The competition for salt and kinematic interactions between minibasins during density-driven subsidence: observations from numerical models

Stratal geometries of salt-floored minibasins provide a record of the interplay between minibasin subsidence and sedimentation. Minibasin subsidence and resulting stratal geometries are frequently interpreted by considering the minibasins in isolation and implicitly assuming that internal geometries are the result of purely vertical halokinetic processes. However, minibasins rarely form in isolation and may record complex subsidence histories even in the absence of tectonic forces. In this study we use numerical models to investigate how minibasins subside in response to density-driven downbuilding. We show that minibasins subsiding in isolation result in simple symmetrical minibasins with relatively simple internal stratigraphic patterns. In contrast, where minibasins form in closely spaced arrays and subside at different rates, minibasins can kinematically interact due to complex patterns of flow in the encasing salt, even during simple density-driven subsidence. More specifically, we show that minibasins can: (1) prevent nearby minibasins from subsiding; (2) induce lateral translation of nearby minibasins; and (3) induce tilting and asymmetrical subsidence of nearby minibasins. We conclude that even in areas where no regional or dominant salt flow regime exists, minibasins can still be genetically related and the minibasin subsidence histories cannot be fully understood if considered in isolation. Thematic collection: This article is part of the Mechanics of salt systems: state of the field in numerical methods collection available at: https://www.lyellcollection.org/cc/mechanics-of-salt-systems

Minibasins are small basins formed by subsiding into relatively thick autochthonous or allochthonous salt (e.g. ). Due to the specific properties of salt, which can flow under very low stresses, subsidence rates of minibasins can be orders of magnitude higher than subsidence rates in crustal basins, reaching values of up to 10 000 m Ma −1 (Worrall & Snelson 1989). Because they can contain important thicknesses of sedimentary rocks that may include potential hydrocarbon reservoirs, minibasins have been widely studied in hydrocarbon-bearing salt basins (e.g. Hudec & Jackson 2007).
The stratigraphic infill of minibasins provides a record of their subsidence histories. In simple terms, minibasin stratal geometries reflect the interplay between the two primary controls: minibasin subsidence and sediment accumulation. On the one hand, the bulk sediment accumulation rate is constrained by the sediment delivery system. On the other hand, the subsidence rate of a minibasin, which creates the accommodation space for new sediment, depends on minibasin geometry and density, and the patterns and vigour of salt flow below and around the minibasin (e.g. Hudec et al. 2009). As a result of the strong coupling between minibasin subsidence and sedimentation, changes in subsidence style are recorded by synkinematic stratal packages within minibasins (e.g. Giles & Lawton 2002;Prather 2003;Giles & Rowan 2012;Sylvester et al. 2015;Jackson et al. 2019).
Based on 2D seismic reflection data from the northern Gulf of Mexico, Rowan & Weimer (1998) documented different types of seismic-stratigraphic packages that can be linked to different styles of minibasin subsidence. Bowl-or layer-shaped symmetrical packages record a broadly symmetrical subsidence, while asymmetrical subsidence and minibasin tilting result in wedge-shaped packages. In the simplest possible geometry, a minibasin that has a purely vertical subsidence history would be characterized by vertically stacked, symmetrical, bowl-shaped depocentres (Fig. 1a). Many other stratal geometries are possible though. For example, a basal symmetrical 'bowl' overlain by an asymmetrical 'wedge' indicates an initially symmetrical subsidence followed by minibasin tilting and subsequent asymmetrical subsidence ( Fig. 1b  and c). Thus, minibasin depocentres do not necessarily stack vertically and need not be symmetrical, as they may be wedgeshaped and shift gradually or abruptly ( Fig. 1b and c). The transition from a bowl-to a wedge-shaped package is interpreted by Rowan & Weimer (1998) as the timing of minibasin welding. However, Hudec et al. (2009) proposed other non-welding related processes that can also lead to asymmetrical subsidence, including the response to an asymmetrical sediment load, synsubsidence shortening and horizontal translation during canopy spreading.
Minibasin subsidence is commonly studied by considering the minibasin as an isolated element. Internal stratal geometries of isolated minibasins would passively record the interplay between the inflation of surrounding salt structures as the minibasin subsides, and the sediment accumulation in the minibasin (e.g. Koyi 1998; halokinetic sequences: Giles & Lawton 2002;Giles & Rowan 2012). However, minibasins are rarely found in isolation, and are instead part of arrays of closely spaced minibasins bounded by complex networks of salt walls and diapirs forming minibasin provinces. Minibasin provinces form in different types of tectonic settings, ranging from collision zones, such as the Precaspian and Sivas, to passive margins, such as the northern Gulf of Mexico and Brazil (e.g. Worrall & Snelson 1989;Schuster 1995;Volozh et al. 2003;Rowan & Vendeville 2006;Fiduk & Rowan 2012;Callot et al. 2014). During shortening of minibasin provinces, contraction is preferably accommodated within the weaker salt and, as a result, diapirs become squeezed or welded shut (e.g. Rowan & Vendeville 2006). During their translation, minibasins can interact with each other as they collide, jostle and/or slide past one another, resulting in complex geometries (e.g. Rowan & Vendeville 2006;Callot et al. 2016;Duffy et al. 2017). However, minibasins may still exhibit complex stratigraphic geometries indicative of complex subsidence histories in cases when shortening is not coeval with subsidence  The basin-fill model proposed by Banham & Mountney (2013) for areas such as the Precaspian Basin predicts that adjacent and coeval minibasins can have very different subsidence rates. The model also predicts that minibasins that are isolated from the dominant sediment transport systems within the setting can still be infilled by the deposits resulting from: (a) evaporitic-dominated processes and aeolian-dominated processes in the case of arid climates; and (b) lacustrine sediments in the case of more humid climates (modified after Banham & Mountney 2013). and/or where minibasins have not collided or are not welded laterally (e.g. Jackson et al. 2019). This is especially true in settings where adjacent minibasins can have very variable subsidence rates and where apparently isolated minibasins can still be filled by various sedimentary processes (e.g. continental basin-fill areas sensu Banham & Mountney 2013) (Fig. 2). One question that has not been addressed explicitly previously is whether adjacent minibasins can influence each other and interact through salt flow without colliding or being welded together.
In this work we study the interactions between adjacent minibasins separated by diapirs subsiding into a homogenous salt layer with no regional tectonics (e.g. shortening) or dominant regional salt flow. For this purpose, we perform a numerical modelling study that consists of several numerical simulations performed with a 2D finite-element code. The goal of this study is three-fold: first, to demonstrate that within arrays of minibasins subsiding at different rates, minibasins can influence adjacent ones by perturbing the salt flow around them; second, to observe and describe the different ways in which minibasin interactions can occur; and, third, to describe how minibasin stratal patterns record kinematic interactions between adjacent minibasin.

Numerical method and model set-up
We use the 2D finite-element code MVEP2 (Thielmann & Kaus 2012;Johnson et al. 2013). MVEP2 solves the equations of conservation of mass and momentum for incompressible materials with visco-elasto-plastic rheologies, and employs Matlab-based solvers MILAMIN (Dabrowski et al. 2008) for efficiency. The code uses a Lagrangian approach, where material properties are tracked by randomly distributed markers that are advected according to the velocity field that is calculated in a deformable numerical grid. Remeshing of the grid is performed every time step. The method and numerical implementation is explained in detail in Kaus (2010).
In the simulations, 384 Lagrangian markers (hereinafter referred to as markers) are used per element to track the material properties, resulting in over 10 million markers in the modelled area. These markers have been perturbed from their initial regular position by applying random noise. The top, and left-and right-hand boundaries of the modelling domain have a free-slip boundary condition imposed, meaning that movement at the boundary can only occur parallel to the boundary. The bottom boundary of the domain has a no-slip boundary condition. An internal free-stress boundary is achieved by using the 'sticky-air' layer approach (Crameri et al. 2012). This approach consists of adding a layer of zero density and relatively low viscosity (three orders of magnitude lower viscosity than salt phase) on top of the rock phases. By adding this layer, topography can develop at the interface between the 'sticky air' and rock phases. Benchmark studies have shown that the 'sticky air' is a good approximation of a 'free surface' (e.g. Crameri et al. 2012).
Two rock phases are used in the model: a phase corresponding to salt rock (e.g. halite) and one to sediments. Salt is modelled as a linear viscous fluid with a viscosity of 10 18 Pa s (e.g. Mukherjee et al. 2010) and a density of 2200 kg m −3 (i.e. halite). Sediments are modelled as visco-plastic materials, with a brittle rheology that is characterized by their cohesion (C ) and effective friction angle (ϕ). In the simulations, the colour of the deposited sediments changes every 0.5 myr for visualization purposes only (i.e. there is no change in physical properties of the sediments associated with the colour change).
Densities (ρ) of salt and sediment phases are modelled as constant and homogenous. Sediment density (ρ sediment ) is set higher than salt density, so that sediment-filled minibasins sink due to excess density. Sediments do not compact in the simulations presented here. This approach results in the density-driven subsidence of minibasins from the very beginning of the simulations, due to a gravity instability (density overturn) that has the added effect of sedimentation (e.g. Biot & Odé 1965;van Keken et al. 1993;Fernandez & Kaus 2015). Assuming that minibasins are initiated by density-driven subsidence is a major simplification in areas where the minibasins are being filled with compacting siliciclastic sediments that would require a considerable thickness for the density overturn to occur (see Hudec et al. 2009). Thus, several mechanisms have been proposed in the literature to explain minibasin initiation and subsidence when sediments are less dense than the underlying salt (e.g. Hudec et al. 2009;Goteti et al. 2012). However, early density-driven subsidence of minibasins might be a valid assumption in areas where minibasins are being filled with denser than salt sediments (e.g. evaporitic and/ or aeolian settings: Prochnow et al. 2006;Matthews et al. 2007;Pichat et al. 2019; see also Fernandez et al. 2017). This is especially the case of evaporite-rich minibasins, whose 50-100% of infill is composed of evaporite-rich facies, and whose size tends to be smaller (e.g. 1-2 km wide) than their siliciclastic counterparts (see Fernandez et al. 2017;Pichat et al. 2019). Additionally, the densitydriven subsidence approach in our numerical models allows minibasins to be initiated with no other additional process (e.g. shortening, sediment progradation, sustained sediment load: e.g. Hudec et al. 2009;Goteti et al. 2012); therefore simplifying the interpretation of the observed stratal geometries.
Sedimentation in the models is simulated by vertically displacing a horizontal reference level according to a specified aggradation rate (S), which in the numerical models is between 0.001 and 0.01 cm a −1 . For each time step, the model assumes that the depositing sediments fill the space up to the horizontal reference level. Therefore, the sediment accumulation rate and the thickness of each newly deposited layer in the model will depend both on the imposed aggradation rate and the subsidence of the underlying minibasin; the latter creating extra accommodation space (e.g. Fernandez & Kaus 2015) (Fig. 3). Numerically, this process is implemented by converting any particle of 'air phase' below the reference level to 'sediment phase' at each time step (Fig. 3). The resulting sediment accumulation rate in each of the minibasins of the simulations has been calculated based on the minibasin thickness variation between time steps. In the numerical simulations, the sediment accumulation rate is variable from minibasin to minibasin, and through time. There is no erosion in the numerical simulations presented here.
Two geometrical model set-ups were used: control simulations with a single seeded minibasin; and simulations with non-seeded arrays of minibasins (Fig. 4). Both set-ups start with an initial 1000 m-thick flat layer of salt (Fig. 4). The control simulations for a single seeded minibasin have a simulation domain of 10 km wide by 4 km high (Fig. 4). In these control simulations, an initial layer of sediments is added on top of the salt at the centre of the model. The purpose of this prekinematic layer is to help nucleate or seed a minibasin at the centre of the modelling domain. The smaller model dimensions are enough to allow the formation of a single minibasin. This isolated minibasin subsides into a thick layer of salt unperturbed by any other minibasins. The modelling domain for simulations with non-seeded minibasin arrays is 30 km wide by 4 km high (Fig. 4). The model dimensions are enough to allow the formation and evolution of several kilometre-scale minibasins, and thus are appropriate to represent subdomains of salt-tectonic systems containing minibasin arrays. This set-up does not contain a prekinematic sediment layer on top of the salt, and thus minibasin position is not explicitly imposed during the simulations. Instead, minibasins develop spontaneously by density-driven subsidence and density overturn as sediments are added during the simulation (e.g. Fernandez & Kaus 2015). The goal of the two set-ups is to compare the behaviour and resulting stratal geometries of a single isolated minibasin to the behaviour and geometries associated with minibasins subsiding as part of minibasin arrays.
Different sediment densities were used in the simulations with nonseeded minibasin arrays (Table 1). For each density, we performed a sensitivity study of sediment properties (C and ϕ: Table 1). A total of 11 simulations of the single seeded minibasin set-up and 112 simulations with the non-seeded minibasin arrays set-up were performed. All the simulations within each geometrical set-up have the position of the markers perturbed by the same noise (mean = −0.0005 m; standard deviation = 0.9021 m; variance = 0.8137 m). The random noise causes heterogeneities of very small amplitude and wavelength in the salt-sediment interface in the initial stages. However, the heterogeneities are exactly the same in all the simulations within each of the geometrical set-ups. During the initial stages of the simulations, it is the heterogeneities with a wavelength closer to the dominant minibasin (or diapir) wavelength that get amplified and evolve into mature minibasins (e.g. Fernandez & Kaus 2015). Thus, any differences between the simulations regarding size, geometry and spacing of minibasins is exclusively due to differences in the parameters used for the sediment properties. Cohesion and friction angle determine the effective strength of the minibasins, resulting in relatively weak (i.e. low cohesion and friction angle) or relatively strong (i.e. high cohesion and friction angle) minibasins. The effective strength of a minibasin affects its overall subsidence history and thus the contained stratal pattern.
During the numerical simulations, the velocity field obtained for each time step is used to extract the X and Z velocity components across the model domain.

Modelling results
In this section we describe three different simulations to illustrate the evolution of minibasins formed by density-driven subsidence in the models. Simulation 1 shows the evolution of one single isolated minibasin that formed from a prekinematic seed. Simulations 2 and 3 are two examples where no prekinematic seeds were used and where arrays of minibasins formed spontaneously across the model. The specific physical parameters of the three simulations are given in Table 2.

Isolated minibasin sinking into thick salt
In simulation 1, an initial prekinematic layer of sediments was added in the set-up. This layer is 1 km long and 200 m thick, with a thicker (400 m-thick) central segment (Figs 4a and 5a). As sediments are denser than salt in the models, the prekinematic layer subsides into the salt as soon as the simulation starts. Density-driven subsidence of the prekinematic layer creates accommodation, so sediment deposition is concentrated above the seed, forming a minibasin that Fig. 3. Schematic sketch of the implementation of the sedimentation in the numerical code. The sedimentation algorithm uses a horizontal flat reference level that aggrades vertically according to an imposed rate. As the minibasin subsides into salt, new accommodation space is created on top of the minibasin, due both to subsidence and aggradation. The newly created accommodation space is filled with sediments. is thickest at the centre (Fig. 5a). As the minibasin becomes thicker and, thus, more difficult to deform in the centre, bending of the flanks is limited to very narrow areas closest to the salt (cf. halokinetic folds of Giles & Lawton 2002;Giles & Rowan 2012). The minibasin is initially widening as it subsides, until it starts narrowing upwards (after time c. 1.56 myr: Fig. 5a). Overall, the isolated minibasin of simulation 1 subsides symmetrically throughout its history, with this being recorded by symmetrical stratal geometries within the minibasin (Fig. 5a).
The mean X and Z velocity components of simulation 1 are shown in Figure 5b. The X component of the mean salt velocity shows a positive peak to the right-hand side of the minibasin, and a negative peak to the left-hand side of the minibasin (Fig. 5b, black solid line). The two mean salt velocity peaks of the X components are of equal magnitude (V X max ¼ ÀV X min ) (Fig. 5b, black solid line). Away from the minibasin, the mean X component salt velocity decreases gradually towards zero. The Z component of the mean salt velocity has the highest negative value below the centre of the minibasin (V Z mean ), and two positive and equal value mean velocity peaks to either side of the minibasin (V Z lpeak ¼ V Z rpeak ) (Fig. 5b, black dashed line). Away from the minibasin, the mean Z salt velocity decreases rapidly towards zero (Fig. 5b). As the isolated minibasin continues to subside into thick salt and becomes thicker, more salt is evacuated from below the minibasin; thus the magnitude of the mean X salt velocity peaks increase until the minibasin welds at the base (Fig. 5b). Overall, salt velocity components indicate that salt is expelled from below the subsiding minibasin to both sides equally, feeding flanking diapirs that rise at similar rates. The generalized plot of the mean salt velocities for an isolated minibasin subsiding into thick salt is shown in Figure 5c.
The velocity field within the sediments is simpler, with the predominant Z component of the velocity illustrating the subsidence of the minibasin as a downward-directed symmetrical flow (Fig. 5b, red solid and dashed lines). Interestingly, when the minibasin is thin and weak enough to be able to accommodate deformation, the velocity in Z direction shows a maximum value in the centre of the minibasin decreasing toward the flanks; this suggests deformation by folding. As the minibasin becomes thicker and stronger, the Z velocity shows a constant value across the width of the minibasin, indicating no internal deformation (i.e. folding). In both cases, the plots are symmetrical.
The evolution of the sediment accumulation rate through time is shown in Figure 5d. At the very early stages, the sediment accumulation rate increases very fast, until it reaches a maximum of 0.05 cm a −1 . Afterwards, the sediment accumulation rate decreases steadily until the minibasin welds (at time c. 4.00 myr). After welding, the sediment accumulation rate of the minibasin corresponds to the imposed aggradation rate of 0.002 cm a −1 .

Minibasin arrays sinking into thick salt
Having investigated how a single isolated minibasin subsides in simulation 1, we now explore the evolution of minibasin arrays in simulations 2 and 3 (Fig. 6). These two simulations differ only in the properties used to model the sediments (C and ϕ: Table 2). The minibasin initiation process and overall minibasin evolution is similar in both simulations, so both models are described together. The simulations start with a flat layer of salt without a capping prekinematic sediment layer (Fig. 4b). Once the simulation begins, the first sediment layer deposited is very thin, and not completely uniform in thickness due to the random noise used to perturb the position of the markers. This tiny variation in the thickness of the early sediment load produces differential subsidence into the salt and the formation of individualized thin minibasins ( Fig. 6a and b: time c. 1.96 myr). It must be emphasized that the initial layers of sediments are thin compared to subsequent ones, because at this early stage the subsidence into salt is minimal. As the minibasins subside into the salt, accommodation for new sediments is created on top of them, and the initially thin minibasins eventually evolve into thicker and wider minibasins ( Fig. 6a and b: time c. 1.96 myr and onwards). The minibasins formed in the two simulations are numbered 1-13 (Fig. 6). In each simulation 6 to 8 minibasins form, ranging in width and thickness (Fig. 6). A striking characteristic of these simulations is that minibasins initiate asynchronously. Initially, thin sediment pods are roughly regularly spaced across the model, but a few of them start subsiding faster than others (e.g. minibasins 3, 7, 10 and 13: Fig. 6). As a result, at any given time, minibasins of different thicknesses are subsiding at different rates. This asynchronous subsidence is also reflected in the sediment accumulation rates in the minibasins shown in Figure 7, where each minibasin reaches a peak sediment accumulation rate at a different time. The minibasins that subside fastest weld to the base of the salt before the slower-subsiding minibasins. Once the first minibasins (e.g. minibasins 3, 7, 10 and 13) weld, other minibasins (e.g. minibasins 1, 4, 6, 11 and 12) subside more quickly (Fig. 6). The process of minibasin formation described above results in varied stratigraphic patterns within the minibasins. While some minibasins are symmetrical in cross-section, many others exhibit very asymmetrical geometries because of their complex subsidence histories. Next, we will look in more detail at various examples of minibasins to illustrate stratigraphic geometries.

Symmetrical minibasins
Symmetrical minibasins with continuous subsidence. Minibasin 3 (Fig. 6a) is an example of a minibasin that records symmetrical subsidence throughout its evolution, resulting in symmetrical sediment fill composed of a basal symmetrical bowl and overlying layers (Fig. 8a). Minibasin 3 is also one of the depocentres that undergoes initially rapid subsidence and increased sediment accumulation rates (Fig. 7a). Minibasin 3 initiates with a bowlshaped geometry (e.g. Fig. 8a), indicating a higher rate of subsidence in the centre. Minibasin 3 welds to the base of salt at  around time c. 2.96 myr and therefore cannot subside vertically anymore (Fig. 6a). However, due to the fact that the overall salt level is rising in the simulation (by evacuation of salt from beneath surrounding minibasins), accommodation is still generated above the now-welded minibasin 3 ( post-weld layer: Fig. 8a). After its welding, sediment accumulation in minibasin 3 is only occurring due to the background sediment aggradation and, thus, the sediment accumulation rate of minibasin 3 corresponds to the imposed aggradation rate at this stage (Fig. 7a). As accommodation is created only by aggradation at this stage, layers deposited after welding are thinner than during the preceding phase of vertical subsidence into thick salt (Figs 6a and 8a: time c. 3.96 myr and onwards). Furthermore, the minibasin narrows upwards at this stage, which indicates that salt inflation, driven by continued subsidence of other minibasins in the array, is faster than sediment aggradation (Fig. 8a).
Other minibasins also display symmetrical geometries (6, 10, and 13: Figs 6 and 8). Minibasins 10 and 13 occur in the same simulation, simulation 3 (Fig. 6b); thus, we examine their velocity profiles together (Fig. 9). At an early stage (Fig. 9a), subsidence of minibasins 10 and 13 is clearly visible in the mean Z sediment velocity plot (marked with S in Fig. 9a). Also, their sediment accumulation rate reaches their peak value before any of the other two examples and other similar simulations is the different subsidence rates of the minibasins (minibasins can be initiated at different times) and the resulting complex stratal geometries of the minibasins, including symmetrical (e.g. minibasins 3 and 6) and asymmetrical geometries (e.g. minibasins 4 and 11). minibasins in simulation 3 (Fig. 7b). The horizontal and vertical flow of salt around minibasins 10 and 13 is visible in the mean salt velocity plots as more complex variations in amplitude (Fig. 9a). However, the mean salt velocity profiles of minibasins 10 and 13 are very similar to the velocity profile of a single isolated minibasin (cf. Figs 5 and 9). As minibasins 10 and 13 continue to subside, horizontal (X ) and vertical (Z ) salt flow velocities increase until welding, when they decrease again (Fig. 9). Minibasins 10 and 13 initiate first in simulation 3, so they subside into a fairly unperturbed salt layer. Furthermore, they are far enough from each other so that their velocity perturbations do not overlap or affect each other.
Symmetrical minibasins with discontinuous subsidence. Minibasins 9 and 12 also initiate early in simulation 3, at which time they develop symmetrical geometries formed in response to early symmetrical subsidence into thick salt (Figs 6b and 9b). Early subsidence of minibasin 12 is observed in the velocity plot as a characteristic mean sediment Z velocity signature defined as a small downward undulation (marked S in Fig. 9b). However, as denoted by the absence of the same characteristic velocity signal in Figure 9c, at time c. 3.46 myr, minibasin 12 is not subsiding. By time c. 4.76 myr, minibasin 12 is again subsiding as indicated by the strong downward undulation in the Z velocity plot (marked S in Fig. 9d). We interpret that subsidence of minibasin 12 was interrupted by a short period of no subsidence (Fig. 9c) before resuming rapid subsidence later in the simulation (Fig. 9d). This discontinuous subsidence is reflected in the lack of sediment accumulation (accumulation rate equals zero) in minibasins 9 and 12 for a period time (Fig. 7b). Why should this be so? To begin, the mean salt velocity signal beneath the early-formed minibasin 12 is small compared to nearby minibasins 11 and 13, which are subsiding more rapidly during this early phase (Fig. 9b). Later, the strong velocity perturbation generated by rapid subsidence of minibasin 11 extends across minibasin 12, completely overprinting the (X and Z ) velocity signal of minibasin 12 (Fig. 9c). The lateral and upward flow of salt from beneath minibasin 11 towards minibasin 12 prevents minibasin 12 from subsiding. Instead, minibasin 12 moves laterally (cf. Fig. 9c and d). Minibasin 12 resumes its subsidence when minibasin 11 approaches the base of the salt, and the rate of expulsion of the salt from beneath it decreases (Fig. 9d). At that stage, minibasin 12 resumes its symmetrical subsidence into a relatively quiescent salt compartmentalized in between two welded minibasins. Velocity profiles of minibasin 12 at this stage are similar to the profiles of single isolated minibasins (cf. Figs 5 and 9d). We conclude that subsidence of one minibasin can inhibit the subsidence of another.

Asymmetrical minibasins
Abrupt shifts of depocentres, where minibasins transition from a symmetrical basal bowl-shaped geometry to an asymmetrical wedge-shaped geometry, have been observed in the Gulf of Mexico (Rowan & Weimer 1998), the Precaspian Basin (Jackson et al. 2019) and in other salt basins (e.g. Sivas Basin: Kergaravat et al. 2016). The bowl to wedge transitions observed in some minibasins of the Gulf of Mexico had been interpreted as being the result of minibasin welding and subsequent lateral collapse (Rowan & Weimer 1998). However, other mechanisms (e.g. synsubsidence shortening, salt emplacement on top of a minibasin) may trigger tilting prior to welding (e.g. Hudec et al. 2009;Jackson et al. 2019).
Our models show minibasin tilting both before and after welding. About half of the minibasins in Figure 6 are symmetrical but the others show significant degrees of asymmetry, as indicated by sediment fill that thickens towards one side of the minibasin. Several of the minibasins in our models begin tilting prior to welding (e.g. minibasins 4 and 11: Fig. 8c and d). Others show tilting only after welding, and still others show tilting both before and after (sometimes in opposite directions, e.g. minibasin 4: Fig. 4d). In this subsection we discuss the origin of minibasin tilting both before and after welding, along with controls on the direction and timing of tilt.
Minibasin tilting prior to basal welding. Minibasins 11 and 4 initiate as bowl-shaped minibasins, recording a period of symmetrical subsidence ( Fig. 8c and d). On top of the symmetrical bowl sequences, wedge-shaped sequences form due to tilting and asymmetrical subsidence. This initial tilting occurs prior to welding, and in both cases the tilt is away from the nearest actively subsiding minibasin ( Fig. 8c and d).
Minibasin 11 initiates relatively early in the simulation, at a time when the minibasin immediately to its left, minibasin 10, is already subsiding rapidly (Figs 8c and 9a, b). On its right-hand side, by contrast, minibasin 12 is much thinner and has a slower subsidence, which eventually stops at a later stage (cf. Fig. 9b and c). Even further to the right, minibasin 13 is nearly welded by the time minibasin 11 starts its main phase of subsidence, so minibasin 13 is not expelling much salt (Fig. 9c). Thus, during its main phase of subsidence, salt flow around minibasin 11 is asymmetrical, most heavily influenced by the expulsion of salt from beneath minibasin 10 ( Fig. 9b and c). In fact, the mean salt velocity signal around minibasin 11 shows that the peak of V X 11max ( positive value) is more prominent than the low V X 11min (negative value) (Fig. 9b). As a result of this asymmetrical salt flow around it, minibasin 11 starts subsiding asymmetrically (mean sediment velocity marked with A in Fig. 9c), tilting towards the direction in which the salt flow has been increased (to the right). Once minibasin 10 is welded and the associated salt flow stops (Fig. 9c), minibasin 11 resumes a purely symmetrical subsidence, recorded by a constant-thickness sedimentary layer deposited just before welding (t = 3.96 myr: Fig. 8c). Other minibasins showing pre-welding asymmetrical subsidence (e.g. minibasin 5: Fig. 8d) can also be explained by appearing to tilt away from the nearest actively subsiding minibasin. Thus, we conclude that tilting before welding of a minibasin can be induced by nearby minibasin subsidence and the resulting alteration of salt flow patterns.
Minibasin tilting after basal welding. Tilting of minibasins also occurs in the simulations after basal welding. For example, the upper, strongly wedge-shaped sequences of minibasins 4, 7 and 11 all form late, after the minibasins weld (e.g. Figs 6 and 8b, c). Focusing again on minibasin 11, this minibasin welds at its base after a complex history of tilting followed by a late stage of symmetrical subsidence (Figs 8c and 9d). When minibasin 11 welds, minibasin 10 to its left is already welded, but minibasin 12 to its right starts subsiding more rapidly (Fig. 9d). Accelerated symmetrical subsidence of minibasin 12 is reflected in the strong and symmetrical velocity signal visible in the X velocity component of the mean salt velocity plot (Fig. 9d). Expulsion of salt from below minibasin 12 into the diapir between minibasins 11 and 12 induces pivoting of minibasin 11 away from the inflating salt structure (Fig. 9d).
From this we conclude that once minibasins (symmetrical or asymmetrical) weld at their base, their subsequent evolution (tilting v. symmetrical aggradation) depends not only on whether there are nearby actively subsiding minibasins that can induce salt inflation and subsequent tilting, but also on the minibasin basal geometry. Minibasin geometry affects the potential for the minibasin to pivot around the weld contact point (e.g. Callot et al. 2016). We suggest that broadly symmetrical minibasins with a centred basal weld contact point are potentially more stable and able to resist tilting even in the presence of nearby subsiding minibasins (e.g. minibasin 10: Fig. 6b). In contrast, a minibasin with an off-centred basal weld contact point (asymmetrical minibasins) will more easily pivot and tilt (e.g. minibasins 4 and 11: Fig. 6).

'Competition' for salt between minibasins subsiding at different rates
In our single minibasin numerical simulations, minibasins subside symmetrically (e.g. Fig. 5). Tilting before welding only occurs in our simulations with multiple minibasins, suggesting that the presence of multiple minibasins subsiding at different rates facilitates the formation of asymmetrical minibasins. In the numerical models by Gradmann & Beaumont (2017), asymmetrical minibasins are formed as a result of sustained and localized sedimentation with a pre-established optimal wavelength (Goteti et al. 2012). In the absence of shortening, the rotation and tilting of the minibasins that form synchronously in the simulations might be related to the containment of the salt basin and the presence of a directional salt flow towards the basin centre (Gradmann & Beaumont 2017). In the numerical simulations presented here, minibasins subside at different rates (asynchronously) and there is no slope that would promote an additional lateral component of salt flow. If minibasin subsidence is purely density-driven, thicker and bigger minibasins subside faster, and thus displace salt at higher rates than smaller and thinner minibasins. The salt being expelled from below each subsiding minibasin moves into the surrounding salt structures (typically diapirs: Fig. 9). If several minibasins are subsiding simultaneously, a complex salt flow will result from the combination of all the individual velocity perturbations. Bigger velocity perturbations induced by bigger minibasins will overprint the smaller velocity perturbations of smaller minibasins. Overall, subsiding minibasins affect each other's subsidence histories through the velocity perturbations they induce in the salt flowing around them. We thus propose that minibasins, even if not in contact or connected by a roof, are kinematically interacting, so that subsidence history of each minibasin cannot be understood without looking at the subsidence history of the surrounding minibasins.

Minibasin interaction styles and implications
Based on observations from our numerical models, we propose that interactions between adjacent minibasins that are not in contact with each other can occur. However, we also found that some minibasins within the arrays do not interact with other minibasins. The simplest possible scenario for a lack of minibasin interactions is the case in which a minibasin forms in isolation and subsides vertically thorough its evolution, resulting in purely symmetrical stratigraphic geometries (e.g. simulation 1 in Fig. 5). Minibasins rarely form in complete isolation in nature and are invariably part of broader minibasin arrays. However, within minibasin arrays, a minibasin can also subside without interacting with adjacent minibasins if there are no minibasins sinking nearby (minibasins 3, 10 and 12: Fig. 6). There are two factors that can influence if minibasins within the array will interact. The first factor to consider is the timing of minibasin subsidence. Some of the symmetrical minibasins observed in our simulations are the ones that subside early in the simulations, when other minibasins have not yet formed, and so are effectively subsiding in isolation (e.g. minibasins 3 and 10: Fig. 6). In this regard, observations from the Green Canyon area in the deepwater Gulf of Mexico support this scenario, since one of the minibasins that subsided earlier (Miocene) into a thick salt canopy displays simple symmetrical geometries compared to the later subsiding minibasins (Pliocene) that were formed coevally in between other minibasins (Moore & Hinton 2013). Some other minibasins in our simulations subside later within minibasin arrays and, yet, also display overall symmetrical geometries. Latesubsiding minibasins may do so, after adjacent minibasins have grounded and thus are not expelling any salt. As a result, these latesubsiding minibasins sink into a relatively unperturbed salt in between grounded minibasins and can subside symmetrically, developing symmetrical stratigraphic geometries. Effectively, these late-subsiding minibasins are also not being affected by any salt flow perturbation induced by nearby subsiding minibasins. The second factor that can explain the lack of interactions within arrays of minibasins is the spacing or distance between subsiding minibasins. A minibasin subsiding within an array may be far enough from the closest actively subsiding minibasin so that it is not affected by the associated salt flow perturbations.
Having outlined the scenarios in which minibasins may not interact with other minibasins of the array, we next discuss the cases in which minibasins do interact. As pointed out before, adjacent subsiding minibasins can interact if they are close enough to affect each other. In our simulations, we have observed numerous styles of minibasin interactions. While some interactions result in asymmetrical stratal geometries of the minibasins, other interactions do not necessarily result in asymmetrical geometries.
In our simulations, we have observed two interaction styles that do not necessarily result in asymmetrical geometries of the minibasins. First, actively subsiding thick minibasins can prevent other nearby thinner minibasins from subsiding (e.g. minibasins 6 and 12: Fig. 10b). Once the actively subsiding minibasins are grounded, the minibasin whose subsidence was prevented can resume its symmetrical subsidence again (Fig. 10b). An important implication of discontinued subsidence is that minibasins can have incomplete stratigraphic sections, with hiatuses representing the time when subsidence was not occurring even if the depositional systems feeding them were still active ( Fig. 10b and c). Second, actively subsiding minibasins can induce the lateral translation of a thinner nearby minibasin ( Fig. 10c and e). In fact, many of the minibasins in the simulations of the minibasin arrays display a certain amount of lateral translation (indicated by the arrows in minibasins 4, 6, 11 and 12 in Fig. 6). Each arrow indicates the distance between the initial and final position of the depocentre during the simulation. Translation occurs wherever there is an asymmetry in horizontal flow on either side of a minibasin (e.g. minibasin 12 in Fig. 9). Thicker and more massive minibasins are more difficult to translate, and we do not see translation in our models after basal welding. As in the case of minibasins with discontinued subsidence, minibasins that are laterally translated may also have an incomplete stratigraphic sequence.
Another style of minibasin interaction is one that can lead to the formation of asymmetrical minibasins before basal welding occurs (Fig. 10d). If the subsidence of nearby minibasins results in an asymmetrical salt flow around a minibasin, salt from below the minibasin is evacuated preferentially towards one side. This scenario results in the tilting of the minibasin towards the side of preferential evacuation, as recorded by the thickening of the sedimentary sequence that is being deposited on top of the asymmetrically subsiding minibasin. For example, minibasins 4 and 11 tilted before basal welding (Figs 6, 8 and 9). The observation that minibasins can tilt before basal welding has important implications for interpreting weld timing. The bowl to wedge transitions in the stratal geometries of minibasins has previously been linked to the basal welding of minibasins (Rowan & Weimer 1998). Our numerical models illustrate that this interpretation may not be appropriate in all cases, as pre-welding tilting of minibasins can occur due to the kinematic interactions between minibasins (see also Jackson et al. 2019).
Finally, as observed in our models, minibasin interactions can also induce tilting of a grounded minibasin (Fig. 10f ). Once a minibasin is grounded, the salt displaced by an adjacent subsiding minibasin can cause the grounded minibasin to tilt away from the inflating salt structure (e.g. minibasin 7: Fig. 6a). After welding, subsidence of minibasin 8 to the right induced the tilting away from minibasin 7 to the left (Fig. 6a). Tilting of asymmetrical minibasins after welding is also common in the simulations. In some cases, the tilt direction reverses after welding (e.g. minibasins 4 and 11: Figs 6, 8 and 9), resulting in the stacking of wedge-shape sequences that thicken in opposite directions.
Although our models have addressed the interactions between minibasins from a two-dimensional perspective, salt flow is a very three-dimensional process. In contrast to our models, in a threedimensional framework, salt can be expelled in any direction within the salt volume, across salt walls and diapirs surrounding the minibasins. On the one hand, because salt may spread in more directions, it is likely that the interactions between nearby Sketches illustrating examples of potential interactions between minibasins that would result in differential subsidence histories and asymmetrical stratal geometries. See the text for details. minibasins described here (e.g. discontinued subsidence and tilting) would be mitigated. On the other hand, it means that there is more potential for differential salt flows in the horizontal plane; this could cause minibasin rotation about a subvertical axis, as observed in physical models where minibasins collide (e.g. Rowan & Vendeville 2006;Callot et al. 2016).

Conclusions
Two-dimensional numerical models were performed to study a scenario in which minibasins were initiated and subsided into salt at different rates, without slope-driven regional salt flow or tectonic deformation. The goal of the study was to test the hypothesis that minibasins are able to interact through the complex patterns of salt flow that result when adjacent minibasins are subsiding at different rates (e.g. Jackson et al. 2019). Our models show that minibasins do indeed interact, and that minibasins may tilt, translate or experience delays in subsidence due to the subsidence of nearby minibasins. These interactions are all results of a competition between subsiding minibasins for the finite available salt volume. Ultimately, the complex subsidence history is reflected in the complex patterns of minibasin sedimentation.
Minibasin interpretation usually assumes either vertical density-driven subsidence or subsidence dominated by a regional salt flow. Regional salt flow can indeed be important, especially in areas where large-scale basinward movement of salt has been identified or where the basin experiences regional tectonics. However, minibasins have not necessarily undergone a simple history of purely vertical subsidence in tectonically quieter areas. Locally induced perturbations to the salt flow can be caused by the differential rates of salt expulsion related to the different subsidence rates of minibasins. The interactions, illustrated by the numerical models shown in this study, suggest that minibasin subsidence occurs in a dynamic system in which minibasins do not act as mere recorders of the salt flow around them, but rather they are also the drivers that can influence and alter that salt flow by themselves.
We suggest that interactions between adjacent minibasins that have not collided should be considered when interpreting stratal patterns within minibasins, particularly in areas where the salttectonic processes are thought to be purely vertical. The models shown in this work illustrate that even in such areas, minibasins can have complex subsidence histories due to the interactions between them.