Seismic interferometry,

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Seismic interferometry, the optical theorem and a
non-linear point scatterer Kees Wapenaar
Evert Slob Roel Snieder Society of Exploration
Geophysicists Houston, October 26, 2009
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Interferometry
Non-linear
Paradox
Point scatterer
Optical theorem
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Interferometry
Modeling Inversion Interferometry Migration
Non-linear
Paradox
Point scatterer
Optical theorem
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Snieder, R., K.van Wijk, M.Haney, and R.Calvert,
2008, Cancellation of spurious arrivals in
Green's function extraction and the generalized
optical theorem Physical Review E, 78, 036606.
Halliday, D. and A.Curtis, 2009, Generalized
optical theorem for surface waves and layered
media Physical Review E, 79, 056603.
van Rossum, M. C. W. and T.M. Nieuwenhuizen,
1999, Multiple scattering of classical waves
microscopy, mesoscopy, and diffusion Reviews
of Modern Physics, 71, 313--371.
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Term 1
a
b
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Term 2
c
d
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Term 3
e
f
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Terms 1 2 3
c
a
e
f
b
d
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Terms 1 2 3, compared with modeled G
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Term 4
g
g
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Terms 1 2 3 4, compared with modeled G
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Terms 1 2 3, compared with modeled G
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Interferometry
Paradox
Point scatterer
Optical theorem
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Substitute into representation for interferometry
(Snieder et al., 2008, Halliday and Curtis,
2009)..
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This gives
Generalized optical theorem (Heisenberg, 1943)
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This gives
For comparison
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Interferometry
Non-linear
Paradox
Point scatterer
Optical theorem
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Isotropic point scatterer
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Isotropic point scatterer
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Interferometry
Non-linear
Paradox
Point scatterer
Optical theorem
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Interferometry
Non-linear
Paradox
Point scatterer
Optical theorem
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Terms 1 2 3
c
a
e
f
b
d
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Terms 1 2 3 4, compared with modeled G
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Interferometry
Modeling Inversion Interferometry Migration
Non-linear
Paradox
Point scatterer
Optical theorem
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Modeling, inversion and interferometry in
scatterering media Groenenboom and Snieder, 1995
Weglein et al., 2003 Van Manen et al., 2006
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Modeling, inversion and interferometry in
scatterering media Groenenboom and Snieder, 1995
Weglein et al., 2003 Van Manen et al., 2006
Limiting case Point scatterer
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Resolution function for seismic migration Miller
et al., 1987 Schuster and Hu, 2000 Gelius et
al., 2002 Lecomte, 2008
Migration deconvolution Yu, Hu, Schuster and
Estill, 2006
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Conclusions

• Born approximation is incompatible with seismic
  interferometry

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Conclusions

• Born approximation is incompatible with seismic
  interferometry
• Seismic interferometry optical
  theorem
• non-linear scatterer seismic
  interferometry
• Consequences for modeling, inversion,
  interferometry and migration

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Conclusions

• Born approximation is incompatible with seismic
  interferometry
• Seismic interferometry optical
  theorem
• non-linear scatterer seismic
  interferometry
• Consequences for modeling, inversion,
  interferometry and migration