The light-exposed outer layer (~1 cm) of the bricks was removed in the Luminescence Dating Laboratory (LumDL) of the Birbal Sahni Institute of Paleosciences (BSIP) in a subdued red light environment. The part of the brick that was unexposed to light was used for dose measurement using luminescence, while the exposed part was used for dose rate estimation.

The brick unexposed to light was gently crushed using an agate mortar and pestle without disturbing the original grain size distribution. The crushed samples were treated with 1N hydrochloric acid (HCl) to remove carbonates and 35% hydrogen peroxide to remove organic materials. The finer grains that were stuck to the coarser grains were deflocculated using 0.01N sodium oxalate. The fine-grained fraction (4–11 μm) of the polymineral was extracted using the settling method based on Stokes' law in an acetone medium (15 cm column) by allowing it to settle for 1.5 min (<11 μm) and 15 min (>4 μm). This fine-grain fraction (1 ml) was deposited on cleaned aluminum discs (9.6 mm) in a flat-bottom vial (6 cm) with acetone (2 ml). Dried aliquots were used to measure the dose using the fine-grained polymineral method. Fine grain polymineral fractions were extracted from both brick samples.

Polymineral grains larger than 11 μm (settled before 1.5 min in acetone medium) were oven dried and sieved to obtain a 90–150 μm portion. The heavy mineral fraction was extracted from this sieved portion using Franz Magnetic Laboratory Separator (LB 1) at 0.5 Ampere current, and subsequently, quartz and bulk feldspar fractions were separated at 1.5 Ampere with a typical flow rate of 2–3 g.min⁻¹, tilt of 17° and slope of 25° (Porat, 2006). Quartz grains were etched using 40% hydrofluoric acid (HF) for 80 min to remove the outer 20–25 μm layer, allowing the ambient alpha dose rate to be ignored in further calculations. These etched quartz grains were treated with 40% HCl for 30 min to remove any spurious luminescent fluoride precipitates and then wet sieved to remove any < 90μm quartz. The oven-dried quartz grains were mounted as a monolayer on silicone-oiled stainless steel (SS) discs, which were used as aliquots (medium size; 3 mm) to measure the dose using the coarse quartz grain method. Only coarse quartz grains for the sample from the middle of the river (ABL) were sufficiently available for measurements. The purity of quartz was checked by measuring the IRSL of the quartz samples and calculating the IR percentage depletion ratio (IRpDR; Ali et al., 2022).

K-feldspar grains (floating grains) were separated from the bulk feldspar fraction (separated using a magnetic separator at 1.5 Ampere) using sodium polytungstate of density 2.58 g/cm⁻³. The K-feldspar grains were then etched using diluted (10%) HF for 80 min, followed by concentrated HCl for 30 min, for reasons similar to the treatment of quartz. Grains sized <90 μm were wet-sieved, and >90 μm were oven-dried. Medium-sized SS aliquots were prepared with the K-feldspar grains and used for dose measurements, applying the coarse K-feldspar grain method. Coarse K-feldspar grains were sufficiently available in the ABL sample only. Overall, the ABL sample was measured using fine-grained polyminerals (ABL PM), coarse-grained quartz (ABL Qz), and K-feldspar (ABL KF), whereas only fine-grained polyminerals (ABR PM) were measured for the ABR.

The light-exposed parts of the samples were crushed using a Retsch disc mill (RS-200) and used to measure the concentrations of uranium, thorium, potassium, and major oxides in these samples.

The dose rate was computed by measuring the concentrations of uranium, thorium, and potassium using a high-purity Ge gamma spectrometer calibrated using the NUSSY standard (Preusser and Kasper, 2001). The crushed samples were stored in airtight plastic boxes for a minimum of 20 days to allow ²²²Rn (half-life = 3.82 days), a radioactive daughter in the ²³⁸U decay series, to reach secular equilibrium with its immediate parent, ²²⁶Ra. This equilibrium is necessary because crushing the samples caused radon, a gas, to escape, disrupting the secular equilibrium. The gamma spectra of NUSSY and the background were obtained over a counting time of 4 days. The samples and subsequent background were obtained after counting for 7–8 and 12 h, respectively. The concentrations of uranium, thorium, and potassium were determined by comparing the background-subtracted NUSSY and sample spectra. Assuming secular equilibrium between the radioactive daughters and parents in the uranium and thorium series, the concentrations of uranium and thorium were calculated by averaging the concentrations of their respective radioactive daughter elements (²²⁶Ra, ²¹⁴Pb, and ²¹⁴Bi for the uranium series and ²¹²Pb, ²²⁸Ac, and ²⁰⁸Tl for the thorium series) in the samples (Singh et al., 2024). The alpha efficiency (a-value) for the fine grain polymineral was assumed to be 0.08 ± 0.04 (no unit) for dose rate calculation (Kreutzer et al., 2014). The concentration of internal potassium (K_int) was assumed to be 12.5 ± 0.5% (Huntley and Baril, 1997). For quartz, the attenuation factors of Brennan et al. (1991) and Guerin et al. (2012) were used for alpha and beta particles, respectively. For K-feldspar, they were from Bell (1980) and Mejdahl (1979) for alpha and beta particles, respectively. The conversion factors of Adamiec and Aitken (1998) were applied. The water content of ABL was measured to be 0.97%. Assuming the bricks, at least ABL, were in the water most of the time, the water content was assumed to be 5 ± 2%. Considering the thickness of the structure (Figure 3), the gamma dose rate does not need any geometric correction. As the brick was taken from one layer below the multi-layered brick structure of the size of 2–3 m³ and considering the effective water column variation with time, 30 cm was considered as depth of the sample below the surface for dose rate computation. The cosmic ray dose rate was computed using the latitude, longitude, altitude, and depth of the samples (Prescott and Hutton, 1994). Finally, the dose rate was calculated using DRAC, a freely available online calculator (Durcan et al., 2015).

All luminescence measurements and beta irradiation were performed using a Risoe TL/OSL Reader TA-20 (Lapp et al., 2015). A calibrated beta source (⁹⁰Sr/⁹⁰Y) was used to irradiate the samples. The dose rates were 0.089 Gy.s⁻¹ and 0.062 Gy.s⁻¹ for the SS and Al discs, respectively at BSIP, and 0.045 Gy.s⁻¹ for the SS discs at the Physical Research Laboratory, Ahmedabad (PRL). Infrared-stimulated luminescence (IRSL) signal was used to estimate the dose of the fine-grained polymineral and coarse K-feldspar grains, whereas blue stimulated luminescence (OSL) signal was used for the coarse quartz grains.

The IRSL_{50°C; 200°C} and IRSL_{50°C; 250°C} (the first subscripted value indicates the stimulation temperature and the second one indicates the preheat temperature) were measured respectively from a preheated polymineral (to 200°C) or K-feldspar (to 250°C) sample by stimulating with infrared (IR) photons (850 ± 40 nm) at 50°C. Thus, IR stimulated signals were detected in the violet-blue range using combined BG-39 and Corning 7–59 filters in front of the photo-multiplier tube (PMT; PDM 9107Q-AP-TTL-03). Preheat plateau tests (from 175 to 275°C at 25°C interval) and dose recovery tests were done to check the efficiency of the dose measurement protocol.

The post IR IRSL was also measured from the coarse K-feldspar grains, but the measurement of this signal was not possible for the fine polymineral grains due to our laboratory specific logistic reasons. The pIR IRSL_{290°C; 320°C} signal was measured after a IRSL (IRSL_{50°C; 320°C}) measurement on a preheated K-feldspar (to 320°C) sample by stimulating with IR photons and detecting photons in the violet-blue range. This was done in PRL. A dose recovery test was carried out on this signal as well.

The OSL signal was measured on the quartz sample by stimulating with blue photons (470 ± 20 nm) at 125°C, and detecting UV photons using a Hoya U-340 filter of 7.5 mm size in front of the same PMT. A preheat plateau test (from 180 to 260°C at 20°C interval) was carried out to optimize the preheating temperature and a dose recovery test was done as well. As the sample was a heated material, the preheat plateau tests were carried out on the fresh aliquots with natural dose in them and three aliquots were used per preheat temperature. However, due to the unavailability of samples, 6 of already used aliquots were used for the dose recovery tests by recovering a known dose of 1.2 Gy.

A single-aliquot regenerative (SAR) dose protocol was used to estimate the equivalent dose (D_e; Gy) for all three types of samples (Murray and Roberts, 1998; Murray and Wintle, 2000). The dose response curve (DRC) was constructed using sensitivity-corrected IRSL (PM and KF) or OSL (Quartz) for five laboratory doses, including three increasing doses with one repetition and one zero dose. Aliquots were accepted for D_e estimation if they had a recycling ratio within 10% of unity, a relative test dose error within 10%, and recuperation within 5%. The fading-uncorrected D_e was estimated by interpolating the natural IRSL (L_n/T_n) onto the DRC.

The IRSL signal fades over time (Wintle, 1973; Visocekas et al., 1994) and occasionally does the quartz OSL as well (Tsukamoto et al., 2007), so this fading needs to be corrected. The fading rate of the IRSL (from fine-grained polymineral), IRSL_{50°C; 320°C} and pIR IRSL_{290°C; 320°C} (from coarse-grained K-feldspar) and OSL (from coarse-grained quartz) were measured using the single-aliquot regenerative-dose protocol (Auclair et al., 2003) and the fading rate parameter, ρ′–a dimensionless number—was obtained by fitting the data using the fading equation of Huntley (2006). Fading was corrected using the Huntley and Kars Method (Huntley, 2006; Kars et al., 2008). In this method, each point (L_x/T_x) in the DRC used for D_e estimation was corrected for fading that occurred during the respective irradiation times (in minutes at 0.062–0.089 Gy.s⁻¹ in BSIP, and at 0.045 Gy.s⁻¹ in PRL) of the laboratory dose using ρ′. This corrected DRC is called the unfaded DRC. Each data point of the unfaded DRC was further adjusted to account for fading that would have occurred if the laboratory dose had been administered at a natural dose rate (in thousands of years at 4–6 Gy.ka⁻¹), resulting in what was called the natural DRC. The fading-corrected D_e was calculated by interpolating L_n/T_n onto the natural DRC (Morthekai et al., 2011; Biswas et al., 2013; Singh et al., 2023). The representative D_e for age calculation was optimized using the central age model (CAM; Singh et al., 2023). Error in the fading corrected age was calculated by error propagation (quadrature addition of fractional errors of D_e and dose rate) and an added component. The added component was the increase in the error between the fading corrected and un-corrected age as obtained from the Luminescence package of R using calc_Huntley2006() and calc_CentralDose() methods sequentially (Kreutzer et al., 2018; R Core Team, 2020).

The ages were synthesized using two methods. The first method was based on conventional statistical methods. The equations provided below were used to calculate the mean and standard deviation of the synthesized age, and from these values, the age range was established.

and

where μ and σ are the mean and standard deviation of two given ages of a and b, respectively. Likewise any number of ages can be subsequently added, and the order of the ages to be combined does not matter. The second method involves modeling within a Bayesian framework. ChronoModel v2.0 18, a free software for hierarchical Bayesian modeling, was used to synthesize the ages (Banks, 2015; Binder et al., 2017; Lanos and Philippe, 2017; Lanos and Dufresne, 2019). The requirement for synthesis is that the ages must be independent to some extent. The structure was created within the age uncertainties at a particular time, representing the Event (only one) here. The posterior age estimates and variances were verified by checking the convergence of Markov chains to equilibrium (History plots) and the correlation between successive values in the Markov chain (Autocorrelation). All calculations were conducted in calendar years, with the reference year being 2019 CE.

The X-ray diffraction spectra were measured on the extracted quartz and K-feldspar grains to study the phase of quartz (whether it is α- or β-quartz) and K-feldspar. The powder X-ray diffraction patterns were measured on a Rigaku instrument (MiniFlex 600) having Cu-target that emits wavelength of 1.54060 Å (Sharma et al., 2024). The scan speed was 0.01°/s over a 2θ range of 10 to 80°. The pXRD patterns were analyzed using Crystal Impact Match software (https://www.crystalimpact.de/match/), and the mineralogical compositions were quantified.

The major oxides were measured using XRF to determine the geochemical compositions of the samples. The samples were initially ground to ~200 μm mesh using a Retsch Disc mill (RS-200). The powdered samples were oven-dried (~100°C for 12 h) and pressed into pellets (Stork et al., 1987; Khanna et al., 2009). The analysis was performed using the Wavelength Dispersive X-Ray Fluorescence (WD-XRF) model: Axios max, 4 KW, PANalytical made at BSIP, Lucknow. The precision and accuracy of sample preparation and instrumental performance were checked using international reference standards for sediments (e.g., COQ-1, BCR-2, SGR-1b, Sco-1, JSP-2, RGM-2, and DGH). The accuracy of measurement was better than 2–5%, and the precision was <2%.

The measured concentrations of uranium, thorium, and potassium, computed dose rates, and D_e are listed in Table 1. Coarse grains received 56% dose rate from beta particles and 39% from gamma rays whereas fine grains, in addition to these, also received around 20% of the dose rate from alpha particles (Supplementary Table S1). The high thorium concentration in the sample might be due to the presence of monazite and sillimanite in the nearby beach sands of this region (Lakshmi et al., 2019; Abishek et al., 2022).

Quartz was not contaminated by IRSL signals, as inferred from IRpDR values of <2% (Supplementary Figure S1). A D_e-plateau was observed between the preheating temperatures of 220–260°C for coarse quartz grains (Figure 4A), and hence 240°C was selected for further D_e analyses and age calculation. For the IRSL_50°C signal of the coarse grain K-feldspar, no D_e-plateau was observed for the preheat temperature range of 175–275°C (Figure 4B). This is contrary to what has been observed by Murray et al. (2009). However, such an increase with the preheat temperature was observed on polymineral fine grains by Zhang et al. (2015). For their sample, Zhang et al. also observed a decreasing fading rate with increasing preheat temperature, and consequently, a fading-corrected age plateau was observed in the range of 180–320°C. The dose recovery tests using coarse quartz and K-feldspar grains (using IRSL_{50°C; 200°C}, pIR IRSL_{50°C; 320°C} and pIR IRSL_{290°C; 320°C}) recovered the laboratory administered dose (1.2 Gy) within 10% (Figure 4C).

Both the measured ages (Age) and fading corrected ages (Age_fc) are provided along with the respective fading parameter, ρ′ (Table 1). The measured dose response curves (DRC) were standardized and given in Figure 5A. The DRC of ABR PM was not shown in this figure, but it was indistinguishable from that of ABL PM. Till around 1.5 Gy, all the signals grow indistinguishably with dose, and both IRSL_{50°C; 320°C} and pIR IRSL_{290°C; 320°C} from K-feldspar slightly deviates after that dose (Figure 5A). The observed fading rate in both samples was high, particularly for the K-feldspar samples (Figure 5B, Table 1). The commonly known fading rate parameter, g-value (directly proportional to ρ′) for t_c = 1 h (Huntley and Lamothe, 2001) varied from 9.6 ± 0.2%·decade⁻¹ (APL PM, IRSL_{50°C; 200°C}) to 15.5 ± 0.2%·decade⁻¹ (ABL KF, IRSL_{50°C; 250°C}) with an intermediate value of 10.4 ± 0.2%·decade⁻¹ for ABR PM using IRSL_{50°C; 200°C}. Interestingly, the supposedly stable signals such as pIR IRSL_{290°C; 320°C} of K-feldspar and OSL of quartz exhibited fading at a rate of 3.4 ± 0.2%.decade⁻¹ and 3.1 ± 1.3%.decade⁻¹, respectively. Such high fading rates resulted in fading corrected ages that were more than 2.5 times the measured fine grain polymineral ages (Supplementary Figures S2A, B, S3A, B) and ~4.5 times the measured age for the coarse grain K-feldspar (Figure 6A, Table 1, Supplementary Figure S3D). High values of fading rate of IRSL signals both from polymineral and K-feldspar, and fading of otherwise stable quartz OSL signal as if it were a volcanic quartz (Tsukamoto et al., 2007), demand explanation. The pXRD pattern of coarse grain K-feldspar revealed the presence of ~46% sanidine in it (Figure 7, Supplementary Figure S4A), which is a high temperature and hence disordered K-feldspar phase whose luminescence fades rapidly (Li et al., 2016). However, the pXRD pattern of quartz grains revealed that no presence of β-quartz (phase transition after heating beyond 574.3°C) was observed (Figure 7, Supplementary Figure S4B).

The IRSL signals measured after preheating to 320°C i.e., pIR IRSL_{290°C; 320°C} and IRSL_{50°C; 320°C} from the K-feldspar grains of ABL yielded fading corrected ages of 520 ± 20 years and 590 ± 40 years, respectively (Figures 6C, B, Table 1). Both these ages are not significantly different from the fading corrected age of IRSL_{50°C; 250°C} of ABL KF i.e., 520 ± 40 years, and thus validates the fading correction procedure despite large values of fading rate (Table 1). As the bricks had been heated with a variable temperature range of 500 to 1,000°C while baking in the kiln (Krishnan and Hegde, 1988), the unbleachable luminescence signal would be near to nil and hence the age using pIR IRSL_{290°C; 320°C} might be correct. Thus, the consistency of three corrected ages obtained by different signals (fading corrected ages being 1.4 times, 2.9 times, and 4.5 times the measured age for pIR IRSL_{290°C; 320°C}, IRSL_{50°C; 320°C} and IRSL_{50°C; 250°C}, respectively; Supplementary Figures S3D–F) increases the reliability of the age of ABL.

The ages of both fine grain polymineral (320 ± 30 years) and coarse grain quartz (330 ± 10 years; Figure 6D, Table 1) were significantly younger compared to the coarse grain K-feldspar ages (Table 1). A similar age (385 ± 90 years) of ABR (using IRSL_{50°C; 200°C}) as to that of ABL using both quartz OSL and polymineral fine grain (IRSL_{50°C; 200°C}) warrants our attention. There must be a systematic offset that caused underestimation, and that needs to be addressed. Probably the pIR IRSL_{290°C; 320°C} measurement on fine grain polymineral samples will help, and it is a future endeavor as there is no sample now left. Regarding quartz age, there is one report where almost 50% underestimation of quartz ages (fine grain) was observed, compared to the polymineral ages, and there is no conclusive reason for this unusual behavior (Perić et al., 2021). In that study, the possible reasons were the thermal and a-thermal (anomalous fading) instability, difference in the natural and laboratory growth curves (Perić et al., 2021). If these ages (of quartz and fine grain polymineral; around 340 years) were correct, then adequate reasons are to be sought to discard the ages of coarse grain K-feldspar of around 540 years, which would be even more difficult. Until further investigation shows the ages of fine grain polymineral and coarse grain quartz are correct, these ages are not included in the final calculation.

So, excluding coarse-grain quartz ages of ABL and both the fine grain polymineral ages of ABL and ABR, all the ages of coarse grain K-feldspar of ABL were synthesized to one age using: a) conventional statistical method (1456–1522 CE); and b) ChronoModel (1427–1534 CE). These age ranges are within 95% confidence (Supplementary Figure S5, Table 1). It should be noticed that the assumption of independent ages necessary to apply ChronoModel is not strictly true here since the three ages were calculated with the same dose rate.

Similar ages, however lower due to a systematic error in the D_e measurement protocol, for the bricks collected from the structures found both at the right side (ABR; 385 ± 90 years) and the middle of the river (ABL; 320 ± 30 years) using fine grain polymineral (fading corrected), suggest that both the structures were most probably contemporaneous. This, in turn, implies that these two structures were constructed at the same time, thereby excluding the possibility of reworking by rivers from elsewhere. The similar geochemical composition (Table 2, Figure 8) of the bricks from both locations further supports the inference that these structures were not reworked from elsewhere but were likely parts of a single structure. Had both the bricks (ABL and ABR) been made from different places and came to the present location by reworking, the geochemical compositions of the mud most probably would be different unless they were brought from shorter distance. Thus, the contemporaneity of the studied two bricks and their similar geochemical composition and moderately weathered nature of the constituting mud suggest these bricks are part of a single structure.