Seismic apparition is a recent signal-processing advance that trades signal interference and aliasing between different spatial (and temporal) dimensions. In particular, an important application of seismic apparition is for simultaneous-source separation to better exploit the available data space in the frequency-wavenumber (f-k) domain with energy from different simultaneous sources. The introduction of periodic modulation functions in seismic acquisition produces an effect where parts of the energy of one or more sources are partially shifted to different empty parts within the f-k domain. This so-called apparated energy then can be used to perfectly predict (at low frequencies) the remaining part of the signal in the regions of the f-k domain where the wavefields from the different sources overlap and to deterministically separate the sources at predetermined (repeated) positions — a prerequisite for 4D seismic processing. At higher frequencies, the apparition separation is dealiased using directional information, taking full advantage of the perfect separation at lower frequencies to achieve the required low-error separation. To apparate seismic energy to different portions within the f-k domain, we introduce a periodic modulation function, consisting for instance of a small time delay/advance or an amplitude scaling to every second shot. Our simultaneous-source approach is thus opposite to established industry practices of maximizing randomness using dithered sources. A deterministic simultaneous-source-separation approach in which shot points and simultaneous-source patterns are repeated accurately is a major advantage over industry-standard stochastic simultaneous-source-acquisition approaches, particularly for 4D applications. We demonstrate the suitability of the seismic-apparition simultaneous-source technique to time-lapse seismic, having a permanent-reservoir-monitoring context in mind, by investigating two operational scenarios of single-vessel acquisition where two sources are excited simultaneously. Single-vessel simultaneous-source acquisition represents the most challenging case for shot separation in general and for time-lapse seismic applications in particular. The quantitative and qualitative wavefield decomposition results analyzed pre- and poststack are highly encouraging on synthetic data and warrant further testing of seismic-apparition technology in a real 4D seismic test case.