Elastic wave propagation in anisotropic media is well rep-resented by elastic wave equations. Modeling based on elas-tic wave equations characterizes both kinematics and dynam-ics correctly. However, because P- and S-modes are bothpropagated using elastic wave equations, there is a need toseparate P- and S-modes to efficiently apply single-modeprocessing tools. In isotropic media, wave modes are usuallyseparated using Helmholtz decomposition. However, Helm-holtz decomposition using conventional divergence and curloperators in anisotropic media does not give satisfactory re-sults and leaves the different wave modes only partially sepa-rated. The separation of anisotropic wavefields requires moresophisticated operators that depend on local material param-eters. Anisotropic wavefield-separation operators are con-structed using the polarization vectors evaluated at each pointof the medium by solving the Christoffel equation for localmedium parameters. These polarization vectors can be repre-sented in the space domain as localized filtering operators,which resemble conventional derivative operators. The spa-tially variable pseudo-derivative operators perform well inheterogeneous VTI media even at places of rapid velocity/density variation. Synthetic results indicate that the operatorscan be used to separate wavefields for VTI media with an ar-bitrary degree of anisotropy.
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