Alford rotation, ray theory, and crossed‐dipole geometry

Two generalizations of Alford rotation have been proposed for processing 2 × 2-component data containing nonorthogonal split shear waves: singular value decomposition (SVD) and eigenvector‐eigenvalue decomposition (EED). Using a simple crossed‐dipole synthetic model, we demonstrate that the physical model behind the EED method is invalid. It incorrectly assumes that a vector source aligned with the particle motion of an anisotropic pure mode will excite only that one mode. Ray theory shows that a vector point‐force source embedded in a homogeneous anisotropic medium instead excites all those modes with particle motions that are not perpendicular to the direction of the applied force, just as a vector point receiver detects all modes with polarizations that are not perpendicular to the receiver. Correctly generalized Alford rotation synthesizes vector sources and receivers such that each component is perpendicular to all but one of the pure modes of the medium. Although this ray‐theory result does not allo...