Ray Velocity Derivatives in Anisotropic Elastic Media. Part II - Polar Anisotropy

In Part I of this study, we obtained the ray (group) velocity gradients and Hessians with respect to locations, directions anisotropic model parameters, at nodal points along trajectories, considering general (triclinic) media both, quasi-compressional quasi-shear waves. Ray derivatives for higher symmetries were considered particular cases anisotropy. part, II, follow computational workflow presented in I, formulating directly polar (transverse isotropy tilted axis symmetry, TTI) coupled qP qSV waves SH The acoustic approximation is a special case. medium properties, normally specified regular three-dimensional fine grid points, are five material parameters: axial compressional shear velocities three Thomsen two geometric angles defining local direction symmetry axis. All parameters assumed spatially (smoothly) varying, where their can be reliably computed. Two case examples considered; first represents compacted shale/sand rocks (with positive anellipticity) second, unconsolidated sand strong negative anellipticity (manifesting triplication). part tested by comparing them corresponding numerical (finite difference) derivatives. Additionally, show that exactly same results (ray derivatives) if transform given (five geometric) into twenty-one stiffness tensor components medium, apply theory derived I.