Pseudoacoustic anisotropic wave equations are simplifiedelastic wave equations obtained by setting the S-wave velocityto zero along the anisotropy axis of symmetry. These pseudoacousticwave equations greatly reduce the computationalcost of modeling and imaging compared to the full elastic waveequation while preserving P-wave kinematics very well. For thisreason, they are widely used in reverse time migration (RTM) toaccount for anisotropic effects. One fundamental shortcomingof this pseudoacoustic approximation is that it only preventsS-wave propagation along the symmetry axis and not in otherdirections. This problem leads to the presence of unwantedS-waves in P-wave simulation results and brings artifacts intoP-wave RTM images. More significantly, the pseudoacousticwave equations become unstable for anisotropy parameters? < δ and for heterogeneous models with highly varying dipand azimuth angles in tilted transversely isotropic (TTI) media.Pure acoustic anisotropic wave equations completely decouplethe P-wave response from the elastic wavefield and naturallysolve all the above-mentioned problems of the pseudoacousticwave equations without significantly increasing the computationalcost. In this work, we propose new pure acoustic TTIwave equations and compare them with the conventionalcoupled pseudoacoustic wave equations. Our equations canbe directly solved using either the finite-difference method orthe pseudospectral method. We give two approaches to derivethese equations. One employs Taylor series expansion toapproximate the pseudodifferential operator in the decoupledP-wave equation, and the other uses isotropic and ellipticallyanisotropic dispersion relations to reduce the temporal frequencyorder of the P-SV dispersion equation. We use severalnumerical examples to demonstrate that the newly derived pureacoustic wave equations produce highly accurate P-wave results,very close to results produced by coupled pseudoacousticwave equations, but completely free from S-wave artifacts andinstabilities.
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