Tutorial on Green

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Tutorial on Greens Theorem and Forward Modeling,
SRME, Interferometry, and Migration
..
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Outline

• Greens Functions
• Forward Modeling

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What is a Greens Function?
Answer Point Src. Response of Medium
Answer Impulse-Point Src. Response of Medium
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What is a Greens Function?
Answer Point Src. Response of Medium
Answer Impulse-Point Src. Response of Medium
Far field approx
k
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Wave in Heterogeneous Medium
(2)
wt
kr (kc ) r /c
r
Valid at high w and smooth media
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Outline

• Greens Functions
• Forward Modeling
• SRME
• Acausal GF, Stationarity, Reciprocity
• Interferometry
• Migration

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What is Huygens Principle?
Answer Every pt. on a wavefront is a secondary
src. pt.
Common tangent kinematically defines next
wavefront.
T
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What is Huygen-Fresnel Principle?
Answer Every pt. on a wavefront is a secondary
src. pt.
Next wavefront is sum of weighted Greens
functions.
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What is Huygen-Fresnel Principle?
Answer Every pt. on a wavefront is a secondary
src. pt.
Next wavefront is sum of weighted Greens
functions.
T
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Problem with Huygens Principle?
T
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Problem with Huygens Principle?
T
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Problem with Huygens Principle?
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Problem with Huygens Principle?
PdG/dn

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Greens Theorem Forward Modeling

2
d x
G(xx)
P(x )
P(x )

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Outline

• Greens Functions
• Forward Modeling
• SRME
• Acausal GF, Stationarity, Reciprocity
• Interferometry
• Migration

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Reciprocity Eqn. of Convolution Type
0. Define Problem
Given
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Reciprocity Eqn. of Convolution Type
1. Helmholtz Eqns

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Reciprocity Eqn. of Convolution Type
3. Integrate over a volume
4. Gausss Theorem
G(AB)
Free surface
x
A
B
Integration at infinity vanishes
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Reciprocity Eqn. of Convolution Type
3. Integrate over a volume
4. Gausss Theorem
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Reciprocity Eqn. of Convolution Type
1st interface
Remember, g(A) is a ½ space shot gather with src
at B and rec at A
1st interface
Dashed yellow ray is just a primary and
ghost reflection off of sea-floor. .Higher-order
multiples will also contribute..but we assume
they are weak
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Summary
1st interface
Dashed yellow ray is just a primary and
ghost reflection off of sea-floor. .Higher-order
multiples will also contribute..but we assume
they are weak