期刊
GEOPHYSICAL JOURNAL INTERNATIONAL
卷 207, 期 1, 页码 129-149出版社
OXFORD UNIV PRESS
DOI: 10.1093/gji/ggw262
关键词
Fourier analysis; Inverse theory; Seismic attenuation; Seismic tomography; Wave propagation
资金
- SEISCOPE consortium
- BP
- CGG
- CHEVRON
- EXXON-MOBIL
- JGI
- PETROBRAS
- SAUDI ARAMCO
- SCHLUMBERGER
- SHELL
- SINOPEC
- STATOIL
- TOTAL
- WOODSIDE
- Rhone-Alpes region [CPER07_13 CIRA]
- OSUG@2020 labex [ANR10 LABX56]
- Equip@Meso project [ANR-10-EQPX-29-01]
- HPC resources of CINES/IDRIS [046091]
In this paper, we study 3-D multiparameter full waveform inversion (FWI) in viscoelastic media based on the generalized Maxwell/Zener body including arbitrary number of attenuation mechanisms. We present a frequency-domain energy analysis to establish the stability condition of a full anisotropic viscoelastic system, according to zero-valued boundary condition and the elastic-viscoelastic correspondence principle: the real-valued stiffness matrix becomes a complex-valued one in Fourier domain when seismic attenuation is taken into account. We develop a least-squares optimization approach to linearly relate the quality factor with the anelastic coefficients by estimating a set of constants which are independent of the spatial coordinates, which supplies an explicit incorporation of the parameter Q in the general viscoelastic wave equation. By introducing the Lagrangian multipliers into the matrix expression of the wave equation with implicit time integration, we build a systematic formulation of multiparameter FWI for full anisotropic viscoelastic wave equation, while the equivalent form of the state and adjoint equation with explicit time integration is available to be resolved efficiently. In particular, this formulation lays the foundation for the inversion of the parameter Q in the time domain with full anisotropic viscoelastic properties. In the 3-D isotropic viscoelastic settings, the anelastic coefficients and the quality factors using bulk and shear moduli parametrization can be related to the counterparts using P and S velocity. Gradients with respect to any other parameter of interest can be found by chain rule. Pioneering numerical validations as well as the real applications of this most generic framework will be carried out to disclose the potential of viscoelastic FWI when adequate high-performance computing resources and the field data are available.
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