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Arbitrary‐order Taylor series expansion‐based viscoacoustic wavefield simulation in 3D vertical transversely isotropic media
Author(s) -
Zhang Yabing,
Liu Yang,
Xu Shigang
Publication year - 2020
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/1365-2478.12999
Subject(s) - taylor series , transverse isotropy , seismic migration , mathematical analysis , attenuation , operator (biology) , anisotropy , wave propagation , isotropy , mathematics , physics , optics , geophysics , biochemistry , chemistry , repressor , transcription factor , gene
Taking the anisotropy of velocity and attenuation into account, we investigate the wavefield simulation of viscoacoustic waves in 3D vertical transversely isotropic attenuating media. The viscoacoustic wave equations with the decoupled amplitude attenuation and phase dispersion are derived from the fractional Laplacian operator and using the acoustic approximation. With respect to the spatially variable fractional Laplacian operator in the formulation, we develop an effective algorithm to realize the viscoacoustic wavefield extrapolation by using the arbitrary‐order Taylor series expansion. Based on the approximation, the mixed‐domain fractional Laplacian operators are decoupled from the wavenumbers and fractional orders. Thus, the viscoacoustic wave propagation can be conveniently implemented by using a generalized pseudospectral method. In addition, we perform the accuracy and efficiency analyses among first‐, second‐ and third‐order Taylor series expansion pseudospectral methods with different quality factors. Considering both the accuracy and computational cost, the second‐order Taylor series expansion pseudospectral method can generally satisfy the requirements for most attenuating media. Numerical modelling examples not only illustrate that our decoupled viscoacoustic wave equations can effectively describe the attenuating property of the medium, but also demonstrate the accuracy and the high robustness of our proposed schemes.