The variety of coral reefs morphologies highlights their sensitivities to several forcings; fossil reefs stack in sequences that are accordingly diverse. In order to understand their genesis and architectures, we devised a numerical approach, accounting for Quaternary sea level oscillations, vertical land motion, initial slope, wave erosion, and reef growth. We first test our model on the subsiding sequence of Hawaii and on the uplifting sequence of Wangi-Wangi (Sulawesi) that bears active barriers. We then construct a parametric study that we analyze based on a comprehensive yet compact description of sequences as barcodes, that depict the vertical distribution of a few geometrical characteristics (number, width, and height of the terraces and barriers). We find that geological factors suffice to explain the variety of architectures of reefal sequences at first order, regardless of additional ecosystemic processes. Vertical land motion and foundation slopes are the prime players, while reef growth rates only play a minor role. Barriers may develop both in uplift and subsidence mode, and their preservation attests for the erosional power. Last, we reappraise the genesis of sequences and find that sequences do not fingerprint discrete events of sea level oscillations but a continuous process harrowed by stochastic events: Major sea level fluctuations can be overrepresented by several terraces or conversely absent; reoccupations may yield composite terraces representing multiple events. Overall, sequences shall not be regarded as stacks of reef bodies forming during sea level highstands, which implies that the commonly assumed bijective relationship between sea level highstands and terraces shall be abandoned.