One interpretation of a seismic image is the instantaneous scattered wave response of a colocated pseudo-source and pseudo-receiver at each point in the subsurface model. If there is no model perturbation at a point then there will be no instantaneous scattered wave so nothing will be imaged; if something is imaged then there must be a perturbation at that location. By extension, so-called extended images (EIs) represent the full spatio-temporal response between offset subsurface pseudo-sources and pseudo-receivers which can be used to constrain elastic properties around each image point. However, one-sided illumination of the subsurface (from the Earth's surface), errors in the initial velocity model estimate, and the use of a linearized, single-scattering assumption (as is usual in seismic imaging) cause errors in EI gathers such as missing events, incorrect amplitudes, and spurious energy. By creating elastic (P-to-P and P-to-S) EIs in a synthetic example of subsalt imaging, we demonstrate the advantages of incorporating multiply scattered waves correctly by non-linear imaging, and of including transmitted waves by using two-sided receiver arrays, and discuss how the recently developed autofocussing methods could provide us with the various required subsurface wavefields. Pre- A nd post-imaging f-k filtering procedures are introduced to further improve the quality of the EIs by (explicitly or implicitly) limiting the directions of waves arriving at the subsurface pseudo-source and receiver survey line. These filters suppress strong linear events that arise from the erroneous interaction of near-horizontally propagating waves which are not naturally accounted for due to the lack of sources and receivers on either side of the imaging target. Finally, we analyse the sensitivity of elastic P-to-P EIs to errors in the migration velocity models and show that events in the EI are shifted in opposite directions when constructed using reflection or transmission data. In other words, velocity errors are mapped into the EIs differently in the case of one-sided from two-sided illumination. This leads to the potential for new methods of migration velocity analysis when surface and borehole seismic data are jointly acquired.