Arbitrary‐order Taylor series expansion‐based viscoacoustic wavefield simulation in 3D vertical transversely isotropic media

Abstract

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.

Weibull analysis of ceramics and related materials: A review

“…Using the first two terms in the Taylor series expansion they got the subsequent estimators given in equations (13.2)–(13.5) [ 212 , 213 ]: where: where is known as the inverse distribution function for the 3-parameter W d . Though the Fisher data matrix was applied to get asymptotic alterations and covariance as it occurs for , it is also possible to find the MML estimators for [ 214 , 215 ].…”

Modified pure-viscoacoustic wave propagation and compensated reverse-time migration in transversely isotropic media

“…Although many Q-RTM applications are implemented to improve the resolution of seismic imaging Li et al, 2016;Wang et al, 2018;Wang et al, 2019;Chen et al, 2020), however, most of these implementations ignore the anisotropy of seismic velocity and attenuation, which will inevitably harm the imaging results. Recently, some anisotropic viscoacoustic and viscoelastic wave equations have been derived to simulate the effect of attenuation and anisotropy on wavefield propagations (Bai and Tsvankin, 2016;Da Silva et al, 2019;Hao and Alkhalifah, 2019;Qiao et al, 2019;Qiao et al, 2020;Zhu and Bai, 2019;Zhang et al, 2020). Considering the significant computational cost and the complexity of wave-mode decomposition in viscoelastic wavefield propagation, the viscoacoustic wave equation is probably a better choice for anisotropic Q-RTM (Mu et al, 2022;Qiao et al, 2022).…”