Carbonate clumped isotope thermometry of fault rocks and its possibilities: tectonic implications from calcites within Himalayan Frontal Fold-Thrust Belt

Disentangling the temperature and depth of formation of fault rocks is critical for understanding their rheology, exhumation, and the evolution of fault zones. Estimation of fault rock temperatures mostly relies on conventional geothermometers of metamorphic minerals and element partitioning analysis, which are largely inapplicable in shallow crustal fault rocks. Here, we demonstrate the applicability of the carbonate clumped isotope thermometer in low-grade carbonate-bearing fault rocks from the Himalayan frontal wedge (northwest India). Coalescing carbonate clumped isotope thermometry and calcite e-twin morphology allows us to constrain the temperature and depth of formation of the two main thrusts of the Himalayan frontal wedge, the Nahan thrust (170 ± 10 °C; 6–7 km depth), and the Main Boundary thrust (262 ± 30 °C; 10–11 km depth). The integration of the adopted analytical techniques can promote the application of calcite-based clumped isotope thermometry to the fault zone processes and refinement of shallow crustal fault zone models.


Introduction
Carbonate clumped isotopes refer to the CO 2 generated by the CaCO 3 -acid reaction, which contains two or more heavy isotopes like 13 C and 18 O (Ghosh et al. 2006a). The clumped isotope measurements are represented by mass 47 anomaly (Δ 47 ) in the generated CO 2 gas. The Δ 47 values, therefore, indicate the abundance anomaly of 13 C-18 O bonds from the stochastic distribution (Affek and Eiler 2006;Eiler and Schauble 2004;Kluge et al. 2015). The degree to which these heavy isotopes bond to each other depends on rotational and vibrational frequencies of the bonds (Wang et al. 2004) and entropy of the system (Schauble et al. 2006;Swanson et al. 2012) and decreases with increasing temperature (Ryb et al. 2017).
Carbonate clumped isotope (Δ 47 ) thermometry has become a robust technique in the past decade and has been primarily used for carbonates formed in surface environments at temperatures below 35°C (Eiler 2007;Ghosh et al. 2006a). At about > 100°C temperatures, initial Δ 47 values may decrease through solid-state reordering and reflect values characteristic of higher temperature crustal settings (Passey and Henkes 2012;Stolper and Eiler 2015). Existing application of carbonate clumped isotope thermometry addresses queries from a variety of geological settings that include burial in sedimentary basins (Henkes et al. 2014;Shenton et al. 2015), exhumation in orogenic belts Huntington and Lechler 2015;Ryb et al. 2017), and palaeothermometry in low-temperature (< 400°C) contact and regional metamorphic belts (Ferry et al. 2011;Lloyd et al. 2017). However, the application of Δ 47 thermometry in calcite-bearing rocks and syn-tectonic veins is limited till date MacDonald et al. 2019;Siman-Tov et al. 2016;Swanson et al. 2012).
Presently, estimation of deformation temperature from low-grade calcite-bearing metamorphic fault rocks relies primarily on the identification and characterization of the deformation twin patterns (Burkhard 1993;Ferrill et al. 2004;Ferrill and Groshong 1993;Rybacki et al. 2013), which is a semi-quantitative technique and provide a range of deformation temperatures. The generation of deformation twins in calcite is grain-size sensitive (Lacombe 2010;Newman 1994;Rybacki et al. 2013) and dependent on the amount of strain hardening (Ferrill et al. 2004;Parlangeau et al. 2019;Rowe and Rutter 1990). In contrast, the Δ 47 thermometry provides temperature estimation independent of grain size and effects of strain hardening (Ghosh et al. 2006b;Henkes et al. 2013;Schauble et al. 2006) but is dependent on carbonate mineralogy (e.g., calcite, aragonite, or dolomite) that affects the kinetics, closure temperature, and re-ordering of clumped isotopes (Bonifacie et al. 2017;Eiler 2011;Ferry et al. 2011;Stolper and Eiler 2015). Hence, both the techniques independently has certain limitations and must be used with caution.
The present study is focused on syn-tectonic calcite veins and skeletal (bio-clasts) calcite in deformed limestones present within the Himalayan frontal wedge, bounded between the Nahan thrust (NT) and the Main Boundary Thrust (MBT) (Fig. 1). This study aims to correlate the temperature estimation from deformation microstructures (primarily deformation twins of calcite) with Δ 47 thermometry, elucidating the deformation temperatures and depth of generation of these fault rocks. This information is crucial to grasp fault behavior at different crustal depths. A large database exists regarding metamorphic mineral growth, P-T-t path, and exhumation rate from the rocks of the Higher Himalayan Sequence (HHS) and the orogenic core (Bollinger et al. 2004;Chakraborty et al. 2017;Chakraborty et al. 2016;Martin 2017;McQuarrie and Ehlers 2015;Schultz et al., 2016;Webb et al. 2011;Yin 2006). In comparison, data on P-T estimates from the MBT, the Sub Himalayan Sequence (SHS), and adjoining thrusts in the frontal fold-thrust belt (FTB) are limited (Mukhopadhyay and Mishra 2005;Sharma et al. 2019;Singh et al. 2015), mainly due to the non-availability of suitable thermometers for these unmetamorphosed to low-grade metamorphosed rocks. Peak metamorphic temperatures not exceeding~330°C have been reported from the Lesser Himalayan Sequence (LHS) in the MBT hanging wall Fig. 1 a Large-scale map of the north-western Himalayas modified after Saha et al. (2016). Inset show the locality and simplified schematic cross section of Himalayas after Bose et al. (2009). MHT Main Himalayan Thrust, MCT Main Central Thrust, MBT Main Boundary Thrust, RT Ranon Thrust, ST Surajpur Thrust, BT Bilaspur Thrust, NT Nahan Thrust, MFT Main Frontal Thrust. The sample localities are indicated by red star. The red rectangles are shown as enlarged areas in (b) and (c). The X′-X line represents the transect between NT and MBT along which the schematic structural section and depth-temperature data have been presented in Fig. 7. b Map of MBT at Gambarpul with sample location and bedding data. c Map of NT with lithological variation, sample location and bedding data. (GPS data of the samples are presented in Supplementary Table 1S) Sarkar et al. Progress in Earth and Planetary Science (2021) (Célérier et al. 2009;Colleps et al. 2018) from NW Himalaya where at most places these rocks were never buried to temperatures greater than 230-250°C (Yu 2014). The data and thermal modeling reveal cooling and exhumation initiated at~4-5 Ma in SHS and by2 -4 Ma; it affected the entire SHS (Colleps et al. 2018;Gavillot et al. 2018;Patel and Manmohan 2020). The current study also aims to bridge the gap of thermometric data within SHS, through the amalgamation of calcite twin morphology and clumped isotope studies to provide more accurate estimates of deformation temperatures. It also examines the reliability and applicability of independent usage of Δ 47 thermometry in estimating deformation temperatures of calcite-bearing unmetamorphosed to low-grade metamorphosed rocks.

Geological setting and samples
The Himalayan fold-thrust belt comprises of three main regional thrusts. From north to the south these are the Main Central Thrust (MCT), the Main Boundary Thrust (MBT), and the Main Frontal Thrust (MFT; Fig. 1a), which merge at depth to a single mid-crustal detachment named the Main Himalayan Thrust (MHT; Fig. 1a) (Chemenda et al. 2000;Cottle et al. 2015;Gibbons et al. 2015;Hodges 2000;Martin 2017;Webb et al. 2011;Yin 2006). These regional thrusts separate the major tectonostratigraphic units in the Himalayan belt which, from north to south are the Higher Himalayan Sequence (HHS), the Lesser Himalayan Sequence (LHS), the Sub Himalayan Sequence (SHS), and the Indo-Gangetic alluvium (Yin 2006). A southwest verging forward-propagating thrust sequence has been proposed with sequential emplacement of the MCT at ca. 22-20 Ma (DeCelles et al. 1998;Hodges 2000;Metcalfe 1993;Searle and Godin 2003), the MBT at ca. 11-10 Ma (Burbank et al. 1996;Lavé and Avouac 2000;Meigs et al. 1995;Sangode and Kumar 2003), and the MFT at~2 Ma (Burbank et al. 1996;Kumar et al. 2006;Lavé and Avouac 2000;Meigs et al. 1995;Sangode and Kumar 2003;Sapkota et al. 2013). Thermal models of the age data demonstrate high thrust-related exhumation rates (≥ 1 mm/year) within the SHS (Colleps et al. 2018;Gavillot et al. 2018;Yu 2014), while the LHS jointly with the HHS nappes has been exhumed at a much faster rate (~5 mm/ year) along the MBT (Bollinger et al. 2004). Active faulting accompanied by rapid differential tectonic uplift (~4-15 mm/year) has also been deciphered along the MFT, from northwestern India to central Nepal (Kumar et al. 2006;Lavé and Avouac 2000;Patel and Manmohan 2020;Wesnousky et al. 1999).
The Himalayan frontal wedge, bounded between the MBT and MFT, is essentially made up of unmetamorphosed to low-grade metamorphosed but strongly deformed Tertiary rocks of the SHS (Fig. 1a). In northwest Himalaya, the MBT is marked by the contact between the Proterozoic LHS and the Cenozoic SHS (Thakur et al. 2010;Valdiya 1984). The MFT, however, is usually not exposed at the surface and identified by the tectonic contact between the Indo-Gangetic alluvium and the late-Cenozoic Siwalik rocks of the SHS (Powers et al. 1998;Thakur 2013). In the presently studied transect of the Himalayan frontal wedge (Fig. 1), the southernmost bounding thrust is marked by the NT (Célérier et al. 2009;Thakur et al. 2010) near Pinjore town, while the northern bounding thrust is the MBT at Gambarpul town. Lithologies between NT and MBT include fluvial sandstone and shallow marine fossiliferous limestone of the Paleogene Subathu and Dagshai formations ( Fig. 2a-g). Several slices of the Paleogene Subathu-Dagshai rocks (ca. 41-25 Ma) forming an imbricate structure get exposed within this wedge (Najman and Garzanti 2000). The intermediate major thrusts, progressively from the south are the Bilaspur thrust (BT), the Surajpur thrust (ST), and the Ranon thrust (RT) (Bose et al. 2009). The NW-SE trending NT separates the conglomerate bed of the Neogene Siwalik Group from the overlying sandstone-shale beds of the Paleogene Dagshai Formation (Fig. 1c). The damage zone has a well-developed gouge zone (~100 m) containing fragments of calcite veins (Fig. 2a). The MBT is exposed near the Gambarpul area and separates the fossiliferous limestone (Fig. 2e, f) and calcareous siltstone of Paleogene Subathu Formation on its footwall from the overlying predominantly siliciclastic rocks of the LHS of Neo-Proterozoic age (Fig. 1b). Discrete stromatolitic limestone bodies ( Fig. 2h) of the Krol Group (ca.~540 Ma) (Dey et al. 2020;Kumar 2020) are present within the dominantly siliciclastic rocks of the Infra-Krol sequence in the hanging wall LHS rocks. The major thrust contacts from NT to MBT are all characterized by the presence of pervasive calcite veins as compared to the rest of the thrust sheet ( Fig. 2). The veins show deformation with brecciated nature in NT (Fig. 2a), while in BT, ST, RT, and MBT, they show co-folding with the deformed rocks ( Fig. 2b-f). The preferential occurrence of the veins along the major thrust planes and their co-deformation along with the thrust zone rocks prompted us to infer these veins as syn-tectonic veins. The current study focuses on these syn-tectonic calcite veins ( Fig. 2a-f) and deformed calcite-bearing limestones (Fig. 2g, h) occurring within the Himalayan frontal wedge bounded between the MBT and the NT.
Ten calcite samples were collected across the thrust splays from NT in the south to MBT in the north. Sampling localities and sample types are given in Supplementary Table 1S  splay thrust in the RT sheet and RT respectively. Samples GM8, GM6a were collected from thrust-related foliation-parallel calcite veins (Fig. 2e, f) within the footwall block of the MBT while GM8a was from an older dilatational vein truncated by thrust-related foliation at the same site. GM4 and GM5I were collected from the MBT hanging wall stromatolitic limestone of the Krol Group (Fig. 2h).

Microstructural studies
The microstructural studies of the calcite samples were performed on polished thin sections using a polarizing microscope. Additionally, the crystallographic preferred orientation (CPO) maps of the calcite grains were obtained using the Nordlys electron backscattered diffraction (EBSD) detector attached to a scanning electron microscope (SEM) JEOL JSM6390A at Hiroshima University. An accelerating voltage of 15 kV and sample tilt of 70°was used for the EBSD analyses. The EBSD patterns were indexed using HKL Channel 5.0 software package. Automatic detection of the center of 6-12 Kikuchi bands using the Hough transform routine (Adams et al. 1993) was followed by comparing the obtained solid angles from the patterns with HKL calcite match unit containing 60 reflectors to index the pattern. Usage of a smaller number of bands was not preferred since it drastically increases the amount of systematic mis-indexing (Bestmann and Prior 2003).

Clumped isotope analysis
The isotope analyses (δ 13 C, δ 18 O, and Δ 47 ) of all the carbonate samples were measured at Kyushu University, Japan in two sets. The first set (SET 1) of samples were analyzed in December 2018 while the second set (SET 2-1 and 2-2) from September to October 2019 (Table 1  and Supplementary Table 2S). In the present study, the samples were prepared and analyzed by the same method as mentioned in Kato et al. 2019. The powdered calcite specimens of 6-9 mg were digested by 105% phosphoric acid at 90°C (within 10 min), and the generated CO 2 was trapped immediately and dehydrated using liquid nitrogen and ethanol slush in a stainless-steel vacuum line. The dehydrated CO 2 was removed of all organic contaminants, by passing with helium gas through a 30-m-long capillary column (Supel-Q PLOT) cooled at − 10°C. Purified CO 2 was then analyzed by dual inlet mass spectrometer (Finnigan MAT-253) configured for measurements of masses 44-49 with pressure adjustment that produced an m/z 44 signal of 16 V. The pressure baseline (PBL) correction (He et al. 2012) with the off-peak measurement of the background intensities of masses 45-49 was also applied. Each analysis includes 4-8 sets of measurement sequences that consist of 4.5  (Brand et al. 2010).
Finally, the substitution of the acid correction 0.082‰ at 90°C (Defliese et al. 2015) yielded Δ 47-ARF values of the analyzed samples.
In this study, to convert Δ 47 values to absolute temperatures (T), we applied the following Δ 47 -temperature calibration based on measurements of synthesized calcites reported in Kato et al. (2019). 4 Results and discussion

Calcite twin morphologies and EBSD analysis
Calcite e-twin morphology and width have been correlated with deformation temperatures in experiments to obtain a standard of comparison which can be used for estimating deformation temperatures from naturally deformed calcites (Burkhard 1993;Ferrill et al. 2004;Ferrill and Groshong 1993;Lacombe 2010;Rowe and Rutter 1990). Typically, four types of calcite deformation twins have been reported depending on twin width and morphologies (Ferrill et al. 2004). Type-I twins (width < 3 μm) are dominant at deformation temperatures below 170°C and occur as straight lines. Type-II, Type-III, and Type-IV twins have width > 3 μm and dominate above 200°C. Morphologically, Type-II occurs as tabular thick twins, while Type-III and Type-IV exhibit curved (or lensoid) and thick patchy twins, respectively. In the studied samples, calcite has variable grain size (2 mm-100 μm) and the observations of twin morphology (Fig. 3) in the optical microscope and misorientation data from SEM-EBSD (Fig. 4) confirm the development of deformation e-twins. PJ5 shows the development of predominantly one set of Type-I twins, with few minor grains showing two sets of Type-I twins (Fig. 3a). PWN1 (Fig. 3b) and GM8a (Fig. 3f) show the development of one set and two sets of Type-I twins with few grains developing Type-II twins. Samples CM2 and KP1 (Fig. 3c, d) show predominant development of Type-II twins. GM6a shows the development of both Type-II and Type-III twins (Fig. 3e). CM1, the fossiliferous limestone, shows the limited development of twins (Fig. 3g). Fine-grained recrystallized calcite in GM4 and GM5I show weakly developed Type-II twins (Fig. 3h).
For SEM-EBSD grain size orientation analysis, the step size of 2 μm and 3 μm were used, which being much smaller than the average calcite grain size reduces the possibility of mis-indexing. However, such a step size reduces the probability of mapping Type-I twins (< 3 μm). Hence, EBSD maps of PJ5, PWN1, and CM1 were not obtained. The inverse pole figure (IPF) coloring of the maps of GM6a and GM8a ( Supplementary Fig. 1S) displays the individual grain orientations in relation to the crystallographic axis as shown in the IPF key. The band contrast maps ( Supplementary Fig. 1S) represent surface damage and misorientation boundaries and can be used to verify the reliability of the orientation maps. Misorientation angle distributions are represented in Fig. 4. The random pair misorientation angle distributions vary from the theoretical curve for random orientation distribution ( Fig. 4a-d). The neighbor-pair misorientation angle distributions for the samples show a distinctive peak at about 75°-80°confirming development of etwins in calcite grains. In this context, the dominance of Type-I twins in PJ5, CM1, and GM8a suggests a lower temperature of deformation (~170°C) for these samples while the presence of thicker Type-II and curved Type-III deformation twins in sample PWN1, CM2, KP1, and GM6a suggests a higher temperature (> 200°C) of deformation. The limited development of Type-II twins in GM4 and GM5I indicates the possibility of deformation temperature > 200°C.
4.2 Clumped isotope thermometry: validity and future applicability in studying fault zone rocks Table 1 shows the isotope analyses of the vein and diagenetic calcite samples from the Subathu-Dagshai (samples PJ5, PWN1, CM1, CM2, KP1, GM6a, GM8a, and GM8 and Krol (samples GM4 and GM5I) formations. Fig. 3 a Type-I deformation twins (arrows) have predominantly developed within calcites veins from the gouge of NT (PJ5), implying a temperature of less than 170°C (Ferrill et al. 2004). b Limited development of type-I and type-II twins in the calcite veins of PWN1. c Predominance of type-II twins in the calcite veins of CM2. d Predominance of type-II twins in the calcite veins of KP1. e Type-II (short arrow) and type-III (long arrow) twins with few recrystallized calcite grains (small grains in the left side) occur within footwall calcite veins near MBT contact (GM6a). f Type-I deformation twins (short arrow) have predominantly developed in the older dilational calcite veins occurring in limestones (GM8a) in footwall of MBT. Few grains have developed type-II twins (long arrow). g Fossiliferous limestone sample CM1 showing foraminifera fossils with limited deformation twins. h Few twins (arrows) are developed in the fine-grained stromatolitic bodies occurring in the hanging wall of MBT (GM5I) Sarkar et al. Progress in Earth and Planetary Science (2021)

Krol Formation
The samples from the Krol Formation (samples GM4 and GM5I) are all diagenetic samples from the stromatolitic limestone. The Δ 47 values range between 0.435 ± 0.014 and 0.413 ± 0.016‰ corresponding to temperatures 221.6°C and 262.5°C. The clumped isotope temperature obtained from the diagenetic samples (GM4 and GM5I) of the Krol Formation is~100-150°C higher than the diagenetic sample (CM1) of Subathu-Dagshai formations.

Applicability of Δ 47 thermometry
During cooling from high temperature, Δ 47 values in calcite have been shown to follow solid-state bond reordering till it reaches the blocking temperature of calcite (~150-200°C), where the Δ 47 value gets locked (Passey and Henkes 2012;Stolper and Eiler 2015). Calcite residing in the subsurface at high temperature (ca. > 100°C) for a long period (ca. > 100 Ma) is susceptible to solidstate bond reordering (Bristow et al. 2011;Passey and Henkes 2012;Stolper and Eiler 2015). Therefore, higher apparent temperatures can be preserved through faster cooling/exhumation rates of calcite-bearing rocks (Bristow et al. 2011;Passey and Henkes 2012;Shenton et al. 2015;Stolper and Eiler 2015). In shallow crustal fold-thrust belts, ambient deformation temperatures in fault zones may be high enough (ca.~200°C) to initiate clumped isotope bond reordering in calcite-bearing rocks as well as syn-tectonic calcite veins. However, the established chronology of thrust movements in the Himalayan fold-thrust belt (FTB) (ca.~10 Ma for MBT to~2 Ma for MFT) (Burbank et al. 1996;Kumar et al. Meigs et al. 1995;Sangode and Kumar 2003;Sapkota et al. 2013) is on the much lower side of the required time for calcite solid-state bond reordering to be effective. The intermediate thrust faults namely, RT, ST, BT, and NT are also relatively young (< 10 Ma to > 2 Ma) for calcite solid-state bond reordering to be effective. Additionally, the exhumation rate in the last 7 Ma is 1 mm/year in most places (Clift et al. 2008;Lang et al. 2016;Najman et al. 2009;Turab et al. 2017) to as fast as 6-7 mm/year in the North Himalayan Gneissic Domes (Yin 2006). Hence, the analyzed calcite samples from thrust-related veins which experienced the deformation-exhumation path after crystallization would in all probability preserve the deformation temperature as deduced from measured Δ 47 values. The limestone samples from the Subathu Formation of the SHS (ca.~41 Ma) or the Krol Group of the LHS (ca.~540 Ma), on the contrary, are much older and must have followed a protracted burial or low-T metamorphism-exhumation path after their formation at near-surface environments (ca.~25-30°C) (Eiler 2011) and might be susceptible to solid-state calcite bond reordering (Dennis and Schrag 2010;Lawson et al. 2018). The majority of the studied samples (seven out of ten) belong to the vein-calcite category having little residence time after crystallization for thermal resetting of clumped isotope temperatures to be effective. However, to evaluate the degree of bond reordering, the thermal history reordering models "THRMs" (as defined in Shenton et al. 2015) for all the samples were generated using the ClumpyCool package ) as presented in Supplementary Table 3S and Fig. 5. Calcite reordering parameters are from Stolper and Eiler (2015) that uses the CDES25-temperature calibration. While running THRMs, the initialization (Time 0) was taken as the precipitation age of the calcite. For vein samples, the precipitation age was considered to be synchronous with slip on individual thrust planes with which the veins are associated. For the limestone samples, the precipitation age is the age of deposition of the stratigraphic units from which the samples were collected (Supplementary  Table 3S). For the latter samples, the temperature of burial was assumed to be ca.~230°C-the maximum burial temperature experienced by the LHS rocks (Colleps et al. 2018;Yu 2014). The calcite e-twin based palaeothermometry data were used as the temperature of deformation for all the samples. The generated THRMs (Fig. 5) for the samples indicate that bond reordering did not take place in the vein samples but might have occurred for the diagenetic samples (CM1, GM4, and GM5I). Hence, the Δ 47 -based apparent temperatures of the samples (Table 1 and Supplementary Table 2S) could be interpreted to represent either the calcite precipitation temperature (for the syn-tectonic calcite veins) or the temperature of deformation-metamorphism of the calcite-bearing rocks (as this was the last high- Fig. 6 Scatter plot showing calcite deformation e-twin morphologies against Δ 47 temperatures. The deformation twin types based on e-twin morphologies (Ferrill et al. 2004) are presented for each sample (Table 1). Clumped isotope data of the corresponding samples are plotted from SET 1 and SET 2-1 ( temperature event to reset the calcite isotopic ratios). In other words, the apparent temperatures obtained from the vein and the whole rock samples indicate the deformation temperatures along the successive thrust slices in the studied transect. It is pertinent here to mention that the apparent temperatures obtained from Δ 47 data are within the range of the temperature data estimated from the development of the e-twin morphology of the samples ( Fig. 6 and Table 3S). Thus, both the conventional e-twin related temperature estimates and clumped isotope thermometry data from the same set of samples are in good agreement suggesting the validity of the interpretation that the Δ 47 -based apparent temperatures truly represent the deformation temperature of the rocks. It further points to independent future application potentiality of the latter method in low-grade calcitebearing rocks, provided the calcite samples were not subjected to complete bond reordering. We also find that Δ 47 -based deformation temperatures of most of the fault zone samples (excluding the one from NT, or those from the footwall blocks of MBT, see Table 1) are~40-65°C higher than the temperature commonly observed in slowly exhumed metamorphic rocks (Passey and Henkes 2012;Stolper and Eiler 2015). This discrepancy in the deformation temperature data from the studied transect might be explained if we assume that thrust-related exhumation in the Himalayan FTB is sufficiently rapid to effectively quench the deformation temperature (Bristow et al. 2011;Passey and Henkes 2012;Stolper and Eiler 2015). The welldocumented high exhumation rates of the Himalayan frontal fold-thrust belt (Bollinger et al. 2004;Colleps et al. 2018;Gavillot et al. 2018;Kumar et al. 2006;Lavé and Avouac 2000;Patel and Manmohan 2020;Webb et al. 2011;Wesnousky et al. 1999) bear testimony to the above interpretation.
Thus, in concert with the above lines of evidence, it can be reasonably assumed that the temperatures estimated from Δ 47 data (Table 1 and Supplementary Table  2S) from the samples reflect deformation temperatures (and hence the depth) at which the slip events occurred during the growth of the Himalayan frontal wedge (Chen et al. 2019;Lacroix and Niemi 2019;Passey and Henkes 2012;Ryb et al. 2017;Shenton et al. 2015;Stolper and Eiler 2015). However, CM1 not being in close vicinity to any of the thrusts might reflect the maximum burial temperature (123 ± 8°C) of the Subathu limestone (Henkes et al. 2013;Shenton et al. 2015). Additionally, the higher temperature (269 ± 30°C) of the stromatolitic limestone in the hanging wall of MBT might also reflect the burial temperature of the stromatolitic limestone (Colleps et al. 2018;Yu 2014).  Fig. 1a for location) with depth vs. temperature data estimated from the deformed calcite samples collected within MBT and NT (Table 3S). Deformation along MBT and NT is due to slip at~10 Ma and~5 Ma respectively (Lavé and Avouac 2000). The red star represents the high-temperature deformation while the blue star represents deformation in low temperature. The MBT rocks deformed at depth were exhumed to shallow crustal depths. With evolution of the thrust toward the south, the shallow crustal rocks were deformed at shallower depths, leading to low temperature calcite deformation along the NT. The splay thrusts between MBT and NT show localized increase in deformation temperatures (indicated by the red stars). CM2, GM8 and GM4 are not plotted due to the scale of the sketch The current results are consistent with a general inverted thermal gradient from the structurally higher MBT to the lower-lying NT, which is in conformity with similar inverted thermal gradients documented from a number of transects across the major thrust zones in the Himalayas (Anczkiewicz et al. 2014;Bollinger et al. 2004;Chakraborty et al. 2016;Srivastava and Mitra 1996). The present data show a peak temperature of 269 ± 30°C at the MBT hanging wall (Fig. 7) (samples GM4, GM5I). The vein samples from the footwall of MBT (Fig. 7) also show Δ 47 temperature of 250 ± 26°C (samples GM6a and GM8). Only the sample GM8a show lower temperature (164 ± 10°C) and may be an older dilational vein that had undergone partial reordering. The samples (samples KP1, CM2, PWN1) occurring at the hanging walls of the intermediate splay thrusts (RT, ST, BT) between MBT and NT (Fig. 7), also, show consistent elevated temperatures (242 ± 13-251 ± 20°C) which drops to a lower value (171 ± 11°C) approaching NT hanging wall ( Fig. 7) (sample PJ5). Thus, if the overall temperature variation over a longer distance (MBT to NT) is considered, more realistic values of an inverted thermal gradient can be obtained.
We broadly constrain the crustal depths, at which the studied fault zone samples were deformed, by combining the presently generated clumped isotope palaeothermometry data with the previously published estimates of geothermal gradients in the Himalayan FTB. Previous workers estimated a geothermal gradient of 18-24°C km −1 from SHS rocks of the NW Himalaya (Agarwal 1994;van der Beek et al. 2006) while recent works in Sikkim, Arunachal Pradesh of NE Himalaya have documented a geothermal gradient of 22-26°C km −1 from the LHS rocks (Anczkiewicz et al. 2014;Clarke et al. 2016). Thus, a crustal geothermal gradient of 25°C km −1 (Priestley et al. 2008;Sheehan et al. 2013) for the presently studied transect is considered reasonable in light of the existing data. Utilizing the assumed value of geothermal gradient along with the presently generated deformation temperature data (Table 1), the depth of formation of the fault zone rocks were deduced to be~6-7 km and~10-11 km, respectively for the NT and MBT (Fig. 7). In the presently studied part of the Himalayan frontal thrust belt, the observed height difference is~1000 m between the actual outcrop-scale occurrences of the two successive thrust planes (NT and MBT at Pinjore and Gambarpul respectively) and~4 km depth variation deduced from the two zones. Considering the rate of erosion to be constant over the distance of~15 km and the suggested difference in time of formation of 5 Ma (Mishra and Mukhopadhyay 2012) for the NT and MBT, an average exhumation rate of~1 mm/ year (Clift et al. 2008;Lang et al. 2016;Najman et al. 2009;Turab et al. 2017) is obtained for the frontal thrust wedge in NW Himalaya. Apart from the peak exhumation rate of~40 mm/year at 55-50 Ma in western Himalaya, the presently obtained exhumation rate is similar to the average rate for the last 7 Ma, which is 1 mm/year in most places to as fast as 6-7 mm/year in the North Himalayan Gneissic Domes (Yin 2006).
The data presented here demonstrate the applicability of the new calcite-based geothermometer refining our ability to reconstruct temperature profile across major faults in an active orogenic setting relying on the carbonate minerals only. In this context, it is important to note that carbonate minerals in limestones as well as in syn-tectonic calcite veins are a dominant constituent of shallow to mid-crustal fault rocks in most of the orogenic belts worldwide. Therefore, the Δ 47 thermometry technique would be particularly useful in unmetamorphosed to low-grade metamorphosed terrains where conventional thermometers based on element partitioning in metamorphic minerals are inutile. The Δ 47 thermometry could also act as a preferred mechanism over illite or carbon-based thermometry (Bollinger et al. 2004) from low-grade terrains due to greater availability (than carbonaceous rocks) and lesser analytical complexity (than illite thermometer). Even combining conventional metamorphic mineral-based techniques with the presently practiced calcite clumped isotope thermometry may offer additional significant insights from interior parts of the orogens exposing deeper crustal sections and having experienced greater hydrothermal activity.

Conclusion
The calcite e-twin morphologies, as well as clumped isotope data, show great consistency in determining temperatures from the studied fault rocks. The syn-tectonic nature of the veins indicates the temperatures estimated are representative of deformation temperatures. The lower deformation temperature of NT rocks indicates a shallower origin while the higher deformation temperature from MBT rocks implies their deeper origin. The present study suggests the applicability of Δ 47 thermometry of calcite for estimating deformation temperatures of geologically younger (< 10 Ma) calcite bearing faults, in addition to estimating the cooling history of rocks as reported by other researchers (Chen et al. 2019;Dennis and Schrag 2010;Lawson et al. 2018). The variation of deformation depth for the NT and MBT might help in correlating future studies on deformation microstructures to crustal depths in the context of the Himalayas. Also, the precise estimation of exhumation rates from orogenic belts will require more robust fault-slip chronometric data used in conjunction with clumped isotopic data.