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

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

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

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

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

Modeling Block model & grid model

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

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.

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.

Selection

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;

Reflections and Multiples

Reflections and Multiples Frozen exploding reflector

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

Comparison 0.09 s T 0.07 s 75 m 95 m Distance

Ray path 50 m 100 m 50 m 100 m

Reflection ray tracing 50 m 100 m 50 m 100 m

Multiple ray tracing 50 m 100 m 50 m 100 m

3D ray tracing

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

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

Ray Path 6000 ft 12000 ft 25000 ft 50000 ft

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

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 email: rhe@mines.utah.edu

Thanks 2002 members of UTAM for financial support.