All dating work was undertaken at the BIOMICS laboratory in the Geoarchaeology and Archaeometry Research Group (GARG) of Southern Cross University (Lismore, New South Wales, Australia). U-series measurements were obtained using an ESI NW193 ArF excimer laser ablation unit coupled to a MC-ICPMS ThermoFishers Neptune XT. Each sample was measured by a succession of parallel rasters across the exposed polished cross-section (geochemical imaging), allowing us to reconstruct an isotopic map of the precipitated calcite, or by successive parallel rasters along the concretion formation of the sample. Imaging rasters had different lengths to adapt to the irregular shape of the sample using the following parameters for mapping: a square spot size of 44 μm × 44 μm using the infinite aperture of the laser system matched by a translation speed of 21 μm s−1 and integration time of 2.097 s on the MC-ICPMS Neptune XT. This combination of parameters allowed us to obtain within <0.1% a pixel on the map equivalent to a 44 μm × 44 μm data point (the exact translation speed to obtain an exact data-pixel of 44 μm × 44 μm would be 20.982 μm s−1).
On non-mapped samples, individual rasters had systematically the same length within the same sample around about 700 μm following parameters for mapping: a square spot size of 110 μm × 110 μm using the infinite aperture of the laser system with a translation speed of 5 μm s−1 and integration time of 4.194 s on the MC-ICPMS Neptune XT.
Other parameters for the data acquisition were as follows: 900 ml min−1 UHP He and 6 ml min−1 UHP nitrogen for the gas flow from the chamber to the ICPMSs, rep rate of 100 Hz for the laser frequency and an average of 1.92 J cm−2 sample fluence. 234U and 230Th were measured simultaneously, with uranium in the centre Faraday cup coupled with a secondary electron multiplier (SEM) and thorium on the L3 Faraday cup coupled to an ion counter (IC). All other Faraday cups were set to using high-gain 1011 Ω amplifiers. The cup configuration was as follows: L3/IC(230), L2(232), L1(233), C/SEM(234), H1(235), H2(236) and H3(238). Baseline and drifts were corrected using NIST 610 and NIST 612 glass standards, whereas two corals (the MIS7 Faviid and MIS5 Porites corals from the Southern Cook Islands)37 were used to correct 234U/238U and 230Th/238U ratios and assess the accuracy of measurements.
Image and data processing
Isotopic mapping obtained by LA-MC-ICP-MS data was extracted using the Iolite 4 software package38. The data were accumulated in a single file on the MC-ICPMS Neptune XT as follows: 5 min background, NIST610 (3×), NIST612 (3×), STD1 (3×), STD2 (3×), sample rasters (n×), STD2 (3×), STD1 (3×), NIST612 (3×), NIST610 (3×) and 5 min background. For sample imaging sequences longer than 2 h, a set of standards (for example, STD1 (3×) and STD2 (3×)) was incorporated in the middle of the measurement. Data reduction used NISTs to assess drift and the 5-min background on each side of the measurements for baseline. One standard (MK10) was used for correction of the isotopic ratios, whereas the other one (MK16) was used as known values to check data accuracy (including for matrix effect). The images were produced using a spectrum gradient colour distribution, with either linear or logarithmic scale (specified for each sample on the isotopic maps). Regions of integration (ROIs) were carefully selected on the 232Th/238U and 230Th/238U isotopic ratio maps and Uppm maps to be as close to the paint layer as possible, while avoiding diagenetic zones. Data errors were extracted and reported at 2 standard error. ROIs located immediately above the pigment layers were selected for calculating the minimum ages relating to the underlying paintings. U-series data were integrated for individual ROIs, resulting in U-series ages and associated errors. Sufficient data points were also selected to minimize the errors. The integration area of each ROI is reported in μm2 (Supplementary Table 1).
Raster measurement
The data were accumulated in a single file on the MC-ICPMS Neptune XT as follows: 5 min background, NIST610 (3×), NIST612 (3×), STD1 (3×), STD2 (3×), sample rasters (n×), STD2 (3×), STD1 (3×), NIST612 (3×), NIST610 (3×) and 5 min background. For sample imaging sequences or several raster measurements in the row longer than 2 h, a set of standards (for example, STD1 (3×) and STD2 (3×)) was incorporated in-between samples. Data reduction used NISTs to assess drift and the 5-min background on each side of the measurements for baseline. One standard (MK10) was used for the correction of the isotopic ratios, and the other (MK16) was used as known values to check data accuracy (including for matrix effect). Rasters are placed starting as close as the paint layer and spaced uniformly along the axis perpendicular to the first raster. Yet, to avoid an obvious diagenetic zone, the position of the raster in certain circumstances may have been adjusted (Extended Data Figs. 1, 3, 7). U-series data were integrated for each individual raster, resulting in U-series ages and associated errors (Supplementary Table 1).
Tuning procedures were carried out using a NIST 610 glass standard with the following parameters: a 50 µm spot size, translation speed set to 5 µm s−1, and a fluence of >1 J cm−2 at the sample surface. The Multicollector Zoom Optic is optimized to ensure optimal peak shape for 238U in Faraday cup H3, with signal adjustments made to achieve a minimum of 1 V for 238U and maintain a 0.85 ratio factor between 232Th and 238U voltages (Faraday cups L2 and H3, respectively). In the case of the samples analysed in this study, the average measures for 238U exceeded 3 V. Following tuning with NIST 610, fine-tuning was carried out using A MIS7 (MK10) Faviid coral from the southern Cook Islands37, with particular attention to comparing R48 values between the laser and the solution. For geochemical imaging, a spot size of 44 µm with a laser rastering speed of 21 µm s−1 with a 2.097 s integration time was optimal for most circumstances, with the number of blocks varying depending on the measurement sequence. Yet, on average, measurements were conducted with a total block number of about 10, with 200 cycles per block. Individual raster measurements were carried out a spot size of 100 µm with a laser rastering speed of 5 µm s−1 and a 4.194 s integration time.
The MK10 coral standard is also used to correct the 234U/238U and 230Th/238U ratios. Another coral sample, a MSI5 (MK16) Porite coral also from the southern Cook Islands37, is used to independently check the accuracy of the measurements and dating results. Both coral samples were reduced to powder to homogenize their values before being run by solution MC-ICPMS. The remaining homogeneous powder samples were consolidated using a uranium- and thorium-free resin and used as standards for LA-MC-ICPMS. Standards were measured in the following order: 3× NIST610, 3× NIST612, 3× CoralSTD1 and 3× CoralSTD2 at the beginning of each sample and at the end in a mirroring order. The aforementioned list of standards was measured in between each sample with a maximum of 2 h in-between standard sets. We used the same coral-based laser-ablation U–Th calibration approach as in our previous study, in which we demonstrated that laser ablation and solution U-series ages of calcite crusts were indistinguishable within analytical uncertainty, indicating that any matrix effects between coral (aragonite) and calcite are negligible under comparable analytical conditions5.
It is not unusual for secondary calcium carbonate to contain detrital materials such as wind-blown or waterborne sediments, which can contaminate the sample and lead to U-series ages that appear older than they actually are. This occurs because of pre-existing 230Th in the detrital components. As it is impossible to physically separate detrital/initial 230Th from radiogenic 230Th for measurement, corrections are made using an assumed 230Th/232Th activity ratio. Typically, the average continental crust value of 232Th/238U = 3.8 is used for these corrections, with an uncertainty of 100%. The measured 230Th/232Th activity ratio reflects the degree of detrital contamination, with the higher values (>20) indicating a smaller effect on the calculated age, whereas the lower values (<20) suggest a major correction is needed. In samples with a measured 230Th/232Th activity ratio >20, the detrital 230Th accounts for only a small percentage of the total 230Th in the sample.
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