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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 ,

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ray tracing in matlab

RAY TRACING IN MATLAB

Ruiqing He

University of Utah

Feb. 2003

outline
Outline
  • Introduction
  • Modeling
  • Strategy and steps
  • Reflection and multiple ray tracing
  • Examples
  • Conclusion
introduction
Introduction
  • Role of ray tracing in geophysics
  • Practical requirements:

accuracy, speed, ray path,

reflection, multiples, 3D,amplitude.

  • Matlab
ray tracing methods
Ray Tracing Methods
  • Shortest path methods:

Fischer (1993), Moser (1991)

  • Wave-equation-based:

Sava (2001)

this ray tracer
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
Modeling
  • Block model & grid model
strategy
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
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
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.

reflections and multiples
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 multiples2
Reflections and Multiples

Frozen exploding reflector

examples
Examples
  • Linear gradient model

Travel time field

Sec.

0.08

0.05

50 m

0

100 m

50 m

100 m

comparison
Comparison

0.09 s

T

0.07 s

75 m

95 m

Distance

ray path
Ray path

50 m

100 m

100 m

50 m

reflection ray tracing
Reflection ray tracing

50 m

100 m

50 m

100 m

multiple ray tracing
Multiple ray tracing

50 m

100 m

50 m

100 m

complex model ray tracing
Complex model ray tracing

Salt Dome Model

ft/s

14000

6000 ft

6000

12000 ft

25000 ft

50000 ft

travel time field
Travel Time Field

Sec.

5

3

6000 ft

12000 ft

0

25000 ft

50000 ft

ray path1
Ray Path

6000 ft

12000 ft

25000 ft

50000 ft

speed
Speed

CPU Time on a 2.2 GHZ AMD

CPU

Time

(Sec.)

16

10

2

40,000

90,000

10,000

Grid size

conclusion
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
Thanks
  • 2002 members of UTAM for financial support.