SUMMARY Observations of seismic anisotropy at the base of the mantle are abundant. Given recent progress in understanding how deformation relates to anisotropy in lowermost mantle minerals at the relevant pressure and temperature conditions, these observations can be used to test specific geodynamic scenarios, and have the potential to reveal patterns of flow at the base of the mantle. For example, several recent studies have sought to reproduce measurements of shear wave splitting due to D″ anisotropy using models that invoke specific flow and texture development geometries. A major limitation in such studies, however, is that the forward modelling is nearly always carried out using a ray theoretical framework, and finite-frequency wave propagation effects are not considered. Here we present a series of numerical wave propagation simulation experiments that explore the finite-frequency sensitivity of SKS, SKKS and ScS phases to laterally varying anisotropy at the base of the mantle. We build on previous work that developed forward modelling capabilities for anisotropic lowermost mantle models using the AxiSEM3D spectral element solver, which can handle arbitrary anisotropic geometries. This approach enables us to compute seismograms for relatively short periods (∼4 s) for models that include fully 3-D anisotropy at moderate computational cost. We generate synthetic waveforms for a suite of anisotropic models with increasing complexity. We first test a variety of candidate elastic tensors in laterally homogeneous models to understand how different lowermost mantle elasticity scenarios express themselves in shear wave splitting measurements. We then consider a series of laterally heterogeneous models of increasing complexity, exploring how splitting behaviour varies across the edges of anisotropic blocks and investigating the minimum sizes of anisotropic heterogeneities that can be reliably detected using SKS, SKKS and ScS splitting. Finally, we apply our modelling strategy to a previously published observational study of anisotropy at the base of the mantle beneath Iceland. Our results show that while ray theory is often a suitable approximation for predicting splitting, particularly for SK(K)S phases, full-wave effects on splitting due to lowermost mantle anisotropy can be considerable in some circumstances. Our simulations illuminate some of the challenges inherent in reliably detecting deep mantle anisotropy using body wave phases, and point to new strategies for interpreting SKS, SKKS and ScS waveforms that take full advantage of newly available computational techniques in seismology.