1. School of Geosciences, China University of Petroleum(East China), Qingdao, Shandong 266580, China; 2. Evaluation and Detection Technology Laboratory for Marine Mineral Resources, Qingdao, Shandong 266071, China
Abstract:The condition for linear approximation of weak anisotropy given by Thomsen is that absolute anisotropy is less than 0.2.However,for some highly anisotropic rocks,because the absolute value of anisotropy is large,the phase velocity error calculated by weak anisotropy linear approximation is large.A linear approximation formula for extended anisotropy of elastic wave phase velocity in VTI media is proposed.The formula maintains a linear relationship to anisotropic parameters.Starting from the accurate phase velocity formula of elastic wave in VTI media,a first-order Taylor expansion is performed at the tangent point of the accurate expression function curve and linear approximation function curve of phase velocity,a Jacobi matrix is formed from the first-order partial derivative of the phase velocity at the tangent point to the anisotropic parameter,and the extended anisotropic linear approximation formula is obtained.Theoretical analysis and numerical examples show that,when the absolute value of anisotropy is small,the results obtained by the weak anisotropy linear approximation and the extended anisotropy linear approximation agree well with theoretical values;when the absolute value of anisotropy is larger,the result obtained by the weak anisotropy approximation is larger than the theoretical value,and the result obtained by the linear anisotropy extension is in good agreement with the theoretical value.It’s proved that the extended anisotropic linear approximation is applicable for strong anisotropy by adjusting the tangent point of linear approximation.
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