Highly concentrated geogenic CO2 emissions have been reported worldwide. Although atmospheric CO2 dispersion is the most common occurrence, specific topographic and meteorological conditions can lead to surface accumulation in the form of “CO2 rivers”. Although catastrophic events such as the deadly limnic eruption of Lake Nyos in 1986 are well documented, the behavior of these CO2 rivers is not well understood. This lack of understanding poses challenges for hazard assessment and mitigation. While computational models such as computational fluid dynamics (CFD) and integral models provide analytical insights, their practical application in risk management is limited by computational cost and accuracy constraints. To address these limitations, we simulate the behavior of CO2 rivers using TWODEE, a depth-averaged numerical model that is a computationally efficient alternative for simulating dense flows. We test the model at the Syabru-Bensi Hydrothermal System (SBHS) in central Nepal, where high seismic activity and significant CO2 degassing have been observed. In the field, we measure the airborne CO2 concentration, wind velocity and direction using autonomous sensors at 0, 50, 150, and 300 cm above the ground at each measurement point, as well as surface CO2 flux using the accumulation chamber method. Our results demonstrate the robustness of the statistical approach by providing well-constrained maps of CO2 concentration in the lowest atmospheric layers over large distances from the emission source. This method can be applied to other non-volcanic and volcanic sites. Additionally, we assess the impact of the 2015 Mw 7.9 Gorkha earthquake in Nepal, which triggered additional CO2 degassing vents and changes in surface CO2 flux across the SBHS. Our work aims to improve our understanding of how dense gases disperse in the lower atmospheric layers. We are developing an operational hazard assessment tool with potential applications in real-time risk management. This tool will quantify the CO2 budget of CO2 rivers in various geodynamic contexts and estimate health hazards in volcanic and non-volcanic environments.

In subduction systems, the forearc (FA) serpentinized mantle plays a key role as a reservoir for fluid-mobile elements, especially those prone to early mobilisation from the slab. FA serpentinites therefore provide an indication of the fluid characteristics that have been steamed out of the slab, and allow better quantification of elemental recycling and fluid flow. FA serpentinites outcropping along the Indus Suture Zone are formed by hydration of mantle peridotites by fluids derived from the Indian slab, providing a geochemical record of fluid-rock interactions during the India-Eurasia convergence. Systematic trace and multi-isotope (Sr and Pb) analyses of serpentinites from three major sites, namely Shergol-Tingdo, Kargil and Tso Morari, along the Indus Suture Zone in Ladakh (NW Himalaya) show that these rocks record a major change in the origin of metasomatic agents, from oceanic to continental subduction. The Shergol-Tingdo and Kargil FA serpentinites, formed under low temperature and pressure conditions, are characterised by high B enrichment and As and Sb depletion, high alkali/U ratios and relatively unradiogenic Sr and Pb isotope ratios. These geochemical characteristics are identical to those reported for modern oceanic subduction zones (e.g., Mariana forearc) and are consistent with input by fluids derived from subducted oceanic crust. In contrast, FA serpentinites from the Tso Morari ultra-high pressure unit show enrichment in fluid mobile elements such as As, Sb and U, low alkali/U ratios and radiogenic Sr and Pb isotopic compositions. These features suggest a change in the metasomatizing agent with a strong influence from subducted continental material. Consistent with this scenario, the Sr-Pb isotopic composition of the Kargil FA serpentinites can be reproduced by mixing between an Indian MORB-depleted mantle source and fluids derived from dewatering of blueschist facies oceanic metasediments, whereas in the case of Tso Morari a fluid end-member derived from various eclogitic continental metasediments is required. We propose that the observed geochemical signature of the Indus Suture Zone FA serpentinites can be used to reconstruct the geochemical exchanges between the slab and the overlying mantle from intra-oceanic to continental subduction. This successful systematic approach could be applied to other collisional contexts

With the recent return of extraterrestrial material from the Chang'E 5 and Chang'E 6 missions, and the upcoming Mars Sample Return mission, it is essential to develop optimised methodologies for their analysis. These samples are rare and valuable, typically consisting of low-mass, fine-powdered regolith with very low natural radioactivity. This work, carried out at the Laboratoire National Henri Becquerel (LNE-LNHB), presents an adapted gamma-ray spectrometry methodology to determine the activity concentrations of natural radionuclides in extraterrestrial samples, with a particular focus on understanding the mobility of in planetary regoliths and atmospheres/exospheres. A bespoke sample holder was designed to minimise gamma-ray self attenuation, particularly in the low energy range, while providing the gas-tightness and inert handling conditions necessary to preserve pristine extraterrestrial material. In addition, a high-purity germanium gamma spectrometer with an active anti-coincidence veto was optimised to increase detection efficiency, with a particular focus on the 46.54keV emission of . To validate this methodology, a Martian regolith analog (JSC Mars-1) was analysed immediately after enclosure, with a total measurement time of 36.25 days. This approach allowed for precise quantification of radionuclides in extraterrestrial samples, overcoming the challenges posed by their low mass, precious and difficult-to-handle nature. The measured specific activities (activity per unit mass of material) with expanded uncertainties (k=2) for , , , , and were 28.6 ± 5.7Bqkg-1, 19.8 ± 3.6Bqkg-1, 15.4 ± 2.5Bqkg-1, 0.13 ± 0.03Bqkg-1, 146 ± 12Bqkg-1, respectively, compatible with reported data on much larger sample masses. These results demonstrate the capability of this optimised methodology to aid in the radiological characterization of extraterrestrial materials while ensuring minimal sample usage.

The radioactive gas radon-222, a fluid and aerosol tracer in Earth's lithosphere and atmosphere, can also reveal subtle rock physics processes in extraterrestrial environments, such as those involving water, but remains poorly constrained in planetary bodies due to the limited number of samples available. Here we measure the effective radium-226 concentration (ECRa) of six Martian and nine lunar meteorites to derive radon source terms for Martian and lunar rocks. ECRa values are 0.029-0.78 and 0.045-0.80 Bq kg-1 for Martian and lunar meteorites, respectively (0.041 +/- 0.003 Bq kg-1 for falls and 0.28 +/- 0.02 Bq kg-1 for finds), lower than most terrestrial rocks but similar to other meteorites and terrestrial primitive basalts. The effect of terrestrial alteration on ECRa and its temperature sensitivity are also determined experimentally. Radon emanation coefficient values are 2.1-17% (mean: 8.1 +/- 2.5%) for Martian meteorites and 0.43-11% (mean: 5.5 +/- 1.0%) for lunar meteorites. Mean estimated surface radon fluxes for Mars and the Moon are 0.16-0.60 and 0.33-0.44 mBq m-2 s-1 (78-280 and 160-210 atoms m-2 s-1), respectively, much lower than on Earth (21 mBq m-2 s-1 or 104 atoms m-2 s-1). Our meteorite analyses constrain radon emanation on Mars and the Moon and provide a basis for current and future in-situ measurements.

Radon-222, a radioactive noble gas with a half-life of 3.8 days produced by radium-226, is a health hazard in caves, but also a powerful tracer of atmospheric dynamics. Here we show how airborne radon-222 can be analysed in a cave with multiple openings, the Pech Merle Cave in South-West France. This two-level cave hosts prehistoric remains and Gravettian paintings in its lower level. Radon concentration, monitored at 15 points with one-hour sampling intervals for more than one year, including two points for more than three years, showed mean values from 1274 +/- 11 to 5281 +/- 20 Bq m-3, with transient values above 15,000 Bq m-3. Seasonal variations were observed, with a weak normal cycle (low in winter) at two points in the upper level and a pronounced inverse seasonal cycle (low in summer) at the other points in the cave. The radon-222 source (effective radium-226 concentration, ECRa) was measured in the laboratory for floor deposits, soil and rock samples. While ECRa values obtained for rocks and speleothems are smaller than 1 Bq kg- 1, most ECRa values for soils are larger than 10 Bq kg- 1. Quantitative modelling confirms that the floor fillings inside the cave are responsible for the stationary lower concentrations, while the higher concentrations observed in winter are explained by percolation of outside air, which collects radon-222 as it passes through the soil layers. In addition, Stored Available Radon (SAR) is sufficient to account for transient variations. While air currents occur when visitors enter the cave or when the cave is deliberately ventilated, the climatic processes revealed by their radon222 signatures appear to be essentially natural. These processes, enhanced by global climate change, could cause or accelerate the deterioration of prehistoric paintings. Radon-222 source analysis using ECRa-based modelling and SAR appears essential for the preservation of underground heritage.

Resistor networks are increasingly being considered in heuristic research as models for natural or artificial matter. The equivalent resistance between two nodes, the Two-Point Resistance (TPR), can be calculated using a variety of methods. The transfer matrix (TM) method was originally considered as a numerical tool for estimating percolation thresholds in random networks with a repeating pattern. The TM method is revisited here as an efficient tool to obtain, in a fast and elegant way, iteration relations and exact explicit expressions for leading TPRs that include a node in the last repeated pattern. Several rotationally invariant networks are studied, such as simple cylindrical networks, spider web networks and cylindrical networks with a central resistive axis, in which case the TM matrices are circulant matrices. Examples of explicit expressions are given for orders of rotation <= 4 or 5, depending on the case. The method can be applied in a similar way to networks with less symmetry, such as grids. The general expressions of TPRs obtained using the TM method can provide quantitative guidelines for resistor networks developed in materials science, environmental issues or industrial applications.

Carbonate-bearing sediments, containing calcite, dolomite or magnesite as major carbonate components, are important constituents of sedimentary sequences deposited on passive margins through Earth's history. When involved in collisional orogenic processes, these sediments are metamorphosed at variable temperatures and pressures, and undergo decarbonation reactions. While the orogenic metamorphism of some of these lithologies (i.e. impure limestones and dolostones, marls sensu stricto and calcareous pelites) is relatively well understood, very little is known about the metamorphic evolution and decarbonation history of mixed carbonate-silicate rocks in which either dolomite or magnesite is the dominant carbonate component. Here we present the results of a petrologic study of representative samples of metasediments from Central Nepal, derived from Proterozoic dolomitic and magnesitic protoliths metamorphosed during the Himalayan orogeny. The main metamorphic assemblages developed in sediments originally containing different amounts of dolomite or magnesite are characterised in detail. Forward thermodynamic modelling applied to seven samples allows constraints to be placed on (i) the main decarbonation reactions, (ii) the P-T conditions under which these reactions took place, (iii) the composition of the fluids, and (iv) the amounts of CO2 released. We conclude that the CO2 productivity of dolomitic and magnesitic pelites and marls originally containing 15-40% carbonate is significant (>5.5 +/- 1.0 CO2 wt% and up to 10.5 +/- 1.5 CO2 wt%), whereas for carbonate contents above 60-70%, CO2 productivity is negligible unless aqueous fluids infiltrate from the outside and trigger decarbonation reactions. Since the dolomitic and magnesitic protoliths are significantly abundant in the sedimentary sequences involved in the still active Himalayan orogen, the decarbonation processes described here could contribute to the diffuse CO2 degassing currently observed at the surface. Furthermore, we propose for the first time that the peculiar magnesium-rich assemblages investigated in this study may derive from evaporitic protoliths, and that the whole Upper Lesser Himalayan Sequence may therefore represent the metamorphic product of a Proterozoic sequence consisting of alternating layers of carbonatic, evaporitic and pelitic sediments.

Resistor networks, used to model new types of natural or artificial matter, also provide generic examples for practising the methods of physics for obtaining estimates, revealing the main properties of a system and deriving exact expressions. Symmetric bracelet resistor networks are constructed by connecting n identical resistors in a circle, and then connecting two such circles by another set of n identical resistors. First, using van Steenwijk’s method, we establish that the equivalent resistance or two-point resistance (TPR) between any two nodes is derived when the layer-to-layer resistance R 0 n is known. We then determine R 0 n by an elementary recurrence relation which converges rapidly to its large n limit. Using this reference value of R 0 n , accurate estimates of other TPRs follow for all values of n , characterised by a leading 1/ n variation. In addition, exact explicit expressions of the TPRs can be calculated for any value of n . These networks, prototypes of three-dimensional networks considered in research, can be used to illustrate the diversity of the physical approach, the power of elementary methods, and to learn to be comfortable with approximations. Easy to make and use for experimental tests, they can support hands-on activities and conceptual changes.

Besides carbonates, carbonaceous material in meta-sediments represents an important carbon reservoir on Earth. In orogenic belts, carbon can be stored as graphite, a contribution to the global carbon cycle that remains insufficiently constrained. Here, we focus on the Himalayan belt where moderately crystalline graphite is found at the footwall of the Main Central Thrust. Using various analytical methods, we investigate metamorphic conditions of graphite at increasing spatial scales in the Upper Lesser Himalayan Sequence (upper-LHS) phyllites of Nepal. First, we develop and validate a new SEM-BSE technique to measure total organic carbon (TOC) content. Graphite shows mostly inter- and intra-granular flaky crystals associated with carbonates. Elemental carbon analyses yield large range of TOC content in phyllites with a mean of 3.7 +/- 0.4 vol.%. Inferred from micro-Raman spectroscopy, peak metamorphic temperature (peak-T) ranges from 519 +/- 9 to 590 +/- 8 degrees C. We observe a significant coherence of metamorphic conditions of graphitic phyllites at metric, decametric and kilometric scales using extensive data obtained in the Upper Trisuli valley, Central Nepal (n = 77), and, at larger spatial scales, using data from Far-Western to Eastern Nepal (n = 67). Mean carbon isotopic composition (delta 13C) of -26.3 +/- 0.1 parts per thousand indicates biogenic source. Less negative delta 13C values, also reported in other orogenic belts, suggest interaction with pre-existing sedimentary carbonates, probably related to metamorphic isotopic reequilibration. First-order extrapolations at the upper-LHS scale suggest meta-sediment organic carbon may represent up to 20 % of the total amount of carbon stored in orogens. Central Nepal segment, with higher TOC content and peak-T, is also characterized by the largest current metamorphic carbon dioxide (CO2) emissions of the chain. This hardly coincidental association, at the scale of the Himalayan belt, between organic carbon stored as graphite and mobile inorganic carbon released as CO2, represents an important clue to investigate further for global carbon budget estimations.

Convergent plate boundaries are essential components of the global carbon dioxide (CO 2 ) balance of the Earth. Their role of atmospheric CO 2 sink is controlled by silicates weathering. The Nepal Himalaya appears as a natural laboratory for the study of current spatial and temporal variations of CO 2 release at large scale. This chapter presents an up-to-date overview of the known hydrothermal systems in the Nepal Himalaya. It introduces the main hydrothermal sites and presents the associated results separately for thermal springs and gaseous emission zones from Far-Western to Eastern Nepal in the vicinity of the Main Central Thrust and Main Frontal Thrust. The chapter recalls the different measurement techniques used to identify, detects and measures various parameters in thermal spring waters and gaseous emissions.

•Temperature variations induced by atmospheric pressure variations visible in caves.•Frequency dependent transfer functions (TFs) studied in four caves in France.•TFs inferred from 8 × 10-7 to 8 × 10−4 Hz, amplitude at 12 h from 2 to 14 × 10−3 °C/hPa.•Air to rock surface temperature TFs also evaluated at selected locations.•TF interpreted with a model including heat exchange, phase changes and air motion

This chapter presents an overview of the physico-chemical properties of thermal springs and gaseous emission zones in Nepal, with an emphasis on dissolved inorganic carbon and gaseous CO 2 emissions. It discusses the spatial organization and earthquake-induced temporal variations of the deep metamorphic carbon release, and identifies research perspectives for the coming years. A total of 227 thermal springs have been studied so far in Nepal. Among them, about 20 have enough flow rate and temperature to be used efficiently by the population, and remain therefore important pilgrimage sites. In a given region of the MCT zone, such as the upper Trisuli valley, sites separated by 5–10 km show similar characteristics of the crustal fluid release. This suggests that hydrology and topography locally are not the predominant controlling factors of the small-scale spatial heterogeneity of the CO 2 release.

The inert radioactive gas radon-222, ubiquitous in the environment, is the first cause of lung cancer in non-smokers and a powerful asset to trace geological fluids and constrain atmospheric transport models. In all of these applications, radon flux (RF) from the ground needs to be estimated. However, obtaining a large-scale representative estimate of RF in continental land is a challenging task and a starting basis is to focus on large countries in the world. Here, we collected a total of 2622 direct RF measurements carried out in continental China from 1988 to 2021 using 69 publications in a 494-document pool. Over the whole dataset, the RF results were classified into geographical provinces, time periods and substratum types. Mean RF values yield 180±32, 36.9±4.8, 31.1±1.0, 66.1±1.6 and 1510±100 mBq m−2 s−1 in metamorphic and igneous (n=71), sedimentary (n=24), Quaternary (n=585), faulted areas (n=832) and uranium-related sites (n=898), respectively. Considering geology only, mean RF for China (66±11 mBq m−2 s−1) is larger than most large-scale estimates worldwide. To account for the distribution of soil thickness, RF values were extrapolated to representative soil thickness values per lithology using a scaling law inferred from natural sites. The inferred corrected mean RF for China yields 20.2±6.1 mBq m−2 s−1, corresponding to a total radon-222 emission of (191±43)×109 Bq s−1, and appears compatible with available large-scale estimates in Europe or at global scale. Potential sources of systematic bias and variability, such as vegetation cover, meteorological and seasonal effects, remain. The contribution of urban areas, estimated for the first time, was found significant. Our study suggests future research directions to better constrain the RF source to the atmosphere in China, and, more generally, to extract robust global-scale representative RF values from direct RF measurements.

The outstanding preservation of Paleolithic decorated caves is related to the buffering properties of their karstic environment. However, long-term monitoring of air/wall temperatures and gas compositions has recently revealed disruption signs in cave microclimates that had been maintained stable for hundreds of centuries. High precision and continuous temperature data records are currently monitored in various prehistoric caves in the South of France. Such operations have been promoted since the late 1990s by the French government for risk assessment and conservation. The most striking feature is the positive drift of underground temperatures (air and wall) which is now obvious in most sites except for Niaux Cave (> 300 m undersurface) and in the deepest parts of Mas-d’Azil and Chauvet Caves (> 50 m undersurface). In tourist caves (Pech-Merle, Mas-d’Azil, Gargas, Villars), the positive thermal trends could not be related to the energy increase brought by visitors which number is now stable, nor to the lighting systems whose energy demand was strongly reduced. In addition, the underground thermal drift nearly starts at the same time in many caves with uncertainties of +/- 1 year: 2012 for Chauvet with +0.4 °C/decade, 2011 for Pech Merle with +0.32 °C/decade, 2011 for Marsoulas Cave with +1.09 to +0.36 °C/decade from the entrance to the deep gallery, 2011 for Gargas with +0.69 °C, +0.54 °C and +0.36 °C for the deeper station. It is worth noting that a 0.3-0.4 °C thermal drift is consistent with that predicted from global warming in these regions. The thermal drifts were already in progress when monitoring began in Villars Cave in 1996 (+0.17 °C to +0.39 °C/decade), in Mas-d’Azil in 2012 and in Bruniquel in 2015. Marsoulas (+1.09 °C/decade) and Mas-d’Azil (more than +1 °C/decade in 6 of the 16 stations) present a much higher drift rate compared with that of surface, which suggests a thermal amplification process. As measurements are performed in heterothermal zones, the long-term thermal drifts are modulated by persisting smoothed and out-of-phase yearly variations. A notable exception is the case of Bruniquel main gallery where the temperature records show a quasi-linear increase. In that case, the decadal evolutions of temperature +0.31 °C, +0.175 °C, and +0.24 °C, are not related to the depth of monitoring stations (32 m, 55 m, and 38 m, respectively) nor to their distances from the entrance. In 2018, those drift rates induced a permanent inversion of thermal gradient in the main gallery. In Gargas, the drift rate is more pronounced in the outer parts of the karst body, thus inducing a continuous evolution of the thermal gradients within the galleries. Such underground microclimate disruption of patrimonial caves is a warning signal of direct threat on the preservation of remains. Karst physical organization and its related underground environment are themselves legacies of past climates; the current functioning of transfer zones of karst aquifers which includes the caves, are directly dependent on the outside climate. A more comprehensive approach and modelling of possible tipping points are urgently needed for conservation issues.

Recent studies have demonstrated that kinetic factors can significantly influence garnet nucleation, delaying its appearance with respect to the equilibrium predictions. Overstepping of garnet nucleation occurs in both contact and regional metamorphic settings, with extremely variable degrees: The factors controlling such highly variable degrees of overstepping are still unclear. This study focuses on garnet nucleation and growth in aluminous metapelites from the Barrovian inverted metamorphic pile of the upper portion of the Lesser Himalayan Sequence (Upper-LHS; central Nepal), with the aim of (i) investigating if (and how) the bulk-rock composition can influence overstepping of garnet nucleation and (ii) which are the implications of garnet nucleation overstepping for the P-T evolution of a Barrovian metamorphic sequence. Detailed petrographic, microstructural and compositional data are presented for six phyllitic schists, containing porphyroblasts of garnet, staurolite and/or kyanite. Their P-T evolution is constrained through thermodynamic forward modelling (i.e., isochemical phase diagrams combined with isopleth thermobarometry), assuming that equilibrium was attained at every stage of their metamorphic evolution. Comparison between the P-T conditions inferred for the growth of garnet core, the assemblages predicted to be stable at these P-T conditions and the modelled garnet-in reaction boundary suggests that the studied samples have experienced different degrees of apparent thermal (Delta T) and/or baric (Delta P) overstepping of garnet nucleation. We suggest that the bulk-rock MnO and CaO amounts might have influenced the apparent Delta T and Delta P overstepping of the garnet-in reaction: more specifically, the higher the bulk-rock MnO content, the more pronounced the apparent Delta T overstepping, whereas the lower the bulk-rock CaO content, the greater the Delta P overstepping. However, rather than an effective delay of garnet appearance with respect to equilibrium predictions, the apparent Delta T overstepping of garnet nucleation could reflect the attainment of the critical 0.5% threshold of garnet abundance, below which garnet is not readily detected in thin section. Kinetic factors seem much less critical in controlling the growth of the garnet rim at peak P-T conditions, confirming that peak metamorphic conditions constrained through equilibrium approaches based on the composition of garnet rim and of the matrix assemblage can be considered as reliable. Overall, the P-T paths of the studied samples are characterized by prograde heating coupled with tectonic overload (peak-P conditions of 9.5-10.5 kbar, 580-590 degrees C), followed by heating during exhumation (peak-T conditions of 8.2-8.9 kbar, 610-630 degrees C), supporting those thermo-mechanical models that predict a period of slowdown (or quiescence) of the Main Central Thrust activity.

In underground cavities, temperature variations of the order of 10−3 °C are permanently induced by the variations of atmospheric pressure, even at great depths, with couplings of the order of 0.2 to 20 × 10−3 °C/hPa depending on frequency. In the first part of this study, we established the atmospheric pressure to temperature transfer function (TF) as a function of frequency from 8 × 10−7 to 8 × 10−4 Hz. Here, we use this TF to calculate the expected PIT variations, which, after being subtracted from the observed time-series, provide residual temperature time-series. We calculated such temperature residuals in four natural caves in France: Esparros, Aven d'Orgnac, Pech Merle and Chauvet-Pont d'Arc Caves, the last two containing unique prehistoric wall paintings. Temperature signals, as small as a few 10−3 °C, due to human presence, are then conspicuous, with evidence of relaxation longer than several days and long-term cumulative effects. In addition, we observe temperature signals suggesting non-stationary states characterized by several processes which are not necessarily easy to separate, such as transient air currents, due to barometric winds or locally semi-confined convection cells, transient infiltration, or energy dissipation by evaporation-condensation at the rock surface. This background thermal agitation displays a scale-free amplitude spectrum, from 2 × 10−5 to 4 × 10−4 Hz, of the form f−α, with α varying from 0.1 to 0.6 depending on the site. Furthermore, at the Chauvet Cave, a weak but unambiguous peak emerges during some months at a period of about 82.2 ± 0.8 minutes, suggesting a Helmholtz-type resonance. Small but significant temperature signals are therefore detected in underground cavities once the effect of atmospheric pressure variations is corrected for. These signals reveal subtle coupled processes whose knowledge is essential to evaluate preservation strategies and to establish conditions for resilience of underground systems under artificial or natural influence including climate change.

The rise of novel materials such as graphene compounds or carbon nanotubes recently revived the interest on the role of symmetries upon electrical properties. Among possible solids, symmetrical polytopes, widely realized in natural and artificial matter, deserve particular attention. When equal resistors are attached between neighbouring nodes of Perfect (Platonic) solids (PS) along the edges, the two-point resistance between any pair of nodes was established in the 1990s by van Steenwijk using an elegant and efficient method. Using van Steenwijk's method, Moddy and Aravind subsequently derived the resistance values for two Archimedean and two Catalan solids. Here, with the same method, we derive the exact expression for the two-point resistance between any two nodes for resistor networks made of equal resistors placed along the edges of the thirteen Archimedean solids (AS). While the calculation remains elementary for the simplest AS, a dedicated method using computer assistance was developed for the Snub Cube, the Snub Dodecahedron and the three AS with three different rotation symmetries (the Great Rhombicuboctahedron, the Small Rhombicosidodecahedron and the Great Rhombicosidodecahedron). The largest resistance value (191/90) is obtained between the two opposite nodes of the Truncated Dodecahedron, and the second largest (42815/21114) is obtained between the two opposite nodes of the Great Rhombicosidodecahedron. The smallest resistance value (14137/38016) is obtained between some of the neighbouring nodes of the Snub Cube, whereas the resistance between neighbouring nodes of the Icosahedron (11/30) is slightly smaller. Some general symmetry relations between two-point resistances in AS networks are also derived, as well as some relations with two-point resistances in PS networks. The complete set of exact two-point resistance values for PS and AS networks can be used to check numerical codes or to evaluate the capacity of regular solids to provide appropriate models for given experimental situations.

Substantial terrestrial gas emissions, such as carbon dioxide (CO 2 ), are associated with active volcanoes and hydrothermal systems. However, while fundamental for the prediction of future activity, it remains difficult so far to determine the depth of the gas sources. Here we show how the combined measurement of CO 2 and radon-222 fluxes at the surface constrains the depth of degassing at two hydrothermal systems in geodynamically active contexts: Furnas Lake Fumarolic Field (FLFF, Azores, Portugal) with mantellic and volcano-magmatic CO 2 , and Syabru-Bensi Hydrothermal System (SBHS, Central Nepal) with metamorphic CO 2 . At both sites, radon fluxes reach exceptionally high values (> 10 Bq m −2 s −1 ) systematically associated with large CO 2 fluxes (> 10 kg m −2 day −1 ). The significant radon‒CO 2 fluxes correlation is well reproduced by an advective–diffusive model of radon transport, constrained by a thorough characterisation of radon sources. Estimates of degassing depth, 2580 ± 180 m at FLFF and 380 ± 20 m at SBHS, are compatible with known structures of both systems. Our approach demonstrates that radon‒CO 2 coupling is a powerful tool to ascertain gas sources and monitor active sites. The exceptionally high radon discharge from FLFF during quiescence (≈ 9 GBq day −1 ) suggests significant radon output from volcanoes worldwide, potentially affecting atmosphere ionisation and climate.