A comprehensive review of the theory and nomenclature of doubly substituted isotopologue geochemistry is detailed in Eiler (2007, 2013), Wang et al. (2004) and Young et al. (2016, 2017). Briefly, doubly substituted isotopologue ratios of CH₄ are reported and parameterized as Δ13CH₃D and Δ12CH₂D₂ values, defined to quantify a measured difference in the isotopologue ratios relative to a random distribution: 1Δ13CH3D=Rsample13CH3DRstochastic13CH3D-1,2Δ12CH2D2=Rsample12CH2D2Rstochastic12CH2D2-1.

Where: Rsample13CH3D and Rsample12CH2D2 are the measured isotopologue ratios of 13CH3D/12CH4 and 12CH2D2/12CH4, respectively, and Rstochastic13CH3D and Rstochastic12CH2D2 are the calculated isotopologue ratios of 13CH3D/12CH4 and 12CH2D2/12CH4, respectively, based on the assumption of a random distribution of isotopes amongst all stable isotopologues.

As an effect, the isotopologue ratio approaches that based on a random distribution under high-temperature equilibrium conditions, which by definition results in Δ13CH₃D or Δ12CH₂D₂ values of zero (e.g., Douglas et al., 2016; Eiler, 2007, 2013; Stolper et al., 2014a; Young, 2019). It should be noted that non-zero values of Δ13CH₃D or Δ12CH₂D₂ can result from the simple mixing of two separate CH₄ pools with distinct bulk isotopic compositions, without any chemical or physical processes inducing isotopic fractionation (e.g., Young et al., 2016).

In this paper, the terms “enriched” and “depleted” refer to comparative values of Δ13CH₃D or Δ12CH₂D₂ – higher numbers as enriched and lower numbers as depleted – for example when comparing samples of CH₄, products and reactants of a chemical reaction, or the evolution of CH₄ in a physical process.

The measurement of Δ13CH₃D and Δ12CH₂D₂ is resource intensive, requiring specialised facilities that are currently not widely available (e.g., Eiler, 2007; Liu et al., 2024b; Ono et al., 2014; Sivan et al., 2024; Stolper et al., 2014a; Young et al., 2017). Magnetic sector High Resolution Isotope Ratio Mass Spectrometry (HR-IRMS) is the most common method to measure Δ13CH₃D and Δ12CH₂D₂ (Dong et al., 2020; Eldridge et al., 2019; Haghnegahdar et al., 2023; Liu et al., 2024b; Sivan et al., 2024; Stolper et al., 2014a; Sun et al., 2023; Thiagarajan et al., 2020; Wang et al., 2023a; Young et al., 2016, 2025; Zhang et al., 2021). The first magnetic sector HR-IRMS instrument developed for this purpose was the non-commercial prototype model of the Thermo Scientific 253 Ultra HR-IRMS (developed and installed solely at the California Institute of Technology) that was able to measure a value of the combined ¹³CH₃D and ¹²CH₂D₂ abundances via a parameter defined as Δ18 (Eiler, 2013; Stolper et al., 2014a, b; Stolper et al., 2015). A large-radius gas-source multiple-collector isotope ratio mass spectrometer capable of operating up to a mass resolving power (MRP) of 80 000 (Panorama, Nu Instrument) was the first developed HR-IRMS to measure separately Δ13CH₃D and Δ12CH₂D₂ (Young et al., 2016, 2017). This was followed by the commercially-available production model of the Thermo Scientific Ultra HR-IRMS that can also measure Δ13CH₃D and Δ12CH₂D₂ and routinely achieves a MRP of 30–35 000 (e.g., Eldridge et al., 2019; Thiagarajan et al., 2020; Zhang et al., 2021; Wang et al. 2023a; Sivan et al., 2024). The obtained MRP allows to achieve precise measurements for sample of > 2 mL STP (standard temperature and pressure) of CH₄ (∼ 80 µmol) for Panorama (e.g., Labidi et al., 2020) and 3 ± 1 mL STP for Ultra (Sivan et al., 2024). Measurements of smaller volume of CH₄ sample result in larger uncertainties caused by degraded counting statistic. The detailed description of the performance of these instruments and measurement protocols for different laboratories can be found in the cited references above.

Distinct from mass spectrometry, measurements of Δ13CH₃D and Δ12CH₂D₂ are also possible owing to developments in infrared absorption spectroscopy using quantum cascade lasers (TILDAS, Aerodyne Research) operated in near room temperature with narrow line widths and high power (Chen et al., 2022; Gonzalez et al., 2019; Ono et al., 2014; Prokhorov and Mohn, 2022; Zhang et al., 2025). The first TILDAS instrument to achieve high precision Δ13CH₃D measurements was demonstrated at the Massachusetts Institute of Technology in 2014 (Ono et al., 2014). Δ13CH₃D measurement by the TILDAS instrument are achieved using the absorption line in a spectral region around 8.6 µm, as there are fewer interferences from hot bands (Ono et al., 2014). Gonzalez et al. (2019) presented a possibility to implement TILDAS to measure Δ12CH₂D₂ with precision of 0.5 ‰. Routinely, TILDAS measurements requires 10 mL of CH₄ for Δ13CH₃D measurements and 20 mL for Δ12CH₂D₂ (e.g., Gonzalez et al., 2019; Ono et al., 2014). Recently, Zhang et al. (2025) were able to reduce the required volume of CH₄ to 3-7 mL STP for Δ13CH₃D and to 10 mL STP for Δ12CH₂D₂, via further instrument optimization.

HR-IRMS signal stability of the detected ions at very low ion currents is key to enable precise isotope ratio measurement through signal acquisition over several hours or even days (e.g., Sivan et al., 2024; Stolper et al., 2014a; Young et al., 2016). Across instrumentation, internal precision and external reproducibility are comparable between laboratories and instruments, achieving down to 0.35 ‰ for Δ13CH₃D and 1.35 ‰ for Δ12CH₂D₂, depending on the measurement technique. The TILDAS and Panorama systems were cross-calibrated on the same set of carbon and hydrogen isotopically characterised laboratory working standards for CH₄ to ensure accuracy between different analytical systems (Ono et al., 2014; Young et al., 2017; Zhang et al., 2025).

At thermodynamic isotopic equilibrium, Δ13CH₃D and Δ12CH₂D₂ values can be linked to a CH₄ formation temperature via monotonic functions, presented in Table S1 in the Supplement (Beaudry et al., 2021; Douglas et al., 2017; Eldridge et al., 2019; Gruen et al., 2018; Liu and Liu, 2016; Ono et al., 2014; Stolper et al., 2014a; Thiagarajan et al., 2020; Webb and Miller, 2014; Young et al., 2017; Zhang et al., 2021). Different theoretical calculations have been used to obtain these relationships but discrepancies among them are smaller than the current analytical uncertainties. Currently, equilibrated gas experiments along with these theoretical calculations are the basis for calibrating Δ13CH₃D and Δ12CH₂D₂ measurements via either magnetic sector HR-IRMS or laser spectroscopy (Eldridge et al., 2019; Liu et al., 2024b; Ono et al., 2014; Sivan et al., 2024; Stolper et al., 2014a; Wang et al., 2015).

The compilation of this doubly substituted CH₄ isotopologues database is inspired by similar efforts of existing databases for bulk isotopes of CH₄ (Lan et al., 2021; Menoud et al., 2022a, b; Sherwood et al., 2017, 2021). To verify if the compiled data compares well with previous studies, Fig. 1 and Table 1 present bulk isotopes from this database in the reference to previously reported δ13C-CH₄ and δD-CH₄ (Menoud et al., 2022a; Sherwood et al., 2021). Across compared group types, our additional bulk isotope ratio data fall within the established ranges. Fossil fuel and thermogenic source signatures overlap, however, they are not strictly equivalent. Thermogenic CH₄ in our dataset is slightly enriched (δ13C-CH₄: -39.0 ± 9.6 ‰; δD-CH₄: -169.2 ± 41.9 ‰), compared to fossil fuel. For the comparison, only terrestrial microbial (e.g., agriculture, lakes, wetlands) from this database is compared with previously compiled data and shows strong agreement with the range of previous microbial samples, with depleted δ13C-CH₄ and δD-CH₄ values (δ13C-CH₄: -62.9 ± 13.2 ‰; δD-CH₄: -298.1 ± 47.7 ‰). Pyrogenic methane, though represented by only two samples in the new database, shows δ13C-CH₄ and δD-CH₄ values consistent with previous studies. This alignment supports the representativeness of our inferred doubly substituted CH₄ isotopologues ratio source signatures for use alongside the bulk isotope ratios in global modelling of the CH₄ budget. Our database also provides further additional measurements of the bulk isotopes to aid in further work to refine the source signatures δ13C-CH₄ and δD-CH₄.

The references included in the database of doubly substituted CH₄ isotopologues comprise mostly peer-reviewed articles, with a smaller percentage from conference papers. The aggregated studies were carried out between 2014 and 2025 across 10 laboratories worldwide. As the aim of this study is to include all existing studies of doubly substituted isotopologue ratios, we also incorporated results from laboratory experiments, and of CH₄ dissolved in water (i.e. in oceans, wetlands, and inland waters), which were not included in bulk isotopes databases.

Out of all data entries, field samples comprise 958 entries, while 517 entries come from laboratory experiments. Of these, 53 % of entries report only Δ18 or Δ13CH₃D. Potentially, the lack of ¹²CH₂D₂ measurements can hinder data interpretation, especially for microbial, abiotic or mixed samples, where Δ13CH₃D and Δ12CH₂D₂ can be modified differently (e.g., Douglas et al., 2017; Giunta et al., 2019; Gruen et al., 2018; Thiagarajan et al., 2020; Warr et al., 2021; Young et al., 2016, 2017). To avoid data misinterpretation, other tracers, for example radiocarbon or seismic reflection data, must be measured alongside to Δ13CH₃D (e.g., Chowdhury et al., 2024; Douglas et al., 2020).

Regarding the parameter “group type”, thermogenic samples contribute 32 % to the field samples, while there is low representation of pyrogenic samples (0.21 % of field samples) (Fig. 2). “Others” is a broad group type of field samples with ambiguous origin from various sources (e.g., natural gas, groundwaters from metal mines, marine and mud volcano samples), where it was not possible to clearly determine the group type based on isotopes and other tracers. Hypothesized origins of these samples are given as “source specification” parameter in the database. Also, vehicle exhaust samples are classified as “others”, as different processes can cause CH₄ emissions from the exhaust (Sun et al., 2025b). Additionally, for samples where two different sources of CH₄ were mixed, indicated as group type “mixture”, more information on the type of mixture is added under the parameter “source specification” in the database. For ambient air “group type”, distinction between background samples and mixture of ambient air and gas coming from CH₄ source (e.g., gas sample collected above wetland, (Haghnegahdar et al., 2024; Sun et al., 2025b)) was made using the “group” parameter.

The distribution of measurements in Δ13CH₃D versus Δ12CH₂D₂ space is presented in Fig. 3, both for field samples and laboratory experiments. To simplify data interpretation, field samples categorized as “others” or “mixture” are omitted. Also, samples where ambient air is mixed with the gas from CH₄ source are omitted. The majority of thermogenic samples fall close to the thermodynamic isotopic equilibrium curve, with a few samples having more depleted Δ12CH₂D₂ than predicted (details in Sect. 4.2.). Microbial marine and microbial ff samples are near or at thermodynamic isotopic equilibrium but with some enrichment relative to equilibrium observed. Most of the microbial terrestrial samples (e.g., lakes, wetlands or agriculture) are clearly depleted in both Δ13CH₃D and Δ12CH₂D₂, relative to the equilibrium. Different ratios for microbial terrestrial compared to microbial ff and microbial marine suggests different methanogenesis reactions or additional processes, such as methanotrophy or mixed patterns of microbial carbon cycling within in these environments (details in Sect. 4.2). Regarding abiotic CH₄, most of the samples are out of thermodynamic isotopic equilibrium (e.g., Douglas et al., 2020; Labidi et al., 2020; Lin et al., 2023; Young et al., 2017). It must be noted, that abiotic CH₄ is empirically one of the least well characterized endmembers, both in terms of field and laboratory studies.

For laboratory experiments, the deviation from thermodynamic isotopic equilibrium depends on the studied methanogenesis pathway or the type of methanotrophy (aerobic (AeOM) versus anaerobic (AOM) CH₄ oxidation) (details in Sect. 4.2). For example, AOM methanotrophy experiments show a large enrichment for both Δ13CH₃D and Δ12CH₂D₂ (Liu et al., 2023; Ono et al., 2021). Notably, Gruen et al. (2018), Li et al. (2024, 2025a), and Taenzer et al. (2020), carried out incubations with deuterium-enriched substrate to explore mechanisms behind combinatorial effects. Thus, observed clumped isotopologues do not represent the isotopic values of natural-occurring microbial CH₄ and should be carefully re-interpreted.

Regarding pyrogenic methanogenesis, some samples have doubly-substituted isotope ratio compositions consistent with thermodynamic isotopic equilibrium, while others create more depleted values, due to a combination of kinetic isotope effects, combinatorial effects, and varying degrees of hydrogen isotope exchange (Dong et al., 2021; Eldridge et al., 2023; Shuai et al., 2018a). The abiotic synthesis of CH₄ in laboratory-controlled experiments shows enriched Δ13CH₃D, consistent with thermodynamic isotopic equilibrium, associated with systematically depleted Δ12CH₂D₂, due to combinatorial effects (Young et al., 2017, Labidi et al., 2024).

About 27 % of the laboratory experimental entries come from studies on microbial methanogenesis, focused on various pure cultures of methanogenic archaea (e.g., acetoclastic, hydrogenotrophic and methylotrophic methanogenesis) (Fig. 4) (Douglas et al., 2016, 2020; Giunta et al., 2019; Gruen et al., 2018; Rhim and Ono, 2022; Stolper et al., 2015; Warr et al., 2021; Young et al., 2017). Notably, Li et al. (2025a) conducted methanogenesis experiment where few data points come from extremely deuterium-enriched water (δD of water about 3000 ‰ and 8000 ‰). Such high δ2H of water cannot be found in the nature, thus obtained CH₄ has very atypical isotopic values (Fig. 5).

4.4 % of laboratory samples, classified as sediment incubation, were collected in the field and incubated in controlled laboratory conditions (Douglas et al., 2020; Haghnegahdar et al., 2023, 2024; Ijiri et al., 2018; Wang et al., 2024a). A single laboratory experiment focused on photochemical oxidation by OH and Cl was also conducted, however, only Δ13CH₃D was measured (Whitehill et al., 2017). A laboratory experiment focused on mixing of two CH₄ sources, containing different bulk isotopic compositions, was conducted to confirm mixing curve delivered from theoretical calculation, related to the definition of Δ13CH₃D and Δ12CH₂D₂ (Young et al., 2016).

Methane is produced at the surface and in subsurface environments via biogenic (microbial), thermogenic, or abiotic processes, while the majority of the CH₄ emitted to the atmosphere comes from microbial, thermogenic, and pyrolytic (biomass and biofuel burning) sources (e.g., Saunois et al., 2025; Schoell, 1988; Stolper et al., 2018). Thermogenic CH₄ forms by the thermally-activated breakdown of organic molecules, where “primary thermogenic” is a term used to describe CH₄ produced from kerogen and “secondary thermogenic” is used to describe the breakdown of long-chain hydrocarbons (e.g., Lalk et al., 2023; Stolper et al., 2018). Stolper et al. (2014b) proposed that thermogenic CH₄ is predominantly in thermodynamic isotopic equilibrium at its formation temperature, which was supported by studies focused on natural gas or volcanic samples (Beaudry et al., 2021; Douglas et al., 2016, 2017; Jiang et al., 2024; Kim et al., 2023; Rumble et al., 2018; Stolper et al., 2014b, 2015, 2018; Thiagarajan et al., 2020; Wang et al., 2015; Xie et al., 2021; Young et al., 2017). Formation temperatures calculated from doubly substituted isotope ratio measurements can help to determine the natural gas maturity and distinguish “atypical” thermogenic gas (from shallow or immature systems to deep or over-mature systems) from abiotic CH₄ (Jiang et al., 2024; Kim et al., 2023; Li et al., 2025b; Shuai et al., 2018b). Some exceptions of doubly substituted isotope ratios deviating from thermodynamic isotopic equilibrium were observed from unconventional, oil-non-associated or oil-associated gas reservoirs (Fig. 6) (Douglas et al., 2017; Kim et al., 2023; Lalk et al., 2022; Stolper et al., 2018; Xie et al., 2021), which is consistent with laboratory pyrolysis experiments and gas generation models implying at least partly kinetically-driven signatures (Dong et al., 2021; Eldridge et al., 2023; Shuai et al., 2018a; Xia and Gao, 2019). For low maturity or oil-associated natural gas, a contribution from microbial sources can occur, for example due to CH₄ generation during oil biodegradation (e.g., secondary microbial CH₄). However, the likelihood that microbial CH₄ has both Δ13CH₃D and Δ12CH₂D₂ within the thermogenic range remains low (Giunta et al., 2019; Lalk et al., 2022; Thiagarajan et al., 2020; Xie et al., 2021).

Microbial CH₄ is produced by microorganisms via three main pathways: hydrogenotrophic, acetoclastic, and methylotrophic methanogenesis, with the first two being the predominant (Conrad, 2005; Thauer, 1998). Typically, subsurface microbial CH₄ from geological basins is mostly generated through the hydrogenotrophic pathway, where doubly substituted isotope ratios tend towards thermodynamic isotopic equilibrium (Figs. 3 and 5) (Ash et al., 2019; Douglas et al., 2016, 2017, 2020; Giunta et al., 2019; Shuai et al., 2021; Stolper et al., 2015; Thiagarajan et al., 2020; Wang et al., 2024a; Warr et al., 2021; Young et al., 2017). Studies of pore water from the Michigan Basin, showed that deep subsurface CH₄ can also be generated by acetoclastic methanogenesis at thermodynamic isotopic equilibrium for ¹³CH₃D but at substantial disequilibrium for ¹²CH₂D₂ (Jautzy et al., 2021). The majority of microbial CH₄ from shallow freshwater environments is generated during acetoclastic methanogenesis, which can result in strong depletion for both ¹³CH₃D and ¹²CH₂D₂ (Figs. 3 and 5) (Conrad, 2005; Douglas et al., 2016, 2017, 2020; Haghnegahdar et al., 2024; Li et al., 2025a; Stolper et al., 2014b; Wang et al., 2015; Whiticar, 1999; Young et al., 2017). In systems with presumed slow CH₄ generation rates, favouring enzymatic isotopic reversibility, microbial CH₄ likely can form at or near thermodynamic isotopic equilibrium, while in systems with rapid CH₄ formations, microbial CH₄ tends to depart from thermodynamic isotopic equilibrium (Douglas et al., 2020; Shuai et al., 2021; Stolper et al., 2015; Wang et al., 2015).

Methane can also be produced abiotically, for example via Sabatier reactions linked to hydrogen production from serpentinization in hydrothermal systems (Cumming et al., 2019; Douglas et al., 2017; Labidi et al., 2020; Nothaft et al., 2021; Ojeda et al., 2023; Suda et al., 2022; Wang et al., 2018; Young et al., 2017). It has been observed from deep groundwater seeps accessed via or within deep subsurfaces layers, for instance in metal mines, where it can also mix with microbial CH₄ followed by re-equilibration (Nothaft et al., 2021; Warr et al., 2021; Young et al., 2017). Typically, abiotic CH₄ is produced at temperatures exceeding 250 °C in seafloor hydrothermal fluids or in the continental seeps, springs and fracture waters at temperatures lower than 100 °C (Etiope and Sherwood Lollar, 2013; Labidi et al., 2024; Young et al., 2017). During controlled laboratory synthesis under hydrothermal conditions, the majority of the Δ13CH₃D measurements closely reflect the temperature of abiotic CH₄ generation (based on thermodynamic isotopic equilibrium). Δ12CH₂D₂ was observed with depletions down to -40 ‰, which can be attributed to a D/H combinatorial effect associated with the various steps of hydrogen addition to carbon occurring during CH₄ formation (Labidi et al., 2024).

Using doubly substituted isotope ratio measurements, the mixed thermogenic-microbial origin of CH₄ was observed in marine environments, including CH₄ clathrates (Giunta et al., 2021; Zhang et al., 2021), lakes (Douglas et al., 2016), mud volcanoes (Lin et al., 2023; Liu et al., 2024a; Rumble et al., 2018), oil fields (Tyne et al., 2021) and natural gas (Douglas et al., 2017; Giunta et al., 2019; Kim et al., 2023; Lalk et al., 2022; Stolper et al., 2014b, 2015; Thiagarajan et al., 2020, 2022). Mixing between different CH₄ sources (containing different bulk isotopic compositions) in different proportions creates a non-linear relationship in Δ12CH₂D₂ vs Δ13CH₃D space. Measurement of both doubly-substituted isotope ratios therefore provides additional information to help define the mixed end members and understand if physical or chemical transformation processes have taken place (e.g., Douglas et al., 2016; Young et al., 2016; Zhang et al., 2021).

Notably, existing studies showed a range of doubly-substituted isotope ratios for mud volcano samples, suggesting their different origins (thermogenic, microbial, abiotic or mixed) and potentially reflecting subsequent alteration processes such as AOM (Ijiri et al., 2018; Lalk et al., 2022; Lin et al., 2023; Liu et al., 2023, 2024a; Rumble et al., 2018). Additionally, Δ13CH₃D was used to demonstrate a microbial origin of CH₄ in deep subsurface coal beds in the north-western Pacific (Inagaki et al., 2015) and shallow subsurface mud volcano in the Nankai accretionary complex (Ijiri et al., 2018), which could otherwise be incorrectly identified as thermogenic sources. Also, Δ12CH₂D₂ vs Δ13CH₃D suggested mixing of thermogenic and microbial CH₄ in coal bed reservoirs (Wang et al., 2024b, c).

Combinatorial effects occur when a molecule contains indistinguishable atoms of the same element derived from pools with different isotope ratios. This purely mathematical phenomenon comes from the definition of doubly-substituted isotope ratio in reference to the stochastic distribution and has been predicted theoretically (Röckmann et al., 2016; Yeung, 2016) and demonstrated experimentally for CH₄ (Labidi et al., 2024; Taenzer et al., 2020; Wang et al., 2024a). Among the two mass-18 isotopologues of CH₄, only Δ12CH₂D₂ can be influenced by combinatorial effects, as it features two indistinguishable deuterium substitutions for hydrogen. Combinatorial effects for Δ12CH₂D₂ values must be taken into account in low-temperature abiotic or biotic systems where the hydrogen atoms of CH₄ originates from multiple reservoirs, which has been observed in microbial samples (Giunta et al., 2019; Jautzy et al., 2021; Young et al., 2017), mud volcanos (Liu et al., 2024a), natural gas (Shuai et al., 2021; Xie et al., 2021), or during abiotic, microbial and pyrogenic methanogenesis experiments (Dong et al., 2021; Eldridge et al., 2023; Labidi et al., 2024; Li et al., 2025a). Notably, Eldridge et al. (2023) showed that combinatorial effects alone cannot explain the non-equilibrium of Δ12CH₂D₂, observed in their pyrogenic methanogenesis experiments focused on CH₄ formation from methyl precursors (i.e. ethane). They pointed out the role of other important processes such as the influence of kinetic isotope effects and inheritance reactions (i.e., inheriting “clumps” from methyl groups in the precursor molecule), in addition to combinatorial effects.

Before emission to the atmosphere, CH₄ can be consumed through aerobic oxidation (AeOM) or anaerobic oxidation (AOM). In terrestrial ecosystems (e.g., wetlands) and oxygenated marine water columns, AeOM plays a crucial role, while in gas seeps and sulphate-rich marine sediments, AOM likely dominate causing inhibition of CH₄ emissions to the atmosphere (e.g., Wang et al., 2016 and references therein). Minor depletions in Δ13CH₃D and Δ12CH₂D₂ were observed in AeOM-dominated systems, but low-temperature equilibrium or significant enrichments in Δ13CH₃D and Δ12CH₂D₂ were observed in the case of AOM (Figs. 3 and 7) (Giunta et al., 2022; Kim et al., 2023; Liu et al., 2023; Ono et al., 2021). One hypothesis states that the reversibility of initial steps of AOM promotes thermodynamic equilibration (Ash et al., 2019; Giunta et al., 2022; Ono et al., 2021; Zhang et al., 2021). Alternatively, another hypothesis proposes that near-thermodynamic equilibrium of doubly substituted isotope ratios in marine sediments can be attained via a slow rate of methanogenesis, with reversible enzymatic reaction steps (Douglas et al., 2020; Shuai et al., 2021; Stolper et al., 2015; Wang et al., 2015). As AeOM and AOM have distinctive kinetic isotope effects in natural settings, doubly-substituted isotope ratios may be used to track and differentiate both AeOM and AOM in nature (Adnew et al., 2025; Ash et al., 2019; Giunta et al., 2019, 2022; Krause et al., 2022; Li et al., 2024; Tyne et al., 2021; Warr et al., 2021; Zhang et al., 2021).

In the troposphere, reaction with OH is the primary removal mechanism of CH₄ (90 %), with other minor contributions from microbial oxidation in soils and vegetation, loss to the stratosphere, and reactions with tropospheric Cl (e.g., Saunois et al., 2025). Overall, isotopologues containing bonds of lighter isotopes are preferentially removed through photochemical oxidation, leading to an enrichment in heavier isotopologues of the remaining CH₄ pool (Table S2 in the Supplement) (e.g., Haghnegahdar et al., 2017; Whitehill et al., 2017). Laboratory experiments showed that photochemical oxidation by OH has only a minor impact on Δ13CH₃D of tropospheric CH₄ (i.e. the ¹³C-D bond does not react significantly slower than that calculated based on equivalent singly substituted reactants) (Whitehill et al., 2017). Thus, measurements of Δ13CH₃D in the atmosphere can provide constraints on CH₄ source strengths, while Δ12CH₂D₂ is predicted to provide information on CH₄ sink strength, as implemented in global scale atmospheric models (Chung and Arnold, 2021; Haghnegahdar et al., 2017; Whitehill et al., 2017). Aside from the atmospheric models, Wang et al. (2023b) used machine learning incorporated with a random forest model to predict steady-state atmospheric CH₄ doubly substituted isotope ratios. The first measurements of the doubly substituted isotope ratio of CH₄ in the atmosphere were more depleted for both Δ13CH₃D and Δ12CH₂D₂ than predicted by atmospheric models and available source signature information (Chung and Arnold, 2021; Haghnegahdar et al., 2017, 2023; Sivan et al., 2024). Haghnegahdar et al. (2023) proposed that differences between measurements and predictions required depleted doubly substituted isotopic signature values for the (total) source flux than previously assumed. On the other hand, Sivan et al. (2024) highlighted that the observed discrepancy could also be caused by inaccuracy in the theoretical values of the kinetic isotopic effect (KIE) of CH₄ reactions with OH, Cl and soils sinks. They indicated that a small adjustment in the sink KIE, along with slightly lower source mixture than previously assumed, could align atmospheric and source doubly substituted isotopic signatures (Sivan et al., 2024).

The distribution of Δ13CH₃D and Δ12CH₂D₂ derived from field samples per simplified subcategory is plotted on Fig. 2b, while Figs. 6 and 7 present box plots for measured doubly substituted isotopes from field samples and laboratory experiments, respectively. For simplicity, in Figs. 2b and 6, and thereafter, some subcategories are merged. Gas installation and natural gas subcategories are merged into natural gas. Hot spring, spring, and hyperalkaline spring are unified as spring. Marine sediment, marine seep, pore fluid and pockmark are grouped as a marine subcategory. Hydrothermal and volcano steam samples are unified as volcano. Finally, swamp and ponds are merged as wetlands, while lakes are in a separate subcategory. Around 40 % of field samples were collected from reservoirs of natural gas (Fig. 2b). About 3 % of field samples come from coal seam gas and 12.5 % come from microbial terrestrial sources. There is a significant representation of marine (12.5 % of field samples) and volcano mud samples (6 % of field samples), although, their emissions to the atmosphere are negligible. For samples categorized as microbial terrestrial, the majority of entries come from lakes (75 % of microbial terrestrial), with a small contribution from agriculture (6 %) or wetland (12 %) samples, which are significant CH₄ emitters to the atmosphere. Only Δ13CH₃D was measured for four ruminants samples (Lopes et al., 2016; Wang et al., 2015). Only three samples from rice paddies have so far been collected, where both Δ13CH₃D and Δ12CH₂D₂ were measured (Haghnegahdar et al., 2023; Wang et al., 2023a). So far, no waste samples have been collected directly from the source for studies of doubly substituted isotope ratios. The recent studies of Sun et al. (2025a) focused on collection of big volume ambient air samples, where background air was mixed with gas coming from microbial CH₄ sources, like wetlands and landfills. Application of a Keeling plot method (Pataki, 2003), allowed determination of targeted sources (Sun et al., 2025a).

Published Δ13CH₃D and Δ12CH₂D₂ for natural gas are consistent with a thermogenic origin (Figs. 3 and 6, Tables S3 and S4). Observed outliers come from low maturity or oil-associated natural gas where a microbial contribution could be significant (Kim et al., 2023; Lalk et al., 2022; Thiagarajan et al., 2020; Xie et al., 2021). No significant variation has been observed in measurements made of biomass burning, dairy cows (ruminants), or rice paddies within the available, limited dataset but this may not reflect the variation within the true population (Tables S3 and S4). Significant variation in both Δ13CH₃D and Δ12CH₂D₂ is observed for spring and mud volcano subcategories, as these samples have varying microbial, thermogenic, abiotic, or mixed origins. Finally, a wide distribution is observed for lake samples, potentially originating from seasonal variation in CH₄ production, oxidation in the lake subsurface or methanogenic metabolisms involved (Lalk et al., 2024).

For the laboratory experiments, culturing of different strains of archaea and wide variations in experimental parameters resulted in a wide distribution of observed doubly substituted isotopic compositions, especially for Δ12CH₂D₂ (Fig. 7, Tables S5 and S6). AOM methanotrophy experiments show significant enrichment in both Δ13CH₃D and Δ12CH₂D₂ relative to the other categories.