Preconditioning least-squares RTM in viscoacoustic media by Q-compensated RTM

Junzhe Sun, Sergey Fomel, Tieyuan Zhu

Research output: Contribution to journalConference article

18 Citations (Scopus)

Abstract

Reverse-time de-migration (RTDM) is formulated as the ad-joint operator of reverse-time migration (RTM). In acoustic medium, RTM provides a good approximation to the inverse of RTDM, and can be used to iteratively invert for the reflectivity image in least-squares RTM (LSRTM). In viscoelastic medium, however, the adjoint of the RTDM operator is far from its inverse because of amplitude attenuation during both forward and backward wave propagation. As a result, LSRTM in attenuating medium may suffer from a slow convergence rate due to the ill-conditioned wave-equation Hessian. To improve the convergence rate, we propose preconditioning LSRTM by replacing the original RTM operator with a better approximate inverse to the RTDM operator, namely the Q-compensated RTM (Q-RTM). Since the inverted matrix is numerically non-Hermitian, we use the Generalized Minimum Residual (GMRES) method instead of the Conjugate Gradient (CG) method as the iterative method. Numerical tests demonstrate that the proposed Q-LSRTM approach converges significantly faster than LSRTM, and is capable of producing high-quality attenuation-compensated images within the first few iterations.

Original languageEnglish (US)
Pages (from-to)3959-3965
Number of pages7
JournalSEG Technical Program Expanded Abstracts
Volume34
DOIs
StatePublished - Jan 1 2015
EventSEG New Orleans Annual Meeting, SEG 2015 - New Orleans, United States
Duration: Oct 18 2011Oct 23 2011

Fingerprint

Resin transfer molding
preconditioning
reaction time
resin transfer molding
Conjugate gradient method
operators
Wave equations
Iterative methods
Wave propagation
Acoustics
attenuation
conjugate gradient method
backward waves
wave equation
reflectivity
wave propagation
wave equations
iteration
acoustics
reflectance

All Science Journal Classification (ASJC) codes

  • Geotechnical Engineering and Engineering Geology
  • Geophysics

Cite this

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title = "Preconditioning least-squares RTM in viscoacoustic media by Q-compensated RTM",
abstract = "Reverse-time de-migration (RTDM) is formulated as the ad-joint operator of reverse-time migration (RTM). In acoustic medium, RTM provides a good approximation to the inverse of RTDM, and can be used to iteratively invert for the reflectivity image in least-squares RTM (LSRTM). In viscoelastic medium, however, the adjoint of the RTDM operator is far from its inverse because of amplitude attenuation during both forward and backward wave propagation. As a result, LSRTM in attenuating medium may suffer from a slow convergence rate due to the ill-conditioned wave-equation Hessian. To improve the convergence rate, we propose preconditioning LSRTM by replacing the original RTM operator with a better approximate inverse to the RTDM operator, namely the Q-compensated RTM (Q-RTM). Since the inverted matrix is numerically non-Hermitian, we use the Generalized Minimum Residual (GMRES) method instead of the Conjugate Gradient (CG) method as the iterative method. Numerical tests demonstrate that the proposed Q-LSRTM approach converges significantly faster than LSRTM, and is capable of producing high-quality attenuation-compensated images within the first few iterations.",
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Preconditioning least-squares RTM in viscoacoustic media by Q-compensated RTM. / Sun, Junzhe; Fomel, Sergey; Zhu, Tieyuan.

In: SEG Technical Program Expanded Abstracts, Vol. 34, 01.01.2015, p. 3959-3965.

Research output: Contribution to journalConference article

TY - JOUR

T1 - Preconditioning least-squares RTM in viscoacoustic media by Q-compensated RTM

AU - Sun, Junzhe

AU - Fomel, Sergey

AU - Zhu, Tieyuan

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Reverse-time de-migration (RTDM) is formulated as the ad-joint operator of reverse-time migration (RTM). In acoustic medium, RTM provides a good approximation to the inverse of RTDM, and can be used to iteratively invert for the reflectivity image in least-squares RTM (LSRTM). In viscoelastic medium, however, the adjoint of the RTDM operator is far from its inverse because of amplitude attenuation during both forward and backward wave propagation. As a result, LSRTM in attenuating medium may suffer from a slow convergence rate due to the ill-conditioned wave-equation Hessian. To improve the convergence rate, we propose preconditioning LSRTM by replacing the original RTM operator with a better approximate inverse to the RTDM operator, namely the Q-compensated RTM (Q-RTM). Since the inverted matrix is numerically non-Hermitian, we use the Generalized Minimum Residual (GMRES) method instead of the Conjugate Gradient (CG) method as the iterative method. Numerical tests demonstrate that the proposed Q-LSRTM approach converges significantly faster than LSRTM, and is capable of producing high-quality attenuation-compensated images within the first few iterations.

AB - Reverse-time de-migration (RTDM) is formulated as the ad-joint operator of reverse-time migration (RTM). In acoustic medium, RTM provides a good approximation to the inverse of RTDM, and can be used to iteratively invert for the reflectivity image in least-squares RTM (LSRTM). In viscoelastic medium, however, the adjoint of the RTDM operator is far from its inverse because of amplitude attenuation during both forward and backward wave propagation. As a result, LSRTM in attenuating medium may suffer from a slow convergence rate due to the ill-conditioned wave-equation Hessian. To improve the convergence rate, we propose preconditioning LSRTM by replacing the original RTM operator with a better approximate inverse to the RTDM operator, namely the Q-compensated RTM (Q-RTM). Since the inverted matrix is numerically non-Hermitian, we use the Generalized Minimum Residual (GMRES) method instead of the Conjugate Gradient (CG) method as the iterative method. Numerical tests demonstrate that the proposed Q-LSRTM approach converges significantly faster than LSRTM, and is capable of producing high-quality attenuation-compensated images within the first few iterations.

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