Many ray tracers based on the anisotropic ray theory yield distorted results or even collapse when shear waves propagating in inhomogeneous weakly anisotropic models are computed. The coupling ray theory provides more accurate polarizations and travel times of S-waves in inhomogeneous models with weak anisotropy than the anisotropic ray theory and solves the problematic behaviour of S-wave polarizations. We test the application of the prevailing-frequency approximation of the coupling ray theory to 3D ray-based Kirchhoff pre-stack depth scalar migration and compute migrated sections in two simple inhomogeneous weakly anisotropic velocity models composed of two layers separated by a curved interface. The recorded complete seismic wave field is calculated using the Fourier pseudospectral method. We use a scalar imaging for the complete wave field in a single-layer velocity model with the same anisotropy as in the upper layer of the velocity model used to calculate the recorded wave field. We migrate reflected PP, converted PS1 and PS2 elementary waves without the separation of the recorded complete wave field. For migration of the S-wave part we use the prevailing-frequency approximation of the coupling ray theory and for comparison we apply the anisotropic-ray-theory approximation. Calculations using the prevailing-frequency approximation of the coupling ray theory are without problems for both models. On the other hand, for the anisotropic-ray-theory approximation in the model with weaker anisotropy we have to use limitation of Green function maxima otherwise the migrated sections are wrong. In spite of complex recorded wave fields, without decomposition, the migrated interfaces for the vertical component of the PP reflected wave, radial and transversal components of PS1 and PS2 converted waves are in all stacked migrated sections relatively good with exception of spurious interface images close to the correct ones.