An Approximate Acoustic Wave Equation for VTI Media

Abstract

AbstractAcoustic approximation is an effective way to simplify modeling and migration of quasi‐P waves in the presence 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 differential equation through inverse Fourier transform. Quantitative computations show that the phase velocity specified by the new acoustic wave 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 snapshots from finite difference modeling demonstrate that the new acoustic wave equation is a pure quasi‐P wave equation.