This paper presents implementation techniques for the coupled wavenumber integration approach that is occasionally used in the underwater acoustics community to address larger scale problems in seismo-acoustics. This numerically efficient method is suitable for detailed wavefield representation of the long, thin waveguide propagating geometries such as those within subducting plate. It therefore represents an attractive alternative to ray-based solutions and finite element methods when thin layers with strong velocity contrast are expected. This wavefield modelling technique is based upon range-dependent wavenumber integration combined with Kirchhoff approximation. Examples of the details of the propagating wavefield with a dipping slab-like structure and the effects of low-velocity layers (LVLs) are presented. These results include the propagation of the wavefield through the wedge and through very LVLs as a function of setups of different complexity as well as a function of horizontal range. By identifying the existence of a sediment-like layer, the presence of a source within and the effects of the changes in the receiver range location, we demonstrate the ability of the coupled wavenumber technique to capture the physics associated with LVLs configuration, and provide classification features for effective identification of these, often intricate, subducted slab structure characteristic.