Eigenrays in 3D heterogeneous anisotropic media: Part I -- Kinematics, Variational formulation

摘要: Parts V, VI and VII of this study are dedicated to the computation paraxial rays dynamic characteristics along stationary obtained numerically in Part III. In part (Part V), we formulate linear, second-order, Jacobi ray tracing equation. VI, compare Lagrangian Hamiltonian approaches heterogeneous isotropic anisotropic media; demonstrate that two compatible derive relationships between Lagrangian's Hamiltonian's Hessian matrices. VII, apply a similar finite-element solver, as used for kinematic tracing, compute source any point ray. The our include relative geometric spreading phase correction factor due caustics (i.e., amplitude Green's function waves propagating 3D media). basic solution equation is shift vector plane normal direction at each central A general defined by linear combination up four solutions, corresponds specific initial conditions related coordinates source. We define solutions with pairs condition sets: point-source plane-wave. For proposed conditions, Jacobian relate it anisotropy. Finally, introduce new parameter, referred normalized geometrical spreading, considered measure complexity propagated wave/ray phenomena, hence, propose using criterion based on parameter qualifying associated given solution.