An Approximate Acoustic Wave Equation for VTI Media

详细信息   

• 责任者：Huang Yijian (State Key Laboratory of Continental Dynamics ; Institute of Oil and Gas of Northwest University ; Xi’an 710069 ; China) ; Zhu Guangming
• 刊名：Chinese Journal of Geophysics
• 出版年：2011
• 卷期：54(8)
• 关键词：声波 ; acoustical waves ; 波动方程 ; wave equation ; 横向各向同性 ; transverse isotropy
• 页码：p.2117-2123
• 图表：4 illus., 1 table, 16 refs.
• 分类号：1600
• issnNo：ISSN0001-5733
• isbnNo：CN11-2074/P

摘要

Acoustic approximation is an effective way to simplify modeling and migration of quasi- P waves in the case of anisotropy. To generate a new acoustic wave equation for VTI media （transversely isotropic media with a vertical symmetric axis） from the accurate phase velocity expression, we make simplification to the square root term by an undetermined coefficients method to get an approximate phase velocity formula, from which we derive a second-order temporal and fourth-order spatial partial derivative equation through inverse Fourier transform. Quantitative computations show that the phase velocity specified by the new acoustic equation is accurate when Thomsen parameter ε is equal to δ （elliptical anisotropy） and the errors of the phase velocity become bigger as the difference between ε and δ gets bigger. The maximum relative error of the phase velocity is 0.13% in the case of ε=0.1 and δ=0.2, and becomes -1.65% in the case of ε= 0.8 and δ= 0.3. The shear-wave-free snap shots from finite difference modeling demonstrate that the new acoustic equation is a pure quasi-P wave equation.