Seismic Imaging and Inversion by Robert H. Stolt & Arthur b Weglein
Viscoelastic scattering potentials and full waveform ...€¦ · (Robert H. Stolt, Professor Arthur...
Transcript of Viscoelastic scattering potentials and full waveform ...€¦ · (Robert H. Stolt, Professor Arthur...
Viscoelastic scattering potentials and full waveform inversion
sensitivities
Shahpoor MoradiKris Innanen
Outline
• Motivations: Scattering and exploration seismology
• Scattering theory• Elastic scattering potential• Viscoelastic scattering potential• Viscoelastic sensitivities• Conclusion and future direction
Motivations
• Quantification of the wave propagation in complex realisticmedia.
• Modeling of inhomogeneous wave propagation.
• Direct inverse scattering for seismic data processing.
• Inversion in attenuating media
• Mathematical form of full waveform inversion updates andsensitivities for determining and .
Scattering theory
Perturbation operatorReference
medium(unperturbed)
Actual medium(perturbed)
Perturbation in the properties of
a medium
Wave-field experienced the
perturbed medium
Forward Scattering
• Reference medium• Reference wave-field • Perturbation operator
Actual wave-field
Backward Scattering
• Reference medium• Reference wave-field • Actual wave-field
Perturbation operator
Lippmann–Schwinger equation
Reference medium
Actual medium
Scattering operator
Lippmann–Schwinger equation
Scattered field operator
Born Series
Elastic scattering potential
For isotropic, elastic earth the wave equation is given by
Scattering potential
Perturbation parameters
P- and S-velocity
Elastic scattering potential
Bulk modulus
.
Scattering Potential transformation(Robert H. Stolt, Professor Arthur B. Weglein Seismic Imaging and Inversion, 2012)
Strain
Stre
ss
Elastic
Viscoelastic Scattering Potential
Strain
Energy loss
Viscoelastic
Stre
ss
1) Viscoelastic Scattering Operator
2) Definition of orthogonal frame constructed by displacement vectors
P-waves S-I waves S-II wavesInhomogeneous
Homogeneous
Inhomogeneous waves
Framework for inhomogeneous waves
n
n
n
Roger D. Borcherdt, Viscoelastic Waves in Layered Media, (2009)
.
Transformation ofScattering Potential
Viscoelastic P-P scattering element
Elastic P-P scattering element
HM-HM HM-IHM
IHM-HM IHM-IHM
0.212
30
Scattering of homogeneous P-wave to inhomogeneous P-wave
Elastic
Difference
Elastic
Difference
VISCOELASTIC SENSITIVITIES
Sensitivity of the P-P field to
1) Construction of the scattering potential for a viscoelastic medium based onStolt and Weglein method.
2) We explicitly demonstrate that the components of the scattering potentialrelated to the scattering of SII-waves to P- and SI waves are zero. In otherwords SII-waves can only scattered to SII-waves.
3) We have shown that viscoelastic scattering potential can be expressed aselastic scattering potential plus an additional perturbing term related to theinhomogeneity of waves and quality factors of P- and S-waves.
4) Investigation of sensitivities to make up the gradient for FWI.5) Q estimation based on amplitude attenuation for inverse Q filtering.6) Viscoelastic AVO approximations.
Conclusions and future direction
CREWES sponsors.Kris Innanen.Shahin Moradi. Hassan Khaniani.