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

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

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

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

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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

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Modeling Block model & grid model

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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

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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.

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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.

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Selection

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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;

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Reflections and Multiples

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Frozen exploding reflector

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

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Comparison T Distance 95 m 0.09 s 0.07 s 75 m

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Ray path 50 m 100 m 50 m

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Reflection ray tracing 50 m 100 m

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Multiple ray tracing 50 m 100 m

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3D ray tracing

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

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Travel Time Field ft 6000 ft ft50000 ft Sec

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Ray Path 6000 ft ft ft50000 ft

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

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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

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Thanks 2002 members of UTAM for financial support.

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