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: rhe@mines.utah.edu

ThanksThanks

• 2002 members of UTAM for financial support.