We describe a newly developed method for recovering high-resolution images of seismic discontinuities, such as subducting slabs, in 3D. Our method makes use of converted S→P or P→S waves observed by dense arrays of seismometers to infer the locations and relative strengths of seismic discontinuities at depth in a target region. Observed direct and converted waves are backpropagated to their times of origin. The time-reversed wavefield is then separated into its constituent P and S components via the Helmholtz decomposition, and those separated wavefields are used to compute imaging functions that characterize the locations and relative strengths of seismic discontinuities. Imaging functions may be designed to use either S→P or P→S waves, so that users can target those arrivals expected to be most dominant in a given dataset. We have previously demonstrated the efficacy of our method in two dimensions, and we now present a 3D implementation of our technique which addresses the significant computational challenges posed by the size of volumetric wavefield data in three dimensions. Through a series of synthetic examples, we demonstrate that our method is capable of recovering the fine scale structure of a subducting slab given realistic station coverage and earthquake sources. We investigate optimal seismic station geometries for our technique and explore image interpretability in regions with poor data coverage. We find that linear station geometries yield more optimal, interpretable imaging functions than collections of small arrays can. We also show that our method can successfully recover bothS→P or P→S images when realistic shear earthquake sources are used, and we explore the additional computational challenges presented by the high frequency content of S waves. Our results demonstrate the potential for our technique to recover high-resolution information about subducting slabs in real-world regions, given that relatively sparse seismic arrays with only approximately 100 stations are capable of recovering interpretable imaging functions from just a few realistic earthquake sources for multiple discontinuities at significant depth in an area of approximately 400~sq~km.