On the Helmholtz Decomposition in Weakly Anisotropic VTI Media

Starting from the VTI wave equation, we derive an extension of the Helmholtz decomposition theorem for vector fields to represent the displacement wavefield in a homogeneous weakly anisotropic VTI medium. We show that the elastic wave equation can be transformed into two simple differential equations and a system of two coupled differential equations. The coupled equations system describes the pseudo-acoustic qP wavefield and the other two equations represent the qSV and qSH wavefields, respectively. This constitutes an elegant generalization of known facts about wave propagation in VTI media. Finally, we show how the decomposition can be applied to perform wave-mode separation in VTI media.