A zircon classification scheme for sedimentary provenance analysis using radiation damage

Detrital single‐grain zircon U–Pb geochronology is a powerful tool for provenance studies if information on the source rocks is available. This paper proposes a new source‐rock classification tool that uses the degree of annealing of radiation damage in detrital zircon; the annealing is expressed by the relationship between the width (full‐width at half‐maximum; FWHM) of the v3[SiO4] Raman band at ~1008 cm−1 and the calculated α‐dose. The host rocks of the zircons are classified into three types according to their emplacement process and/or thermal history: volcanic and rapidly cooled plutonic and high‐grade metamorphic rocks (type 1); rocks with hydrothermal zircons (type 2); slowly cooled igneous and metamorphic rocks (type 3). We construct a naive Bayes prediction model by training it with a collection of zircons of known types. The unknown zircons are assigned a probability of derivation from a specific host‐rock type. This classification scheme is best used as an accessory tool in provenance studies that apply detrital zircon U–Pb geochronology.


| INTRODUCTION
Detrital zircon U-Pb dating is frequently used in sediment provenance analysis because of the resistance of zircon to weathering, transport, and metamorphism (Balan et al., 2001;Feng et al., 2021;Spencer et al., 2016;Zimmermann et al., 2018). The interpretative power of provenance studies greatly depends on the comparison with the age signature of the potential source rocks. If the zircons yield broad and partially overlapping age spectra or underwent multi-stage recycling, this method is ineffective or may lead to misleading interpretations (Anderson et al., 2016;Azdimousa et al., 2019;Gehrels, 2014). Uncertainty also arises from zircon fertility; zircon-rich rocks provide an amplified age signal, while the signal from zircon-poor rocks is suppressed (e.g., Zimmermann et al., 2015).
Extracting other information from single zircons and identifying their host-rock lithologies is a possible solution (Harley et al., 2007).
Owing to the α-decay of U and Th, the zircon crystal lattice is increasingly damaged up to an amorphous state (Chakoumakos et al., 1987;Holland & Gottfried, 1955). The crystalline structure is restored by annealing at high temperatures (e.g., Ende et al., 2021;Geisler, 2002;Geisler et al., 2001;Ginster et al., 2019;Zhang et al., 2000). The accumulated radiation damage in a zircon is a function of the U and Th concentrations, time, and the thermal history (Nasdala et al., 1998(Nasdala et al., , 2001. In general, rocks exposed at the Earth's surface show thermal histories that depend on their emplacement and exhumation. The thermal history can-at least in part-be reconstructed in zircon by the degree of radiation damage (e.g., Bjerga et al., 2022;Marsellos & Garver, 2010). Thus, the petrogenetic information derived from the zircon radiation damage can enhance the database used for provenance studies and support their interpretation. This study developed a classification scheme based on zircon radiation damage density, which assigns probabilities to it being the result of rapid or slow cooling histories. To test the effect of our classification, we re-analysed detrital zircon data from Lower Cretaceous sandstones in South Africa and compared the results with the original study.

| v 3 [SiO 4 ] Raman-band vs. α-dose classifier
The classifier is based on the measured radiation damage of a zircon and the α-dose it accumulated over its lifetime. The recorded damage depends on the zircon's crystallization age and its thermal history (Härtel, Jonckheere, Wauschkuhn, Hofmann, et al., 2021).
Radiation damage can be quantified by the full-width at halfmaximum (FWHM) of the v 3 [SiO 4 ] Raman band (Nasdala et al., 1998(Nasdala et al., , 2001. The accumulated α-dose can be calculated based on the U and Th contents and the age of the zircon (e.g., Holland & Gottfried, 1955;Murakami et al., 1991;Nasdala et al., 2001). The empirical relationship between the α-dose and FWHM is given by Váczi and Váczi and Nasdala (2017) as: where D α is the calculated α-dose. This equation gives the FWHM in case of lacking lattice repair by annealing.
When a rock is rapidly exhumed to the Earth's surface after crystallization ( Figure 1, Route I), little annealing occurs and α-damage in zircon is retained; zircons from such rocks cluster along an empirically-determined exponential line, which traces the Radiation-Damage Accumulation Path in a graph of α-dose versus FWHM ( Figure 2a). In nature, rapidly cooled rocks are volcanics and small-volume plutonic rocks that were emplaced in the upper (cold) crust. Such rocks cool so rapidly that nearly all radiation damage is preserved within the zircons. We classify such rocks as type 1 (Table 1).
In many high-grade metamorphic rocks, zircons recrystallize and thus experience a reset of the U-Pb isotopic system. Such zircons undergo a complete repair of radiation damage and only accumulate new damage after cooling through the temperature range in which annealing occurs (see below ;. When these high-grade metamorphic rocks are rapidly exhumed through this radiation-damage annealing zone, the high cooling rate prevents significant annealing. We classify such rocks as type 1 as well (Table 1); they also plot along the Radiation-Damage Accumulation Path ( Figure 2a). In our training data set (see below), zircons from the Bohemian-Massif granulites (Sláma et al., 2008;Tichomirowa et al., 2005) represent such type 1 highgrade metamorphic host rocks ( Figure 2a). These granulites exhumed at a rate of $4 km/Ma and cooled at $20-50 C/Ma (Kotková, 2007).
Damage annealing in zircon occurs at temperatures higher than 230-370 C (e.g., Pidgeon, 2014) and restores its crystallinity. In nature, zircon annealing is related to: (1) slow cooling that follows crystal formation (Figure 1, Route II) with prolonged retention at elevated temperatures (e.g., Pidgeon, 2014), such as it is the case in large-volume granitoid bodies intruding into the middle and lower crust; and (2) reheating to elevated temperatures over geological time in the course of low-to medium-grade metamorphism (Figure 1, Route III). Greenschist-to amphibolite-facies metamorphism involves temperatures between 300 and 650 C (e.g., Willner et al., 2018). In this case, annealing reduces the FWHM, depending on the temperature-time conditions of the rock (Marsellos & Garver, 2010).
Zircons that underwent annealing because of slow exhumation/ F I G U R E 1 Schematic diagram showing the different emplacement routes of rocks and the temperature range of zircon crystallization and annealing. Route I: rocks cooling at high rates (e.g., volcanic rocks) rapidly pass through the temperature range of zircon crystallization and radiation-damage annealing (Härtel, Jonckheere, Wauschkuhn, Hofmann, et al., 2021;Pidgeon, 2014). Route II: rocks being slowly exhumed reside a prolonged time in the temperature range between zircon crystallization and annealing, e.g., rocks of a granitic batholith. Route III: rocks undergo low-to medium-grade metamorphism in the temperature range between zircon crystallization and annealing, before being exhumed to the surface (e.g., greenschist-facies rocks). This study classifies the rocks of Route I as type 1 and the rocks of Route II and III as type 3.
cooling or reheating thus plot below the Radiation-Damage Accumulation Path; such thermal histories (type 3) are typical for granitic batholiths and medium-and low-grade metamorphic rocks ( Figure 2b).
Hydrothermal zircons (type 2) generally deviate from the accumulation trend at a very low α-dose ( Figure 2b). This means that the damage inferred from the FWHM exceeds the theoretical damage ascribed to a maximal possible radioactive α-dose. The high FWHM is because of significant band asymmetry, likely resulting from substitution-related strain and disorder (Kempe et al., 2018). The band asymmetry is alternatively explained by damage heterogeneity within a single analysis spot because of a contrasting distribution of actinide elements in zircons (Härtel et al., 2022;Nasdala et al., 2005). The very low α-dose of hydrothermal zircons is related to the low concentrations of Th and U compared with most magmatic zircons, because such zircons experience migration of U and Th because of fluid activity (Schaltegger, 2007;Tichomirowa et al., 2005).
F I G U R E 2 Plots of α-dose versus full-width at half-maximum (FWHM) for zircons of different rock types. The lossless radiation-damage accumulation path refers to equation (2) in Váczi and Nasdala (2017) that assumes FWHM = 1.8 cm À1 at zero α-dose based on synthetic zircon. (a) Zircons of type 1 rocks follow closely the radiation-damage accumulation path. (b) Zircons of type 2 (hydrothermal zircons) and type 3 are offset from the radiation-damage accumulation path. References for the plotted data are listed in Appendix S1. Red dashed arrows define the Radiation Damage Deviation and Radiation Path Length that are the two parameters characterizing the differences between zircons.
T A B L E 1 List of major types of zircon source rocks and the number of grains. We also included new data from (1)  Olympus objective with a 0.5 numerical aperture. The lateral resolution was $1.5 μm and the depth resolution was $2 μm. Raman peakposition calibration was verified regularly with the $520.7 cm À1 band of a polished silicon wafer before the measurement. We used a highresolution grating (1800 g mm À1 ) and a narrow slit (50 μm) for peakresolution increase. The proximate spectral resolution is $0.8 cm À1 .
Raman bands were fitted using the Voigt function of the Origin ®  (Figure 2b). Here, we do not directly use the FWHM value to quantify the degree of annealing, because the annealing process causes the FWHM value (i.e., y-axis) to gradually decrease with the accumulation of the α-dose (i.e., x-axis in Figure 2), which is a curve that has a smaller radius of curvature than the Radiation Damage Accumulation Path. The advantage of using the proposed two parameters, rather than the FWHM (i.e., y-value) and α-dose (i.e., xvalue), is that they approximate the real annealing path while maximizing the annealing difference between each zircon. All training zircons were computed in the form of the Radiation Path Length and Radiation Damage Deviation to obtain the mean value and variance for each zircon type (types 1-3, see above). Then, the unknown zircons were compared with the mathematical means of the types 1-3 to get the relative distances to each zircon type; the closer the distance the higher the likelihood that an unknown zircon belongs to a certain zircon type and thus gives a higher probability value. Kernel density statistics shows that type 1 and type 2 rocks can be better discriminated by the Radiation Damage Deviation, whereas type 3 slightly overlaps with type 1 (Figure 3). The slight overlap is because of the existence of zircons of low α-dose and low FWHM values (Figure 2b).
Bayes theory is of great importance to the processing of prior information so as to form a prior distribution for statistical inference (Blanquero et al., 2021;Kim et al., 2020). The prior distribution reflects the proportion of each zircon type (i.e., prior probability), and in our case, the prior probabilities can be viewed as the potential proportions of each zircon type derived from a specific source area. The Bayes algorithm gives a posterior probability to the unknown zircons, assuming that each type of zircon has equal chance to occur; the final F I G U R E 3 Histograms and Kernel density estimates of zircons of types 1-3 based on the Radiation Damage Deviation parameter. The overlap between type 1 and type 3 is partly related to low α-dose zircons (particularly the metagabbro in Figure 2) that lead to a potential classification error.
probability is obtained through a weighted calculation by the prior value. The prior probabilities act as a perturbation to intervene the final probability. This study uses the frequency of training zircons as the prior probability, and we also recommend a global prior probability, which refers to the proportions of global lithologies and zircon fertility, that is, the abundance of zircons in different rocks (Dürr et al., 2005, Appendix S2). Users can assign their own values of prior probability according to the lithologic proportions when studying a particular geological area.

| Model construction and validation test
The model construction uses the package "Naive Bayes" for MATLAB (MathWorks version 2016); details about the codes are in Appendix S4. The classifier gives posterior and prior weighted probability estimates of a zircon belonging to a certain rock type. Table 2 shows the confusion matrices. Most errors come from type 3 zircons; some are misclassified as type 1. The 10-fold cross-validation tests suggest a 95% confidence for a correct classification when removing inherited zircons from the type 1 class and low-damage zircon from the type 3 class (Appendix S2, details in the next section).
We used a published provenance study, investigating Lower Cretaceous sandstones from South Africa ( Type 1  Type 2  Type 3  Type 1  Type 2  Type 3  Type 1  Type 2  Type 3   Trained zircon type   Type 1  226  4  7  227  1  9  220  1  16   Type 2  1  15  0  1  15  0  1  15  0   Type 3  42  0  188  43  0  187  34  0  196 a Posterior probability is calculated assuming that each zircon type has equal weight. b Calculated according to prior probabilities of the frequency of training zircons and the global prior estimates, respectively. for zircon with complex structures (e.g., core-rim structures). Although these complex structures also cause classification bias, such zircon is relatively rare in sedimentary rocks. The proposed classification scheme is mainly for zircon with simple structure that accounts for the majority in sedimentary rocks.

| Influence of priors
The confusion matrices and the visual diagrams show the classification effect and the influence of the prior probability (Table 2,

| Instruction of use
One should be cautious with low α-dose zircons (<0.46 Â 10 15 α/mg). In the legend, the zircon types before and after the dash (À) are the true types and the incorrect identifications, respectively. The red dotted box encloses the low-damage zircons (FWHM <8 cm À1 , α-dose <0.46 Â 10 15 α/mg, Ginster et al., 2019), for example, the metagabbro-derived grains that are a major source of classification error. Another error source are the outliers in the training set (e.g., from ignimbrites and rhyodacites), which lie off the accumulation path and are assigned to type 3. Table 2  particularly for hydrothermal zircon, for which the published database is limited. It is conceivable that some hydrothermal zircon may be misidentified as type 1 (e.g., volcanic zircon) or type 3 (e.g., zircon from slowly cooled granitoids). We suggest that additional information (e.g., zircon textures, trace elements) shall be taken into account when using the classifier in the current version to identify hydrothermal zircon. The classifier can be improved by continually adding more known types of zircon from around the globe and/or training known types of zircon from user research areas.
Priors are only helpful to distinguish zircon types when the posterior probabilities are close to 0.5. Users can set their own prior probabilities for a particular area and a specific era. Suggestions for setting prior probabilities are: (i) use of age spectra from detrital zircons, because a particular age peak usually represents a distinct geological event or a combination of several similar-aged geological events. For example, the zircons of the $120 Ma peak in the South Africa dataset represent the rift-related magmatism and zircons of the $560 Ma peak represent the magmatic and metamorphic events of the Zambezi orogenic belt (Kuribara et al., 2019); (ii) considering petrographic information of clastic rocks; this provides the most direct constraints for priors.

| CONCLUSIONS
Radiation damage in zircon caused by α-decay of U and Th accumulates following crystallization and is repaired at elevated temperatures. This study assumes that the degree of radiation damage in zircons is genetically related to the thermal history of their host rocks. Volcanic extrusions and granitic intrusions usually have contrasting cooling rates and thermal overprints usually occur because of metamorphism. These assumptions are the theoretical basis for distinguishing zircon types in sedimentary rocks by their degree of radiation damage. This study develops a classification scheme using the α-dose versus damage FWHM diagram and divides natural zircons into three types: (1) rapidly cooled, (2) hydrothermal, and (3)