Tracking the migration of the Indian continent using the carbonate clumped isotope technique on Phanerozoic soil carbonates

Approximately 140 million years ago, the Indian plate separated from Gondwana and migrated by almost 90° latitude to its current location, forming the Himalayan-Tibetan system. Large discrepancies exist in the rate of migration of Indian plate during Phanerozoic. Here we describe a new approach to paleo-latitudinal reconstruction based on simultaneous determination of carbonate formation temperature and δ18O of soil carbonates, constrained by the abundances of 13C-18O bonds in palaeosol carbonates. Assuming that the palaeosol carbonates have a strong relationship with the composition of the meteoric water, δ18O carbonate of palaeosol can constrain paleo-latitudinal position. Weighted mean annual rainfall δ18O water values measured at several stations across the southern latitudes are used to derive a polynomial equation: δ18Ow = −0.006 × (LAT)2 − 0.294 × (LAT) − 5.29 which is used for latitudinal reconstruction. We use this approach to show the northward migration of the Indian plate from 46.8 ± 5.8°S during the Permian (269 M.y.) to 30 ± 11°S during the Triassic (248 M.y.), 14.7 ± 8.7°S during the early Cretaceous (135 M.y.), and 28 ± 8.8°S during the late Cretaceous (68 M.y.). Soil carbonate δ18O provides an alternative method for tracing the latitudinal position of Indian plate in the past and the estimates are consistent with the paleo-magnetic records which document the position of Indian plate prior to 135 ± 3 M.y.

climatic conditions 1,2 in relatively dry soils where C 3 type grasses or mixed grasses and shrubs are the dominant vegetation.
The Satpura Basin, located in Central India, has an especially well-preserved record of soil carbonates. Sedimentary sequences comprised of packets of soil carbonate were deposited along the palaeo channel of the present day Narmada River while the Indian plate drifted from its position in the Southern Hemisphere 8,9 . These carbonates capture the isotopic signature of ancient soil water, which resemble the isotopic composition of meteoric water. Since soil waters experience evaporation that leads to enrichment in 18 O, our results place upper limits on meteoric water compositions 5 unless corrected for the isotopic effect due to evaporation. Lithostratigraphic studies of the Gondwana succession in the Satpura Basin indicate that strata bound calcic vertisols are interspersed in a sequence of mudstones, coarse sandstones with cement carbonaceous shale, coals and bio-fossils 8 . These sedimentary units are found in discrete, discontinuous patches within the 5 km-thick basinal package 10 . Post depositional modification of the sedimentary layers was minimal due to the small overburden of sedimentary piles and was restricted to only early diagenetic transformation 9,11 . The sedimentary succession of Satpura was deposited in a mega half-graben confined by faults. Sediment accumulation took place during fault-controlled subsidence regimes with intervening period of tectonic quiescence supported development of soils. The subsidence rate varied across the basin resulting in an asymmetric basin fill with the thickness increasing towards the north 10 . Sedimentation in the basin commenced with deposition of the Permo-Carboniferous (290 M.y. ago) Talchir bed followed by deposition of other sedimentary formations namely the Motur, Pachmarhi, Denwa, Bagra and Lameta with ages varying from 269, 248, 243, 135 and 68 M.y. ago respectively 8 . The focus of the present study is to use the combined temperature and δ 18 O of the carbonates deposited in this succession of fluvial sediments as a geochemical indicator of the palaeo-latitudinal position of the Indian plate.
Age assignments to the soil carbonates are based on biostratigraphic methods as well as relative age dating based on of the position of strata in the lithological section. The presence of vertebrate fossils in the litho-unit and the well-constrained geochronological age of the overlying Deccan basalt, allowed precise assignment of litho and biostratigraphic age to the litho-unit [8][9][10][11][12][13] . The overlying sequence of Deccan basalt restricted water-rock interaction creating an environment for excellent preservation of these soil archives 8 .

Clumped isotope analyses
In order to understand the temperature and fluid composition during precipitation of the soil carbonates, we analyzed clumped isotopic ratios in bulk carbonate samples. XRD analysis reveals that calcite and clays are the prominent minerals present in the samples 5 . The abundance of Δ 47, δ 13 C and δ 18 O of carbonates from the Motur, Denwa, Pachmarhi, Bagra and Lameta formations are given in Table 1 and Fig. 1. The Δ 47 constrains carbonate growth temperature independent of the δ 18 O of waters from which they grew 14 . The Δ 47 temperatures were then used to constrain the δ 18 O of water 14 (i.e., because both the growth temperature and the δ 18 O of carbonate are known). Here we determined soil water δ 18 O values upon using conventional paleo-thermometry equation 15 where temperature (Fig. 1e) of carbonate precipitation and δ 18 O of carbonate ( Fig. 1,b) were derived from the experimental results. This soil water δ 18 O value ranges between 0.25 ± 2.20 (‰, VSMOW) and − 8.1 ± 2.0 (‰, VSMOW). Uncertainty or heterogeneity in the composition of carbonate is due to variability in temperature of carbonate precipitation, water, soil respiration and is denoted by 1σ standard deviations from the mean and are marked in the plots (Fig. 1e) of Δ 47 , calcification temperature, δ 13 C and δ 18 O. The age uncertainties were established based on the bio-stratigraphy of the Motur, Pachmarhi, Denwa, Bagra and Lameta formations [16][17][18][19] . Both surface temperature and meteoric water δ 18 O are grossly linked with latitude. The relationship with δ 18 O of meteoric water and latitude is assumed to remain similar through 250 M.y. Factor like continental configuration is expected to influence the heat transfer process and isotopic distribution across latitude. But the simulation experiment conducted with land configuration resembling Permian 250 M.y. produced a thermal mode of circulation, similar to the modern North Atlantic, supporting our argument of grossly similar or slightly different equator-to-pole temperature gradient than the modern day 20 . These factors were responsible governing the seasonal distribution of isotopic ratios in meteoric water across the latitudes 21 . However, there are evidences which support that the yearly average isotopic ratios across the latitude remain more or less similar and comparable to We used Δ 47 based temperature estimates as input parameter together with δ 18 O of specific soil carbonates to derive the δ 18 O of soil water. Considering soil water as derived from the meteoric water an additional evaporative effect was introduced 5 . The modification of soil water composition likely varied through evaporation depending upon the latitudinal position. An enrichment factor of 2‰ and 2.5‰ are adopted for the samples with palaeo-latitudinal positions south of 50°S and north of 50°S respectively, to reflect this variation (see Table 1). The values obtained for the meteoric water (δ 18 Oppt) are fed into the polynomial equation for the reconstruction of the latitudinal positions and uncertainties of predicted values vary with Latitudes (Extended Data Figs 1 and 2); with higher accuracy been observed for prediction of positions at higher latitudes. The latitudinal dependence of temperature and δ 18 O are known from the IAEA database covering several stations across the Southern Hemisphere. Independent estimates on the pCO 2 level during carbonate precipitation are established from the δ 13 C values of pedogenic carbonates 8 . To account for the influence of changes in atmospheric pCO 2 on air temperature, we compare our results with those from global climate model (GCM) predictions of air temperatures and isotopes ratios in precipitation over a range of atmospheric pCO 2 levels 24 (Extended data Fig. 3). Although   [9][10][11][12][13] . In the absence of any fossil records from the Bagra Formation, several workers have contended that it might be equivalent to or younger in age than Denwa 12,13,25 . Since the age of the Denwa Formation is considered to be between the late Lower to the Middle Triassic 18 , the age of the Bagra formation has been taken to be around the late Triassic [16][17][18] . The fact that the Bagra Formation overlies the Denwa in Central India suggests that it is younger than late Triassic but older or equivalent to the late Jurassic-early Cretaceous (135 ± 14 M.y. ago) 19 . The Lameta Formation in Central India is located at the Lameta Ghat on the Narmada River, 15 km southwest of Jabalpur. The ~35 m -thick fluvial sediments of the Lameta Formation transitionally overlie the fluvial sandstone and mudstone of the Cretaceous 8 , Jabalpur Formation and are conformably overlain by the Tertiary Deccan trap basalts.
Estimation of average air temperature from calcite clumped isotopes. Several empirical formulations have been proposed for deriving temperature (air and calcite growth temperature) from clumped isotope data subsequent to the initial paper on clumped-isotope thermometry 26,27 . We report here calcite precipitation temperatures derived using the relationship proposed by Ghosh et al. 14 Table 2). Similarly, warmest monthly air temperatures estimated based on the equation 28 for our analysis of samples are 31 ± 2 °C for 269 M.y., 14.6 ± 7 °C for 248 M.y., 20 ± 8 °C for 243 M.y., 33.7 ± 6 °C for 135 M.y. and 36.2 ± 8 °C for 68 M.y. The majority of the temperature estimates are within several degree of modern average annual air temperature across the latitudes except for a few samples from the early Cretaceous and Permian, where the estimated temperature are slightly higher than modern day temperatures at those latitudes. It is possible that higher pCO 2 condition during these time periods were responsible for the warmer temperatures recorded in our samples compared to the present day value. The samples recording lowest temperature and lightest δ 18 O are expected to be most pristine, while samples with anomalously high temperatures are likely preserving signature of recrystallization and burial diagenesis which happens at elevated temperatures. In order to rule out the possibility of diffusion related process resetting the original composition, we compared clumped isotope temperature with the inferred temperature expected during deep burial (Extended Data Fig. 3).
We further compare our results with zonal average surface temperatures simulated using a GCM under a range of pCO 2 values 24 . The temperature values observed in our study at different latitudes are cooler than the simulated annual zonal temperatures. This discrepancy might indicate a seasonal bias to calcite precipitation. Calcite precipitation can happen during the period of water saturation or well-drained condition during a year. Studies have shown that the cold dry period with well-drained soil condition induces high soil respiration which is registered as enriched δ 13 C values in the soil carbonates 29 . In contrast, warm wet conditions dampen the rate of soil respiration, which is registered as lighter δ 13 C values in the soil carbonates 29 . A close inspection of the δ 13 C, δ 18 O and deduced Mean Annual Air Temperature (MAAT) for the samples suggests seasonal deposition of Lameta and Bagra soil calcite (Extended Data Fig. 4). Higher rate of soil respiration, low Eh condition and low input of atmospheric CO 2 is inferred for Lameta soil while soil formed during Bagra deposition registered a low rate of soil respiration, high Eh condition and enhance input of atmospheric CO 2 . Soil carbonates analyzed for other time period fall within a wide range of δ 13 C values covering entire year with high and low soil respiration rate, variable Eh and atmospheric CO 2 input conditions. Furthermore, the clumped isotope temperature estimates for soil carbonates support the high CO 2 level predicted earlier using δ 13 C values of soil carbonate and their organic matters 8 .
Latitudinal position of the Indian plate and Uncertainty. The available paleogeographic reconstructions suggest that the Satpura Gondwana basin was positioned at 60°S in the Early Permian and moved to 30-40°S by the Middle Triassic 30-32 and thus traversed through different climatic zones during this period. Existing paleomagnetic data suggest the position of the Indian plate relative to its current position (Fig. 2). Accurate positioning of the Indian plate during Phanerozoic is based upon a variety of archives; including sea-floor magnetic anomalies, geochronology and palaeo-magnetic data on flood basalt and relative position of hot spot track 33 . At present, knowledge the exact positions (with uncertainties) of Indian plate are based on the compilation of data 30,31 from various sources including the on-going PALEOMAP (http://www.scotese.com/) project. The palaeo-latitude of India is determined from global synthetic apparent polar wander paths (APWPs) which place the central Indian region at 53°S during the deposition of the Motur sediments 30,31 . The average position of the Indian plate during the Triassic period was 44°S and shifted to nearly 35°S by the late Jurassic period. Finally, the Indian plate was located at 22°S during the Cretaceous period. There are several reasons not to rely on the global APWP. First, their curve extends back only to 200 M.y., whereas we are interested in motions back to the Permian. A late Permian and Triassic segment to the Besse and Courtillot 34 reconstruction of plate movement was found to be geologically implausible and an alternative approach to validate the position of Indian plate is in high demand 35 .
This use of stable isotope in terrestrial carbonate for predicting latitude has been successfully demonstrated in reconstructing the locations of continents in the northern hemisphere 5,7,36 . However, in majority of these studies the predicted value of δ 18 O in calcite as a function of latitude were likely compromised by absence of information about soil temperature, depth of soil calcite precipitation, and evaporation of soil water. Here we obtained soil temperature from Δ 47 and accommodated evaporation effect. Effect of elevation governing the isotopic composition of precipitation was considered minimal as the palaeo-elevation of the basins is unknown. However, based on sedimentary record documenting structures associated with the strata where soil carbonates were deposited it is concluded that most of the deposition was confined to a flood plain setting at elevation close to mean sea level [9][10][11] . The δ 18 O smow values of water in equilibrium with soil carbonates varies through the section and averages − 8.9‰ in the Motur Formation, − 4.3‰ in the Pachmarhi Formation, − 4.0‰ in the Denwa Formation, 0‰ in the Bagra Formation, and − 3.4‰ in the Lameta Formation. Allowing corrections for the soil water δ 18 O smow values due to the effect of processes like evaporation. We translated the soil water δ 18 O smow to true meteoric water δ 18 O smow values 5 by including a constant evaporative enrichment factor of 2‰ for Motur carbonates and 2.5% for rest of the carbonates from four stratigraphic levels (See Supplementary data). The soil water isotopic values resemble values for the meteoric water after correction and thus been suitably used as input values in the empirical model for predicting the latitudinal position (Extended Data Fig. 1) of Indian plate. However, uncertainties on the calculated δ 18 Ow due to error in determination of isotopic fractionation factor between water and calcite was ignored. The latitudinal position varied during the deposition of sediments across the succession and the average position are 53 ± 1°S during deposition of Motur sediments, 41 ± 6°S for the Pachmarhi sediments, 40 ± 6°S for the Denwa sediments, and 30 ± 5°S and 40 ± 5°S for the Bagra and Lameta Formations respectively. The approach is validated for the modern samples of soil carbonates from India 28 which yielded latitude position of 34 ± 1°N as compared to the actual position of 27-31°N latitude (Table 1) Hydrological circulation during periods of elevated greenhouse gases level. Ghosh et al. 8 previously used the carbon isotopic composition of inorganic and organic remnants from the same set of palaeosol carbonates to derive pCO 2 in the Phanerozoic period. Our previous estimates showed that the CO 2 content of the atmosphere during depositional of the Motur formation was 540-890 ppmv while the concentration increased to 910-1510 ppmv during the period of deposition of soil carbonate in the Denwa formation. Similarly, the pCO 2 content registered analyzing the samples from Bagra formation was 1675-2775 ppmv, while pCO 2 content of atmosphere recorded analyzing the Lameta samples was 1110-1850 ppmv. These estimates are in agreement with the GEOCARB model prediction 37 . In this study, we determine the temperature of carbonate precipitation and obtain more precise estimates of the isotopic compositions of ancient soil waters and precipitation. The estimated water isotopic compositions were used for predicting the latitudinal position for the carbonate depositions and compared with the modal GNIP data for the prediction (Fig. 3). We compare our soil water compositions with precipitation isotopic compositions simulated using the GENESIS GCM for a range of elevated atmospheric CO 2 levels 24 (Fig. 3). The meridional variability of soil water isotopic compositions compares reasonably well with the simulated meridional variability in zonal-average precipitation, indicating that to first order ancient soil water does track paleo-latitude. The comparison also demonstrates a systematic isotopic enrichment of most meteoric waters relative to both modern observed and simulated precipitation. The meteoric δ 18 O values recorded in the carbonates during 269 M.y. until 135 M.y. are enriched compared to modern day average isotopic composition of precipitation across the latitude and even exceeded the simulation trend at higher pCO 2 condition.

Conclusion
The paleosol carbonates were precipitated in fluvial sediments during Permian to Cretaceous periods, coinciding with the movement of Indian landmass towards north and is overlain by the Deccan basalt on the top. The stratigraphic position of the palaeosol carbonates restricted water rock interaction and late diagenetic transformation of the original signatures. Clumped isotopic analysis on these samples reveals the temperature of calcite precipitation and the oxygen isotope ratios of carbonates. We note that the clumped isotope temperatures are lower than GCM-simulated annual surface temperatures, likely indicating a seasonal bias in carbonate precipitation. The isotopes in precipitation show very good agreement with the simulated meridional distribution. Not only does this validate using soil water δ 18 O as a paleo-latitudinal proxy, it also implies that the global-scale hydrological cycle was not fundamentally different during the climates of the late Paleozoic and Mesozoic. The δ 18 O values derived here are more robust than the temperature values as it captured either environmental water at the time of calcite precipitation or later during the process of early diagenesis. The secondary calcites precipitated from the diagenetic water at higher temperature closely resemble the composition of environmental water. This suggests that the early diagenetic water is similar to the environmental water. This is documented in our observation. The temperature trends recorded in the sample are consistent with the model-based estimates, except for the 269 M.a. samples, which is much too warm. Also, pedogenic carbonates have a tendency of becoming increasingly enriched in δ 18 O at higher MAT and evaporation rates 3,32 . A systematic enrichment of 0.5‰ would bring all the points in line with the model predictions. Therefore, any offset in paleo-latitude reconstruction can partly be explained by adopting a systematic isotopic enrichment 7 . The approach of using the latitudinal variability of oxygen isotopic composition in rainfall is used here to estimate the position of Indian plate and shows great promise, especially at mid and high latitudes where isotopic gradients are greatest. This method could be further refined by simulating specific time slices in the past and comparing carbonate δ 18 O with simulated δ 18 O at specific locations. Based on the data we observe variations in the rate of drifting of Indian plate. Assuming the orientation of Indian plate remaining unchanged during its journey to the north, we can deduce the rate of movement of Indian plate with shift in the mean latitudinal position with age. Assuming 111 km correspond to a drift of 1° latitude, we estimate the rate of migration was 51 mm/year between 269 M.y. and 243 M.y., dropping to 10 mm/year during the interval between 243 M.y. ago and 135 M.y ago.