22Minibasins are fundamental components of many salt-bearing sedimentary basins, where they may host 23 large volumes of hydrocarbons. Although we understand the basic mechanics governing their 24 subsidence, we know surprisingly little of how minibasins subside in three-dimensions over geological 25timescales, or what controls such variability. Such knowledge would improve our ability to constrain 26 initial salt volumes in sedimentary basins, the timing of salt welding, and the distribution and likely 27 charging histories of suprasalt hydrocarbon reservoirs. We use 3D seismic reflection data from the 28 Precaspian Basin, onshore Kazakhstan to reveal the subsidence histories of 16, Upper Permian-to-29 Triassic, suprasalt minibasins. These minibasins subsided into a Lower-to-Middle Permian salt layer 30 that contained numerous relatively strong, clastic-dominated minibasins encased during an earlier, latest 31 Permian phase of diapirism; because of this, the salt varied in thickness. Suprasalt minibasins contain a 32 stratigraphic record of symmetric (bowl-shaped units) and then asymmetric (wedge-shaped units) 33 subsidence, with this change in style seemingly occurring at different times in different minibasins, and 34 most likely prior to welding. We complement our observations from natural minibasins in the 35 Precaspian Basin with results arising from new physical sandbox models; this allows us to explore the 36 volumes) is a key challenge when attempting to unravel the geodynamics of continental breakup (e.g. 63 Davison et al., 2012), whereas the timing of salt welding is of critical importance for understanding the 64 potential for and the timing of the transmission of hydrocarbons through welds from subsalt source 65 rocks into suprasalt reservoirs (Rowan, 2004). 66Despite their ubiquity and importance, and although they are typically well-imaged in seismic 67 reflection data and penetrated by numerous boreholes, surprisingly little is known about the variability 68 of minibasin subsidence, and what controls this in time and space (see Clark et al. 1998 for an exception; 69 Fig. 1E). This reflects how few published studies have employed high-quality, regionally-extensive 3D 70 seismic reflection datasets to map their synkinematic strata, the architecture of which preserve a record 71 of salt tectonic-related changes in accommodation. Using 2D seismic reflection and borehole data from 72 the northern Gulf of Mexico, Rowan and Weimer (1998) document four types of seismic-stratigraphic 73 3 packages within Pliocene-Pleistocene minibasins subsiding into thick allochthonous salt. Each type 74defines a different style of minibasin subsidence, with periods of broadly symmetrical subsidence 75 recorded by 'bowls' and 'layers', and asymmetric subsidence and minibasin tilting defined by 'wedges' 76 ( Fig. 1A and C). Rowan and Weimer (1998) conclude the transition from bowl-to wedge-shaped 77 packages is driven by and thus records, minibasin welding during passive diapirism (see Fig. 1A; see 78also Kergaravat et al....