Elastic wave-mode separation for VTI media

Elastic wave propagation in anisotropic media is well rep- resented by elastic wave equations. Modeling based on elas- ticwaveequationscharacterizesbothkinematicsanddynam- ics correctly. However, because P- and S-modes are both propagated using elastic wave equations, there is a need to separate P- and S-modes to efficiently apply single-mode processing tools. In isotropic media, wave modes are usually separated using Helmholtz decomposition. However, Helm- holtz decomposition using conventional divergence and curl operators in anisotropic media does not give satisfactory re- sultsandleavesthedifferentwavemodesonlypartiallysepa- rated.Theseparationofanisotropicwavefieldsrequiresmore sophisticated operators that depend on local material param- eters. Anisotropic wavefield-separation operators are con- structedusingthepolarizationvectorsevaluatedateachpoint of the medium by solving the Christoffel equation for local mediumparameters.Thesepolarizationvectorscanberepre- sented in the space domain as localized filtering operators, which resemble conventional derivative operators. The spa- tially variable pseudo-derivative operators perform well in heterogeneous VTI media even at places of rapid velocity/ densityvariation.Syntheticresultsindicatethattheoperators can be used to separate wavefields for VTI media with an ar- bitrarydegreeofanisotropy.