Imaging both within and beneath subsurface igneous sill complexes is a seismic exploration challenge. A significant aspect of this challenge is due to a lack of understanding of the interaction between the heterogeneous geological structures and the seismic wavefield which includes the seismic response to sub-resolution 'thin' sills. This study aims to provide some insight into the effect of subsurface sills have on the observed seismic wavefield. This is achieved through high resolution full-waveform elastic seismic modelling, using a realistic geological model developed from interpreted seismic data and statistics of sills from wireline logs. We find that little energy penetrates through the sill complex to a target reflector below the sill complex, which is consistent with real-world observations. This is due to a number of factors, including energy lost to strong internal multiples (stratigraphic filtering), converted modes and leaky guided waves within the sills. These processes remove energy from the primary transmitted wavefront, contributing to degraded seismic imaging. Whilst these are all fundamental physical limitations that cannot be overcome, further work should focus on the processing of seismic data to ensure that these aspects of the seismic wave-field around sill complexes are optimally treated within processing workflows.