Seismic parameter estimation

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Seismic parameter estimation
Name Tor Erik Rabben Background Master of
Technology, Industrial Mathematics,
NTNU, Norway (2003) Supervisor Professor Bjørn
Ursin, NTNU, Norway Co-supervisor Professor
Henning Omre, NTNU, Norway Part of URE
Uncertainty in Reservoir Evaluation
http//www.math.ntnu.no/ure
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Vp and Vs
Dan Russell
Dan Russell
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OBS data acquisition
source
receivers
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Amplitude variations

• Amplitude variations are governed by the
  Zoeppritz equations
• Complicated equations depending on
• incident, reflection and transmission angles
• Vp and Vs in both layers and the density ratio
• Amplitude versus angle (AVA) data is needed for
  the inverse problem.

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Offset or angle
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Offset versus angle migration
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Offset versus angle migration
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Angle stacks (Sollid, 2000)
top reservoir
OW contact
PP data maps fluid
PS data maps lithology
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Zoeppritz equations

• Exact too many unknowns
• Linear approximation bias for large contrasts
• Second order valid for larger contrasts
• These approximations reduce the number of
  unknowns by a factor of two

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Zoeppritz equations

• Existing approximations are (among others)
• First order for isotropic media (Aki Richards)
• Second order for isotropic media (Stovas and
  Ursin, 2001)
• First order for transversely isotropic media
  (Rüger, 1996)
• First and second order for transversely isotropic
  media (Stovas and Ursin 2003)
• In addition Buland and Omre (2002) have developed
  analytical solutions to assess the uncertainties
  in linear approximations

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Project work

• Implement algorithm for second order
  approximations for transversely isotropic media
  and test on real data
• Develop approximations for orthorhombic and
  monoclinic anisotropic media
• Extend to amplitude versus angle and azimuth
  (AVAZ)
• Develop methods to assess uncertainties in second
  order approximations, using a Bayesian inversion
  model

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