Previous authors have tried to image seismic reflectivity by crosscorrelating passive seismic data, and treating the resultant correlograms as active source seismograms. We provide a mathematical framework for working with passive seismic correlograms that is both appropriate for V(x,y,z) media, and arbitrary source location. Under this framework, correlograms can be migrated with an imaging condition that is tuned to image particular events. For example, tuning the imaging condition to the kinematics of the Direct-Direct correlation event allows direct imaging of the seismic sources. Similarly, tuning to the Direct-Ghost correlation event allows imaging of subsurface reflectivity. Numerical results with synthetic data partly verify the effectiveness of crosscorrelation migration, but also suggest worse resolution of the image compared to standard Kirchhoff migration.