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**Ruiqing He University of Utah Feb. 2003**

RAY TRACING IN MATLAB Ruiqing He University of Utah Feb

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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(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.

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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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**Reflections and Multiples**

Frozen exploding reflector

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

100 m 50 m 100 m

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Comparison 0.09 s T 0.07 s 75 m 95 m Distance

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Ray path 50 m 100 m 50 m 100 m

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**Reflection ray tracing**

50 m 100 m 50 m 100 m

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Multiple ray tracing 50 m 100 m 50 m 100 m

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3D ray tracing

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**Complex model ray tracing**

Salt Dome Model ft/s 14000 6000 ft 6000 12000 ft 25000 ft 50000 ft

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

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Ray Path 6000 ft 12000 ft 25000 ft 50000 ft

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**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

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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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