Recent advances in marine seismic acquisition allow for the recording of vector-acoustic ([VA] pressure and particle velocity) seismic data from dual-source configurations, i.e., using monopole as well as dipole sources. VA reverse time migration (RTM) can be custom designed to accurately handle amplitude and directivity information from 4C seismic data. We present a method for multicomponent RTM that is based on an adjoint-state formulation using the full VA wave equations for pressure and corresponding displacement fields. This method takes advantage of the directional finite-frequency information contained in the 4C acoustic fields by using source and receiver weighting operators in the adjoint-state imaging scheme. With this adjoint-state method, the source and receiver radiation properties are tailored by choosing specific weighting operators. Weighting operators were chosen so that source- and receiver-side ghost arrivals are jointly migrated with primary energy. Because the dipole field components (e.g., components of particle displacement or acceleration) are proportional to the spatial gradient components of the pressure field, our method is in fact a formulation for reverse-time map migration that images pressure fields while jointly using the directional information contained in its full 3C gradients. As a result, our reverse time 4C map migration method yields less aperture- and sampling-related artifacts when compared to imaging of the pressure-only or 2C seismic data. In addition, our method sets a framework for full-waveform inversion using dual-source 4C seismic data. We demonstrated our findings with synthetic data, including a subsalt imaging example.