x 0,z 0,2)= z 0 ; Step 1: sub-ray tracing from the original source.

10 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.

11 Selection

12 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;

13 Reflections and Multiples

14 Frozen exploding reflector

15 Examples Linear gradient model 50 m100 m 50 m 100 m Travel time field Sec

16 Comparison T Distance 95 m 0.09 s 0.07 s 75 m

17 Ray path 50 m 100 m 50 m

18 Reflection ray tracing 50 m 100 m

19 Multiple ray tracing 50 m 100 m

20 3D ray tracing

21 Complex model ray tracing ft 6000 ft ft50000 ft ft/s Salt Dome Model

22 Travel Time Field ft 6000 ft ft50000 ft Sec

23 Ray Path 6000 ft ft ft50000 ft

24 Speed 10,000 40,00090,000 Grid size CPU Time (Sec.) CPU Time on a 2.2 GHZ AMD

25 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

26 Thanks 2002 members of UTAM for financial support.

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