Formation of the Rustenburg Layered Suite by assimilation – batch crystallization (ABC) and – fractional crystallization (AFC)

Zhuosen Yao Department of Earth Sciences, Carleton University, 2115 Herzberg Laboratories, 1125 Colonel By Drive, Ottawa, K1S 5B6, Canada James Mungall (  JamesMungall@cunet.carleton.ca ) Department of Earth Sciences, Carleton University, 2115 Herzberg Laboratories, 1125 Colonel By Drive, Ottawa, K1S 5B6, Canada https://orcid.org/0000-0001-9726-8545 M Jenkins Department of Earth Sciences, Carleton University, 2115 Herzberg Laboratories, 1125 Colonel By Drive, Ottawa, K1S 5B6, Canada


Introduction
Layered ma c intrusions represent portions of the plumbing systems of many large igneous provinces and are principal repositories of several critically important ore elements, including Cr, Ti, V and the platinum-group elements (PGE)1. Layered ma c intrusions such as the iconic Rustenburg Layered Suite (RLS) of South Africa have historically been considered to represent the solidi ed remnants of vast liquiddominated reservoirs of magma called magma chambers where crystallization-differentiation has occurred by fractional crystallization2-3. However, an emerging consensus in igneous petrology views large magmatic systems as being dominated by interconnected bodies of mush extending from base to top of the lithosphere and only rarely containing more than a few volume percent of liquid at ephemeral and isolated locations4-6.
The paradigm of magmatic evolution by fractional crystallization (FC) has dominated igneous petrology since Bowen's revolutionary advances a century ago7, subject to recognition half a century later of the importance of crustal assimilation to result in the process of assimilation -fractional crystallization (AFC)8. The fundamental processes driving the evolution of magma composition in AFC are dissolution of host rock or xenoliths, accompanied by cooling and crystal growth, and the immediate removal of crystals from the possibility of continued reaction with the melt (Fig. 1a). Given that AFC is explicitly de ned as a fractional process, it is inherent in all AFC models that the system at any given time is composed almost exclusively of melt, into which in nitesimal amounts of contaminant may be titrated, and out of which in nitesimal amounts of solids must be removed due to gravitational sinking. This conceptual underpinning naturally forces the postulate that magmatic evolution occurs within large, liquid-dominated melt reservoirs in the crust (i.e., magma chambers) and drives petrologists to search for the existence of the solidi ed remnants of such bodies in the rock record. A quintessential small example of closed-system FC-AFC processes is the Skaergaard Intrusion of East Greenland2,9; however, the assumption that large layered ma c intrusions must therefore also represent the solidi ed remnants of vast open chambers lled with melt is a re exive model-driven extension of these ideas that has faced some recent challenges10-13.
A simple conceptual alternative to AFC is that of assimilation in conjunction with the textbook process of batch, or equilibrium, crystallization (i.e., ABC; Fig. 1b). Although the conceptual differences between fractional and equilibrium crystallization may appear arbitrary and purely academic, they describe fundamentally different processes when translated into large-scale magmatic systems. In the simplest expression of this concept, during ABC a magma becomes progressively more contaminated by the ongoing dissolution of wall rock or xenoliths; a hypothetical isenthalpic contamination drives the continuous crystallization of an increasing load of suspended solids which may remain broadly at equilibrium with the enclosing melt via intracrystalline chemical diffusion given su cient time14. As the proposed reason for FC, the scenario of gravitational sinking of dense solids in static magmas7 does not universally hold true in magmatic systems, i.e., crystallizing phases may not separate from a magma with high viscosity caused by crystallization and SiO2-enrichment; heat exchange and crystallization in assimilation provide destabilizing buoyancy uxes to drive forcefully disordered convection of ma c magma, where solids can be passively advected by vigorous convection instead of sinking15; and dense crystals may remain in suspension in most turbulent komatiite ows16. Although equilibrium may not be attained at moderate temperatures, it is likely to occur rapidly in ultrama c magmas17. The success of a hypothetical dimensionless thermodynamic black box ABC process has been demonstrated numerous times, reproducing the observed compositions of ultrama c cumulate rocks and their supernatant magmatic liquids in intrusions both large and small10, 18-20. A logical place to test the applicability of the ABC process to igneous petrogenesis at large scales is the Rustenburg Layered Suite (RLS) of South Africa (Fig. 2). Although much has been written about the genesis of the RLS, there is no single published model that seeks simultaneously to account quantitatively for the petrogenesis of all of its constituent units.
Here we propose forward models that recreate the observed bulk rock, mineral, and isotopic compositions of all major constituents of the entire RLS. The spectrum of cumulate rocks observed in the RLS can be described as the products of magma evolution during processes ranging from simple ABC in the ultrama c rocks of the Lower Zone and Critical Zone, through a two-stage ABC process to generate the ma c rocks of the Upper Critical and Main Zones, to classical AFC to form the parental melt for the Upper and Upper Main zones, which then evolved by FC in an essentially closed magma chamber affected by a small number of recharge events.

Results
Application to the Rustenburg Layered Suite, SA The Paleoproterozoic (~2.056 Ga10, 24) RLS is the world's largest layered ma c intrusive complex, containing ~600,000 km3 of ma c-ultrama c cumulates and extensive reserves of platinum-group elements (PGE), chromium and vanadium that dominate global resources of these elements21. The RLS intruded the 2.6-2.3 Ga sedimentary Pretoria Group and 2.061 Ga felsic lavas of the Rooiberg Group at upper crustal levels (~0.06-0.24 GPa)21, 25. In conjunction with the overlying Rashoop Granophyre and Lebowa Granite Suites, they together constitute the Bushveld Complex, comprising an enormous bimodal continental large igneous province in the Kaapvaal Craton (Fig. 2). The closest exposed analogues of Kaapvaal middle crust beneath the RLS are Archean basement amphibolite-to granulite-facies trondhjemitic-granodioritic-granitic gneisses, orthogneisses and metasedimentary rocks exposed in the Vredefort impact structure near Johannesburg26 and in the Southern Marginal Zone (SMZ) of the Limpopo belt to the north of the RLS27.
The RLS is shaped like a dinner plate about 7-9 km thick and ~400 km in diameter (Fig. 2), with moderately inward-dipping marginal zones and atter-lying central portions. Based on lithological and geochemical investigations, the RLS is traditionally subdivided into ve major and laterally continuous stratigraphic zones (Fig. 2)2, 21, 28: (1) the ne-grained, noritic to komatiitic Marginal Zone, which anks the other zones outside the main layered series and includes a Basal Zone encountered only in drill core beneath the other zones29, (2) discontinuous trough-like bodies of ultrama c Lower Zone (LZ) comprising harzburgite, orthopyroxenite and minor dunite interlayers, (3) pyroxenitic Lower Critical Zone (CZL) and noritic Upper Critical Zone (CZU),, de ned by the occurrence within both of them of prominent and laterally extensive chromitite and sul de-bearing layers locally enriched in PGE, (4) gabbronoritic Main Zone (MZ),, (5) uppermost ferrogabbroic-noritic and dioritic Upper Zone (UZ) with abundant magnetite layers (Fig. 2). Moreover, the MZ is sub-divided into the Upper (MZU) and Lower MZ (MZL) via a prominent, 3 m-thick orthopyroxenite which marks a signi cant change of initial Sr isotopic ratios (( 87 Sr/ 86 Sr)i) 23,28. The UZ is also sub-divided into three subzones by the rst appearances of magnetite (UZa),, olivine (UZb) and apatite (UZc) (Fig. 2) [30][31] . It is worth noting that this broad zonal classi cation is oversimpli ed for its regional-scale utility, while the cumulate layers show numerous and complex mesoscale variations in their spatial distribution, e.g., intricate details of the lithological macrolayering in LZ, CZL and CZU (Fig. 2) which cannot be correlated regionally despite the apparent regional correlations implicit in the naming conventions used for the chromitite layers within them32. If the implicit regional correlation of the chromitites is correct, then its regional-scale uniformity is superimposed on a patchwork of locally variable layered cumulate rocks.
The overall stratigraphy of the RLS can be tted into a two-stage pattern23 assuming that layers were deposited in sequence from bottom to top. The formation of the lower portion from LZ to MZL has been referred to as the integration stage (Fig. 2), recording multiple in uxes and extreme oscillations of dramatically different magmas at the scale of individual macrolayers metres to tens of metres thick, as evidenced both by magmatic unconformities and sharp changes in lithology21, 33, and by the distribution of radiogenic isotopes, exempli ed by ( 87 Sr/ 86 Sr)i 23. This is most clearly expressed in the CZU where anorthosite and norite locally alternate with harzburgite, pyroxenite and chromitite at scales of several metres. However, zircon within these contrasting macrolayers has been shown in some cases not to have crystallized in a sequence younging upward through the stratigraphic column, an observation that has called into question the notion of a continuously upward aggrading crystal pile at the base of a long-lived magma chamber10, 12, 33-34. The formation of the upper portion has been referred to as the differentiation stage ( Fig. 2)23, recording relatively uniform parentage as shown by marked uniformity of radiogenic isotope ratios and trace element abundances against a backdrop generally considered to record a well-de ned process of fractional crystallization in a large liquid-lled magma chamber with very few magma recharge events28, 31, 35-36, although some recent studies also attributed it to emplacements of several batches of magmas with constant isotopic compositions30, 37. The boundary between the integration stage and the fractionation stage is marked by the pyroxenite marker layer at the base of the MZU (Fig. 2), and the resulting composite upper body postulated to have crystallized from a large, quiescent magma body can be termed the "Upper and Upper Main Zone", or UUMZ.
It has been presumed that the ma c sills of the Marginal Zone represent samples of the "parental" magmas that generated the RLS3, 25, 38. Cumulate rocks in the complex can be subdivided into plagioclase-rich ma c units that have been postulated to be crystallization products of tholeiitic magmas referred to as A-type magmas and ultrama c units that have been postulated to be products of high-MgO magmas referred to as U-type magmas39. The U-type magmas contained ~12 to 14 wt.% MgO, corresponding to quench-textured norites exposed in the Marginal Zone surrounding the LZ and CZL and referred to as the B1 marginal sills (Fig. 2)25, 38, 40. However, the most primitive olivine and orthopyroxene observed in LZ cannot be crystallized from the melts with the composition of the recognized B1 magma21, 41, and the newfound Basal Ultrama c Sequence beneath the Marginal Zone requires a komatiite as the true parental magma29. The Bushveld U-type magmas are compositionally similar to modern boninites formed by hydrous melting of metasomatized upper mantle38, but Barnes40 proposed a better analogue in the siliceous high magnesium basalts derived from the crustal contamination of komatiites in Archean greenstone belts.
The A-type magmas, thought to have contained ~7-8 wt.% MgO, are tentatively correlated with negrained gabbronorites of the Marginal Zone where it abuts the CZU and MZL, respectively termed the B2 and B3 tholeiitic magmas ( Fig. 2) [38][39] . The origins of the A-type magmas have had less attention than that of the U-type, with most investigators apparently assuming that they are commonplace tholeiitic basaltic magmas somehow derived from the upper mantle. Since the mantle does not directly produce tholeiites containing such low MgO contents there must have been some processing of their parental magmas, though this process has not been clearly de ned in the past1. B2 and B3 are also unconvincing parental magmas due to their partial cumulate characteristics and discrepant crystallization order compared to their interpreted cogenetic cumulates in the RLS21, 25. The bulk composition of the lower portion of RLS is too rich in compatible elements including Cr and the PGE to represent the composition of a liquid42 -it is necessarily regarded as being composed of cumulates deposited from larger volumes of through-going magma that are not presently exposed within the RLS.
The bulk composition of the parental magma that was injected to form the UUMZ was proposed by adding ~15-25% of a hypothetical missing segregated component into a weighted average UUMZ bulk composition, to form a basaltic andesite with ~5-6 wt.% MgO, but a modeled fractional crystallization sequence from this magma does not closely resemble the natural occurring cumulates28, 36.
Recently discovered spinifex olivine margins chilled at the base of LZ strongly argue for a komatiitic parent magma that underwent assimilation of the quartzitic oor22, 29. From this perspective, the remarkable similarities of trace-element features have led to suggestions that the B1 and B2-3 magmas were derived from komatiite via > ~40% contamination by upper and lower crust, respectively10, 22, 25. Sr-and Nd-isotopic data of cumulates were used to support the proposition that primitive melt assimilated ~15-30% partial melt of upper crust produce the LZ and CZL, whereas ~40-50% contamination with the depleted restite in staging chamber beneath RLS is required for the CZU and MZ 43 . Cr-enrichment and cyclic compositional reversals in the LZ have been attributed to episodic in uxes of crystals+liquids slurries derived from komatiite contaminated by 20% crust at 4.5-10 kbar42. Consideration of the Cr budget during chromitite formation indicates that the parental liquids must have been komatiitic10, 20, 42. Contamination in deep-seated chambers before nal crystal-slurry-type emplacement into the RLS was also proposed on the basis of stable and radiogenic isotope systems27, 44.
In contrast to the various suggestions of crustal contamination, radiogenic 187Os/186Os of sul de 45 and unradiogenic εHf of zircon from RLS 46 have been used to suggest that the parental magmas were derived from ancient eclogite-bearing subcontinental lithospheric mantle (SCLM) without extensive crustal assimilation. A role for refractory SCLM was also proposed as a possible explanation for the exceptionally high Pt/Pd of Bushveld U-type magmas and mineral deposits47, but it must also be noted that a large degree of melt production is highly unlikely from relatively cool and previously melt-depleted SCLM48.
Since the alleged SCLM Os isotopic signature could equally well be derived from crustal contaminants49, and melt-rock reaction by asthenospheric melts while they pass through refractory SCLM might affect PGE distributions, in the balance we favor the idea that the massive and very short-lived injection of magma that formed the RLS resulted from rapid melting of an asthenospheric mantle plume.
Considering the need for a komatiitic parental magma for the RLS, we suggest that rather than representing samples of the magmas parental to the RLS, the sills preserved in the Marginal Zone may instead be samples of magma that had already passed through the complex, depositing layered cumulate rocks within the RLS before their eventual expulsion into the surrounding Pretoria Supergroup10. Regarding the marginal zone magmas as the complements to the cumulate rocks rather than as their parents alleviates some of the more serious mass balance concerns.

Thermodynamic modeling
To test the applicability of ABC and AFC to the petrogenesis of the RLS, we have modeled the processes using alphaMELTS thermodynamic software50, supplemented by models of isotopic mass balance constrained by the alphaMELTS results. The working hypothesis was that it might be possible to produce representatives of each cumulate rock type preserved as individual macrolayers in the RLS by ABC processes. We chose to model average compositions for each of several key lithologies (Fig. 3) on the assumption that grain sorting on the macrolayer or hand specimen scale led to much of the observed scatter about the mean values20.
We have considered two distinct scenarios to address the possible origins of the "integration stage" cumulates beneath the base of the UUMZ and a third for the UUMZ, illustrated in Figure 3. In Scenario 1, following the one-stage ABC approach we have already successfully applied to several ultrama c suites worldwide10, 18-20, komatiite is combined with a crustal assimilant in an isenthalpic process, creating a relatively cooler equilibrated mixture of liquid and crystals which then undergoes some degree of cooling while remaining internally at equilibrium. Given the extreme low viscosity (~0.05-0.2 Pa·s), ascent rate as great as m/s and high liquidus temperature (>1550°C) of komatiite16, its emplacement into cooler host rocks (~200-300°C) approximates to forced turbulent convection, where solids are passively advected by chaotic ow and remain in suspension (Fig. 1b)15-16. This stage represents a single batch process of assimilation and cooling during transport through the lithosphere. The mixture is then separated by gravity into a cumulate comprising mostly solids and some trapped liquid, and a supernatant magma comprising mostly liquid and some entrained solids51. This next stage represents the intrusion of the mixture into a sill-like body at the level of the RLS and the resulting dumping of most of the entrained crystal load to form a macrolayer, with internal layering analogous to the strati cations of suspended sediment in water in upper plane bed ow regimes. These successive sill-like magma pulses can be vertically stacked to build up a thick layered pluton based on eld observations, geophysical data and numerical models52. Hence, the model cumulate in this stage is compared with ultrama c cumulate rocks of the RLS, and the supernatant magma leaving the system is compared with B1 marginal sill compositions.
In Scenario 2, representing two successive batch steps, it is assumed that a rst ABC process occurs in the mid-crust, after which the supernatant liquid rises and undergoes a second batch crystallization as it cools and is emplaced at the level of the RLS to form a mushy macrolayer ( Supplementary Fig. 2). During emplacement, this new batch of crystals and melt then separates into cumulate comprising mostly solids and some trapped liquid to represent part of the RLS, and a supernatant magma comprising mostly liquid carrying some entrained crystals that can be compared with the marginal sills. Compositions of solids, liquids, cumulates and marginal sills are shown in Figure 3c, d. This second scenario is therefore a sequence of two batch equilibrium processes which allows for the separation of hidden cumulates from the bulk mixture prior to magma ascent and deposition of the cumulate layer in the RLS-it might be considered as the rst step along a continuum of possible process toward AFC.
In Scenario 3, the assimilation and batch removal of crystals occur in a large number of small steps (e.g., 20 to 50 steps) that approximate to AFC as classically understood, presumably occurring within a complex lower-crustal magma reservoir that may have comprised multiple interconnected sill-and dikelike bodies largely composed of mush4-6.
Liquid that has been processed through this AFC mush zone is extracted and emplaced into a large silllike magma chamber where it subsequently evolves by fractional crystallization, subject to some subsequent magma replenishment events during the formation of UUMZ31.
The parameters used in the models are provided in Supplementary Tables 1-4. Compositions of endmember magmas, contaminants, solids, liquids, cumulates, and ejected magmas are all shown in Figures 3, 4 and 6. The mantle-derived melt is an Al-undepleted komatiite10. Major and trace element and Sr, Nd, and O isotopic compositions of the magmas and contaminants were estimated by comparison with upper crustal and mid-crustal rocks exposed in the Pretoria Supergroup, Vredefort impact structure, and Limpopo Belt as documented in detail in Supplementary Table 4 and Supplementary Figures 3 and 4 Supplementary Fig. 1). The B1 magma is modeled as a mixture of 22% solids equivalent to CZL pyroxenite with 78% liquid. The trace-element compositions of these cumulates and B1 marginal sills coincide well with the modeled results (Figs. 4a-b). Because the B1 marginal sills that envelope the LZ and CZL of the RLS range in thickness from 100-400 m and can penetrate ~100 km into the oor rocks38, their total volume may be regarded as supernatant magmas complementary to emplacement of all of the LZ and CZ pyroxenites.
Ma c rocks of the noritic portions of the CZU and gabbronoritic MZ are modeled under Scenario 2, with the same komatiite parent melt but a mid-crustal assimilant at 0.45 GPa. The corresponding temperature of the contaminant was estimated as 390°C via the geothermal model for continental lithosphere and a higher heat ow for the Paleoproterozoic RLS (~70 mW·m -2 ) than its current value (51±6 mW·m -2 ) 53 . The noritic CZU has a xenolith-rich contact sequence with LZ, and has widely been regarded as an independent sill-like intrusion of progressive mixtures between B1 and B2/B3 magmas21, 25. The similar crystallization sequence of MZL also requires mixed parental magmas that intrude as crystal slurries from a deeper, staging reservoir after crustal assimilation21. We envision that their primitive komatiites experienced ABC assimilation (~21% for CZU and ~24% for MZL) and cooled to ~1240-1250ºC in the middle crust to obtain "Bulk 1" compositions (Figs. 3c, d and Supplementary Fig. 2). Retention of ~90-97% of the solids at the site of assimilation left hidden ultrama c cumulates (compositions not shown) in the middle crust with compositions very similar to the LZ pyroxenites (Fig. 3). The remaining solids and liquid ("Bulk 2" in Figs. 3c, d and Supplementary Fig. 2) were cooled by conduction during ascent and then separated at the level of the RLS into ma c cumulates and ejected supernatant magmas very similar to the B2 and B3 marginal sills. After 40% crystallization at 1181 °C adcumulate norite in the CZU contains only 5% trapped liquid; its ejected liquid complement with only 5% solids resembles the B2 magma apart from the depletion of Rb and Th in the B2 composition (Figs. 3 and 4c). After 63.9% crystallization at 1130 °C the modeled MZL magma settles to form a mesocumulate containing ~3% trapped liquid and is anked by marginal B3 magma that is ejected at a relatively low crystallization degree (~34.2%) and contains ~42% solids (Figs. 3 and 4d). Relative slow cooling and accumulation of crystals may further work on the B3 rocks that are coarser grained than B1-2 and have the lowest traceelements concentrations (Fig. 4). Scenario 3 is applied to the genesis of the UUMZ. The occurrence of numerous titanomagnetite layers within UUMZ (Fig. 2) indicate that the incoming parental magma was iron-rich28, 36, and hence ma c lower crust is favored as the assimilant54. We suggest that slow rates of introduction of primitive magma into hot lower crust (assumed as 770ºC at 1 GPa due to the heat ow of ~70 mW·m-2) after passage of the vast volumes of magma that produced the Main Zone, combined with muted temperature gradients, might have permitted e cient crystal separation during ongoing crustal assimilation15 (Fig.  1a), in contrast to the vigorous forced convection that favored crystal entrainment during formation of Utype magmas at shallow depth. We modelled the genesis of the parental magma of the UUMZ (Fig. 3) by a process of 43.5% AFC contamination in the lower crust plus a further 24% fractional crystallization (FC) during slow upward ascent. After emplacement of this magma in the upper crust, the observed paragenetic sequence and mineral modes of the cumulate rocks (except possible liquid-immiscibilityinduced titanomagnetite28, 55) can be reproduced via a closed-system FC model until ~21% melt remains (Fig. 5a). It is debatable whether the nal residual liquid was then erupted to form the upper portions of the Rooiberg felsites36, but resolution of this controversy is not material to the success of our models because they focus on magma sources, not on their nal residues. Compositional variations of major minerals throughout the UUMZ are tted if the trapped-liquid-driven compositional shift is included (Fig. 5), but also exhibit a series of minor reversals driven by several batches of magma replenishment, which may have resulted in the formation of magnetite layers31, 37.
The isotopic compositions observed in the RLS are compared with the results of our model of transcrustal assimilation and batch or fractional crystallization (Fig. 6). The measured inverse correlation between ( 87 Sr/ 86 Sr)i and εNd values of RLS (Fig. 6a) are matched well by all models except for the B3 magma, which is represented by very few samples25.
Restricted ranges of ( 87 Sr/ 86 Sr)i in B1 vs B2 and B3 marginal sills have been widely used to support assertions that these were samples of the U-type and A-type parental liquids of the RLS, but thess observations are equally consistent with our proposition that the sills represent the liquid residues from deposition of the corresponding cumulates (Fig. 6a). High δ18O (average 7.1‰) without apparent systematic changes in RLS is consistent with the isotopic composition of the proposed crustal assimilants (Fig. 6b), but not with composition of the eclogite-bearing SCLM of Kaapvaal Craton (modẽ 5.9‰) which contains some of the most 18O-depleted (<4.5‰) garnets in the global database56.

Discussion And Conclusions
Our results show that the bulk of the RLS below UUMZ appears to have been generated by either onestage or at most, two-stage episodes of batch crystallization and emplacement in their current locations as crystal mushes (Fig. 3). The melts left over from these processes are represented by the marginal sills.
The application of the ABC concept to magmatic systems in lieu of AFC requires a fundamentally different perspective on the physical form of the magmatic systems in space and time. For crystals to be able to re-equilibrate continuously with the melt during ABC it must be very hot, tending to favor the process in ultrama c magmas but less so in ma c magmas. Furthermore, they must remain suspended and the melt must be well-mixed; both conditions require that the system is undergoing vigorous convection15 and/or turbulent ow16. Free, smooth convection cannot accomplish this. The free magma convection in a hot sill emplaced between cooler host rocks is sluggish and entirely driven by the descent of cool crystal-laden drips to a stagnant base57-58. Once they reach the cool lower boundary, crystals cannot be re-entrained in the convective ow. Except in the exceptional case that a ma c or ultrama c magma reservoir is being heated from below, the requirement of vigorous stirring instead demands that the process is occurring as forced convection in a dynamic owing magmatic setting like a network of dikes and sills4-6. Con nement to a dynamic conduit setting therefore also implies that ABC occurs quickly during transit of magma through the lithosphere rather than during quiescent evolution of a large melt-dominated magma chamber. It is implicit in an ABC model that as soon as the magma comes to rest, dense crystals will separate from the melt, arresting the process and forming masses of cumulates at any point where magma velocity slows.
AFC and ABC therefore offer extremely different views on the mechanism of delivery of crystals to layered intrusions and consequently on the mode of formation of the intrusions themselves. In classic AFC models the crystals form slowly in small numbers in cool zones near the margins, either settling2, 7 or remaining in situ58-59, to form layers, whereas in ABC the crystals form rapidly during transit through the lithosphere and are dumped in intrusions as masses that may subsequently undergo some crystal sorting into layers10, 20-21, 60-61. There can be no doubt that both mechanisms operate, exempli ed by the record of fractional crystallization in, e.g., the Skaergaard Intrusion2, 58, and that of batch emplacement of heavy crystal loads in, e.g., olivine-rich Hawaiian picrite lavas62. Assembly of a large volume of mush through multiple emplacements of magmas generated by the ABC process is an alternative mechanism for the creation of a thick accumulation of ma c or ultrama c crystal mush that will later be recognized as a layered intrusion. This mechanism crucially does not require the layers to have been emplaced in a younging-upward series at the bottom of a classic magma chamber and accommodates recent geochronological10-11 and eld33-34, 63 evidence for out-of-sequence layer formation in major layered ma c intrusions.
Wholesale wall-rock assimilation and thorough internal equilibration is di cult or impossible for multiplysaturated basaltic magmas, in which large degrees of solidi cation are experienced over small ranges in liquidus temperature. In contrast, hot and primitive MgO-rich magmas like komatiites are able to assimilate relatively fusible crustal rocks, including granitoids, basalts, and common sedimentary rocks, in startling large proportions, because their liquidus surfaces are very steep, aided by the latent heat of fusion liberated by the simultaneous crystallization of large volumes of the ma c minerals olivine and pyroxene 10, 18, 64, especially if the crustal rocks are already hot. This is true regardless whether the process is one of AFC or ABC. A typical komatiite melt with as little as 18 wt% MgO can assimilate masses of crustal rock exceeding 50% of its original mass, generating a mass of cumulus olivine and pyroxene approximately equal in mass to the original mass of assimilant 10, 18, 64. The resulting contaminated magma will therefore comprise approximately one third ultrama c solids and two thirds low-MgO basaltic liquid. This solid fraction is well within the range of mobile crystal suspensions that can travel through the crust with essentially Newtonian rheology and density lower than most crustal rocks65. The assimilation process occurs so easily that uncontaminated komatiites are rare and it works to prevent the existence of superheated magmas, which cannot fail to react with and dissolve their containers of host rock. Meanwhile, the extremely high temperatures and low viscosities of komatiites easily drive fast ascent and turbulent ow during emplacement, in which the dense crystals remain in suspension and at equilibrium with the host magma16 -approximating to the conceptual ABC model. It is especially noteworthy that modal proportions of cumulus minerals in ultrama c cumulates such as olivine-chromite or olivine-orthopyroxene mixtures in layered ma c intrusions generally do not conform to the instantaneous modal proportions expected during fractional crystallization, positively requiring that many such cumulates were deposited and mechanically sorted into layers from polyphase suspensions that were broadly at internal equilibrium20, 66. The common occurrence of granular harzburgites (i.e., olivine-orthopyroxene cumulate rocks) and pyroxene-chromite cumulates are explicitly forbidden during fractional crystallization by the peritectic relations among olivine, orthopyroxene, and chromite but are entirely consistent with equilibrium phase relations.
As our modeling of the UUMZ indicates, our goal here is not to argue that AFC and FC are not valid petrogenetic processes, but instead to demonstrate that the idealized ABC concept represents a process su cient to account for much of the spectrum of rock types observed in the world's premier layered ma c intrusion, especially those world-class mineral deposits that are hosted by ultrama c macrolayers, and therefore cannot be ignored.
Furthermore, in those cases where cumulates of contaminated magmas display modal proportions departing from expected cotectic proportions, some form of ABC must be accepted as having occurred. Indeed, a batch process is directly implied by several previous assertions that emplacement of the basal series dunites and granular harzburgites29, CZ chromite-bearing pyroxenites42, and MZ gabbronorites21 must have involved deposition of thick mushy layers, but these previous studies did not explore the implication that their mushy emplacement models are fundamentally inconsistent with AFC processes.
The implications for the mechanism of formation of layered ma c intrusions by injection of crystal mushes are far-reaching because the emplacement of each batch of magma, to form each macrolayer, is entirely independent from all of the other batches. Even in the Peridotite Zone of Stillwater Complex, which is the type locality for cyclic units representing the idealized products of FC, no evidence can be found for genuine cyclicity due to FC processes20. The ABC process does not require a large magma chamber to explain the sequence of rock types or to account for the lack of cyclicity; neither is the hypothetical existence of a magma chamber denied. We can consider layered ma c intrusions as products of numerous separate intrusive events in a long-lived magma column dominated by mushy zones punctuated by rare events when liquid-dominated magmas are transported and emplaced4-6, 52.
Macrolayers do not need to have formed in a younging sequence from bottom to top, although they might have. The hypothesis of mixing of fresh U-type magmas into resident A-type magmas of uncertain provenance to account for sharp reversals in mineral assemblages is not necessary, and the apparently random sequence of ma c and ultrama c layers in the CZU can be regarded as the consequence of injection of crystal-rich magma batches that experienced different paths through the lithosphere either a) in the observed stratigraphic sequence or b) out of stratigraphic sequence-either scenario is consistent with the observed occurrence of alternating ma c and ultrama c layers. Emplacement of one mushy macrolayer into still-hot older cumulates that may or may not remain partially molten need not produce easily recognizable chilled margins10, 66.
A profound implication for ore genesis is that the chromitite and

Methods
Isenthalpic assimilation simulations were carried out using the AlphaMELTS software, version 1.9. We collected the major oxide contents of country rocks (Supplementary Fig. 3) and the closest exposures of middle crust (Supplementary Fig. 4) beneath the RLS, and identi ed potential representatives of the complex lithological association in this region (Supplementary Table 3 Incremental crustal material was added to the system, and an isenthalpic calculation employs entropy maximization to solve for thermodynamic equilibrium between silicate liquid and solid phases at constant pressure. Any resultant crystals can be equilibrated with or discarded from residual liquid (ABC or AFC, respectively), and the remaining system becomes the starting point for next increment of assimilation. Following wholesale crustal assimilation at mid-(0.45 GPa) and lower-crustal levels (1 GPa), further cooling of ascending magmas in the conduit was represented by an isobaric crystallization at 0.2 GPa at the fayalite-magnetite-quartz solid oxygen buffer.  Table 4). Limited to rare data of sedimentary Pretoria Group, the O isotopic data of UC is assumed mainly with reference to the overlying Rooiberg Group and adjacent dolomite.
Pretoria Group rocks have higher δ18O (~9-15‰) than the averages of overlying volcanites (7.36‰), granophyres (6.6‰) and granites (7.35‰), and a moderate value (9.6‰) was set for the upper crustal materials (Supplementary Table 4). Average δ18O values of the Vredefort Dome and Limpopo belt mostly fall in the range from 9-10‰, but we adopted a slightly larger δ18O for MC assimilant (10.6‰) assuming a possible greater contribution from δ18O-enriched metapelites. The proposed LC has moderate Mg # and SiO2/Al2O3 ratios, corresponding to the features of intermediate-type lower crustal granulite xenoliths that has an average δ18O of 9.2‰70.

Figure 1
Schematic illustration of temporal evolution of magmas from left to right. Bulk assimilation mostly occurs on the wallrock-magma boundaries via dissolution and/or from the crustal xenoliths induced by magmatic stoping. a. classical AFC model; heat for crustal assimilation is supplemented by concurrent fractional crystallization while newly formed crystals are immediately sequestered from an almost entirely crystal-free liquid. b. in the ABC model, during assimilation a steadily increasing amount of precipitated solids remains suspended by forced convection during magma ow and is continuously reequilibrated with magma until it comes to rest and the solids are deposited all at once.       Isotope correlation diagrams comparing RLS rocks to assimilation models. Curves represent modelled assimilation of primary, mantle-derived magma with different end-members from the Kaapvaal Craton:

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. YaoMungallJenkinsNCSupplementaryData.pdf