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RAY TRACING IN MATLABRAY TRACING IN MATLAB
Ruiqing He
University of Utah
Feb. 2003
OutlineOutline
• Introduction
• Modeling
• Strategy and steps
• Reflection and multiple ray tracing
• Examples
• Conclusion
IntroductionIntroduction
• Role of ray tracing in geophysics
• Practical requirements:
accuracy, speed, ray path,
reflection, multiples, 3D, amplitude.
• Matlab
Ray Tracing MethodsRay Tracing Methods
• Shortest path methods:
Fischer (1993), Moser (1991)
• Wave-equation-based:
Sava (2001)
This Ray TracerThis Ray Tracer
• Shortest path method:
Grid of velocity is finer than or
equal to the grid of ray path.
• Versatile: reflection & multiples
• Accurate
• Robust
ModelingModeling• Block model & grid model
StrategyStrategy• 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
StepsSteps• 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.
SearchSearch
• 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.
SelectionSelection
Reflections and MultiplesReflections 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 MultiplesReflections and Multiples
Reflections and MultiplesReflections and Multiples
Frozen exploding reflector
ExamplesExamples• Linear gradient model
50 m 100 m
50 m
100 m
Travel time field Sec.
0.05
0.08
0
ComparisonComparison
T
Distance 95 m
0.09 s
0.07 s
75 m
Ray pathRay path
50 m100 m
100 m
50 m
Reflection ray tracingReflection ray tracing
50 m
50 m
100 m
100 m
Multiple ray tracingMultiple ray tracing
50 m
50 m
100 m
100 m
3D ray tracing3D ray tracing
Complex model ray tracingComplex model ray tracing
12000 ft
6000 ft
25000 ft 50000 ft
14000
6000
ft/sSalt Dome Model
Travel Time FieldTravel Time Field
12000 ft
6000 ft
25000 ft 50000 ft
Sec.5
3
0
Ray PathRay Path
6000 ft
12000 ft
25000 ft 50000 ft
SpeedSpeed
10,000 40,000 90,000
Grid size
CPU Time(Sec.)
2
10
16
CPU Time on a 2.2 GHZ AMD
ConclusionConclusion
• 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]
ThanksThanks
• 2002 members of UTAM for financial support.
