Normal Modes in Anisotropic VTI Media

It has been shown that long offset data and surface data inherit additional information about the subsurface. However, due to complexity of the wavefield at long offsets, it is challenging to find a simple link between the response and media parameters even for simple isotropic/isotropic interfaces. The equations become more complicated when anisotropy is included. In marine seismic exploration, the major part of the wavefield recorded at offsets larger than 6-10 km is dominated by the guided waves in the water layer, often referred to as normal modes. We suggest using the periodic equation as a link between the wavefield at long offsets and media parameters. An anisotropic version of the period equation using Thomsen's epsilon and delta is derived based on Anderson's derivation from 1961. We show that the acoustic approximation of the periodic equation for water/VTI interface has a simple form convenient for analysis. We assess the sensitivity of periodic equation to different parameters and conclude that this approach has a potential for estimating the degree of anisotropy for the water bottom which can be useful for geomechanical purposes.