RAY TRACING IN MATLAB
Ruiqing He
University of Utah
Feb. 2003
Outline
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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
0
100 m
50 m
100 m
Comparison
0.09 s
T
0.07 s
75 m
Distance
95 m
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
0
25000 ft
50000 ft
Ray Path
6000 ft
12000 ft
25000 ft
50000 ft
Speed
CPU Time on a 2.2 GHZ AMD
CPU
Time
(Sec.) 16
10
2
10,000
40,000
Grid size
90,000
Conclusion
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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: [email protected]
Thanks
• 2002 members of UTAM for financial
support.