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Migration of natural hydrogen from deep-seated sources in the São Francisco Basin, Brazil

: Hydrogen gas is seeping from the sedimentary basin of São Franciso, Brazil. The seepages of H 2 are accompanied by helium whose isotopes reveal a strong crustal signature. Geophysical data indicates that this intra-cratonic basin is characterized by i) a relatively high geothermal gradient, ii) deep faults delineating a horst and graben structure and affecting the entire sedimentary sequence, iii) an archean to paleoproterozoïc basements enriched in radiogenic elements and displaying mafic and ultramafic units, and iv) a possible karstic reservoir located 400 m below the surface. The high geothermal gradient could be due to a thin lithosphere enriched in radiogenic elements, which can also contribute to a massive radiolysis process of water at depth, releasing an important amount of H 2 . Alternatively, ultramafic rocks that may have generated H 2 during their serpentinization are also documented in the basement. The seismic profiles show that the faults seen at the surface are deeply rooted in the basement, and can drain deep fluids to shallow depths in a short time scale. The carbonate reservoirs within the Bambuí group which forms the main part of the sedimentary layers are crossed by the fault system and represent good candidates for temporary H 2 accumulation zones. The formation by chemical dissolution of sinkholes located at 400 m depth might explain the presence of sub-circular depressions seen at the surface. These sinkholes might control the migration of gas from temporary storage reservoirs in the upper layer of the Bambuí formation to the surface. The very high fluxes of H 2 escaping out of these structures which have been recently documented are, however, in disagreement with the newly developed H 2 production model in the Precambrian continental crust. They either question the validity of these models or the measurement methodology.


Introduction
The natural production of molecular hydrogen (hereafter hydrogen or H2) has drawn increasing scientific attention due to the central role this molecule plays in fueling the deep subsurface biosphere or promoting the abiotic synthesis of organic molecules (Truche et al, 2020 [1]). Natural H2 sources may also represent a new attractive primary carbon free energy resource (Smith, 2002 [2]; Smith et al., 2005 [3]; Truche and Bazarkina, 2019 [4]; Gaucher, 2020 [5]). This latter industrial perspective has motivated recent H2 exploration studies in ophiolite, peralkaline, Precambrian shields and intracratonic geological settings (see recent review by Zgonnik, 2020 [6]).
Natural hydrogen (also known as native hydrogen) sources have been identified for several decades in seafloor hydrothermal vents, and hyperalkaline springs in ophiolite massifs. Serpentinization of ultramafic rocks is the water-rock interaction process responsible for H2 generation in these contexts (Neal and Stranger, 1983 [7]; Coveney et al., 1987 [8]; Abrajano et al., 1990 [9]; Charlou et al., 1996 [10]; Seewald et al., 2003 [11]). However, the recent discoveries of intracratonic H2 seepages and accumulations with no obvious link to an ultramafic formation challenge our current understanding of H2 production and fate in the crust (Larin et al., 2015 [12]; Zgonnik et al., 2015 [13], Prinzhofer et al., 2018 [14]). To date, there is no in-depth understanding of the hydrogen system from source to seep in these latter geological settings. When not fortuitous, as in the Taoudeni Basin in Mali (Prinzhofer et al., 2018 [14]), the discoveries of new H2 seepages were made thanks to the satellite detection of sub-circular soil depressions displaying vegetation anomalies, e.g. Borisoglebsk in Russia (Larin et al., 2015 [12]), Carolina Bay in the US (Zgonnik et al., 2015 [13]). These surface features are the only clues used to detect these H2 seepages. This limited understanding of the H2 systems, and this lack of robust pathfinders prevents the development of a methodic exploration strategy or resource assessment in these environments.
The São Francisco Basin belongs to this short list of intra-cratonic basins where H2 seepages have been discovered. Hydrogen gas is also vented from slight topographic depressions that are circular and barren of vegetation (Prinzhofer et al., 2019 [15]; Cathles & Prinzhofer, 2020 [16]). Also in the area of the São Francisco Basin, Flude et al. (2019 [17]) recorded H2 concentrations ranging from 50% to 80%, mostly accompanied with N2 and several percents of CH4, in the gas mixture from the head of exploration wells and natural gas seeps.
The São Francisco basin provides one of the first H2 case study where geological information can be collected with a sufficient level of details to provide the primary elemental bricks that may compose the H2 system in intra-cratonic basins. Here, we review the different layers of information that compose a supposed H2 system in this basin and lay the foundation of an H2 exploration guide.

The São Francisco basin
Located in the Brazilian states of Minas Gerais and Bahia, the São Francisco Craton presents rocks dating back from the Paleoarchean to the Cenozoic and several Precambrian sedimentary successions (Heilbron, 2017 [18]) ( Figure 1). The basement is mostly composed of Archean TTG (Tonalite-Trondhjemite-Granodiorite) rocks, granitoids and greenstones belts (Anhaeusser, 2014 [21]) together with Paleoproterozoic plutons and supra-crustal successions. This polycyclic substratum assembled during late Neoarchean times under high-grade metamorphic conditions, is intruded by late tectonic K-rich granites, mafic-ultramafic units, and mafic dikes (Teixeira et al., 2017 [22]). The Southern part of the São Francisco Craton consists of several gneiss complexes and greenstone belts from the Mineiro orogeny.
Along the southern edge of the São Franciso basin, the Bambuí Group fills a series of buried grabens. The Bambuí strata exposed along the area of interest in this study are generally flat lying and cover more than 300,000 km 2 . The entire basin is covered by a 450 to 1800 m-thick Neoproterozoic to Cambrian sedimentary successions, which are unconformably overlying the Archean-Paleoproterozoic basement (Delpomdor et al., 2020 [23]) (Figure 1b).

H2 seepages in the Bambuí Group in the Southern part of the São Francisco Basin
To constrain the magnitude of the H2 emission, a permanent monitoring station has been installed in a depression located 16 km North-North East of Santa Fé de Minas in the State of Mina Gerais (Prinzhofer et al., 2019 [15]) ( Figure 2). The recorded emission rates range from 7000 m 3 to 178 000 m 3 of H2 per day with H2 concentrations in the venting gas on the order of 1000 ppm (Cathles & Prinzhofer, 2020 [16]).
In the same area, various geophysical data acquisitions have been previously obtained from surface monitoring or exploration wells. Seismic [19]) and the triangle H2G corresponds to the gas seepage presented in Figure 2

A possible deep origin for H2
In addition to H2 venting at location H2G (Figure 2b), He concentrations (5 ppm above atmospheric reference value) measured by Prinzhofer et al. (2019 [15]) at a depth of 1 m, suggest a possible gas migration from deep horizons, where He is generated. Other analyses of gas sampled at the surface, from the head of exploration wells drilled in the São Francisco basin confirmed that, besides high concentrations of H2 (up to ~20%), He (>1%) is also present, in association with methanedominated hydrocarbons and N2 (Flude et al., 2019 [17]). Stable isotope data also suggest an abiotic origin for the methane, while He isotopes reveal a strong crustal signature ( 3 He/ 4 He < 0.02 R/Ra) (Flude et al., 2019 [17]). The nucleogenic 3 He from the decay of 6 Li could account for the 3 He/ 4 He ratios found in the head of exploration wells drilled in the São Francisco basin, i.e. close to R/Ra = 0.01 for an average granitic crust. Moreover, Neon isotope data also suggest the presence of an Archaean crustal component in the gases, indicating that a component of the gas has likely originated from the underlying crystalline basement, or within Archaean-derived sedimentary rocks (Flude et al., 2019 [17]).
The natural production of the continental H2 can be of various origins (Guélard et al., 2017 [26]). Studies in deep mines from the Witwatersrand basin (South Africa) and the Timmins basin (Ontario, Canada) have suggested a link between dissolved H2 and the radiolytic dissociation of water (Lin et al., 2005a [27]). In addition to radiolysis, hydration of ultramafic rocks coupled to H2O reduction could also be responsible for H2 generation in Precambrian shields (Goebel et al., 1984 [28]; Sherwood Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 July 2020 doi:10.20944/preprints202007.0571.v1 Lollar et al., 2014 [29]). For example, the serpentinization of the gabbroic basement has been proposed as the process responsible for H2 production in Kansas (Coveney et al., 1987 [8]). Radiolysis and serpentinization both require specific environments, which can be identified from geophysical and mineralogical investigations. Regarding the São Francisco basin, we detail these two possible processes of H2 formation in the following subsections.

Production of H2 by water radiolysis
Hydrogen production from water radiolysis requires the presence of radiogenic elements such as U, Th or K, which produce α, β and γ particles. When these particles collide with a water molecule, the latter will dissociate, forming a molecule of H2. Besides, if an α-particle gains electrons, it will become a stable 4 He atom leading to a specific R/Ra ratio as mentioned in the previous section.
Distinct Archean gneissic-granitic complexes characterize the Southern part of the São Francisco Craton basement. They constitute a medium-to high-grade metamorphic terrain that crops out from the Quadrilátero Ferrífero towards the west, and mainly comprises TTG rocks, migmatites and Krich granitic plutons (Teixeira et al., 2017 [22]). These rocks record deformational and metamorphic Archean episodes (from 2.55 Ga to over 3.3 Ga). It is known that the crystalline basement, rich in radiogenic elements and particularly this type of old basement Precambrian rocks, represent potentially fertile deep-seated sources of H2 (Parnell et al., 2017 [30]; Sherwood Lollar et al., 2014 [31]). For the São Francisco Craton, the measured concentrations of uranium (U), thorium (Th) and potassium (K) are presented in  In a coarse-grained rock like granite, beta-irradiation from K is more prone to affect intergranular fluid than the shorter-range alpha irradiation from U. Since K is also more pervasively distributed than U in granite, it can contribute to a larger scale radiolysis process.
Given the rather consistent range of U, Th, and K concentration reported in the São Francisco Basin, we could expect in this zone a production rate of radiolytic H2 in water ranging from 10 -8 to 10 -7 nmol.L -1 .s -1 (Lin et al., 2005b [35]). The methodology proposed by Sherwood Lollar et al. (2014 [31]) to estimate the contribution of the Precambrian continental crust to H2 production via radiolysis may then be applied to infer the regional H2 flux. The total radiolytic H2 production rate in water-filled fractures of the Precambrian crust was estimated to range from 0.16 to 0.47 × 10 11 mol.yr -1 for a corresponding surface area of 1.06 × 10 8 km 2 . Given the surface area of the Sao Francisco Basin of 300,000 km 2 , this corresponds to a H2 diffusive flux of 0.45 to 1.34 × 10 9 mol.yr -1 , i.e. 900 to 2,700 tons.yr -1 .

Production of H2 by serpentinisation
Serpentinization occurs when meteoric or oceanic waters alter ultramafic rocks originating from the Earth's mantle, such as peridotites and volcanic rocks. These rocks undergo changes in pressure and temperature conditions, which cause them to react in presence of water ( , we obtain a H2 production rate from hydration reactions of 0.57 to 5.14 × 10 9 mol.yr -1 , i.e. 1,100 to 10,300 tons.yr -1 . Favorable conditions to produce H2 by a serpentinization process would imply the presence of low-silica mafic and ultramafic rocks as well as an optimum temperature.

Presence of ultramafic rocks
From the seismic section which crosses the São Francisco Craton from East to West (Figure 1b  The basal Paranoá-Upper Espinhaço sequence consists of continental sediments and volcanic rocks associated with anorogenic plutons. Mesoproterozoic anorogenic magmatism associated with multiple rifting episodes might represent a manifestation of the Columbia supercontinent breakup, which started around 1.6 Ga and ended between 1.3 and 1.2 Ga (Reis et al., 2017a,b [42], [43]). The Espinhaço Supergroup is exposed on the East of the São Francisco Basin. The two basal formations of the Espinhaço sequence are composed of alluvial sandstones, conglomerates and pelites and form a ca. 300-m-thick of two coarsening-upward sequences. Despite the potential presence of K-rich alkaline volcanic and intrusives rocks (Chemal et al., 2012 [44]), this formation does not seem suitable for H2 production.
The basement rocks of the São Francisco basin are dominated by Archaean to Palaeoproterozoic migmatites, amphibolite to granulite-grade gneisses, and granite-greenstones (Teixeira et al., 2017 [22]). For example, the Rio Itapicuru low-grade supra-crustal greenstone belt has several lithostratigraphic subdivisions, including a basal mafic volcanic unit composed of massive and pillowed basaltic flows intercalated with chert, banded iron-formation, and carbonaceous shale (Oliveira et al., 2019 [45]). The banded iron-formation is mainly composed of oxidized iron Fe(III) forming a possible mix of hematite and magnetite, which can produce a strong magnetic anomaly (Pereira & Fuck, 2005 [46]) (purple zones in Figure 4) .  [47]). Note that "MG" stands for "Minas Gerais".
In this area, the Bouguer anomaly map exhibits predominantly negative anomalies ( Figure 5) which correlate with granitoids resulting from the crustal rejuvenation of the area, associated with partial re-fusion of the crust during past thermal events. This also suggests that major magmatic sequences affected the basement of the southern part of the São Franscico Basin, which is compatible with the magnetic anomalies ( Figure 4). Since the Quadrilátero Ferrífero (a mineral-rich region with extensive deposits of iron ore) and the "greenstone" belts present the same gravimetric signature, they Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 July 2020 doi:10.20944/preprints202007.0571.v1 could have the same origin (Pinto et al., 2007 [48]). Here again, the basement rock composition presents a high potential for H2 production.

Temperature ranges at depth
The potential presence of ultramafic rocks within the area of gas seepages, could suggest a serpentinization process, but to be active, this process would require a favorable range of temperatures. Crustal thermal models have been developed to examine the implications of the observed intra-cratonic variations in heat flow across the São Francisco Basin (Alexandrino et al., 2008 [49]). The thermal models take into consideration the variation of thermal conductivity with temperature. It is thus possible to get the temperature distribution calculated along a large profile that crosses the São Francisco Basin. It turns out that our zone of interest in the São Francisco Basin, exhibits an abnormally high heat flow value for a craton ( Figure 6). In the gas seepages zone (green ellipse in Figure 5), the temperature gradient is about 25°C/km (Alexandrino et al., 2008 [49]). The optimum temperature for serpentinization was found to be around 250-300°C with a maximum production of magnetite (Klein et al., 2013 [50]). However, some experimental data suggest that below 150°C, H2 can still be produced through the formation of Fe 3+ oxi-hydroxides (Mayhew et al., 2013 [52]; Miller et al., 2017 [53]), with the formation of H2 being possibly catalyzed by the surface of spinelstructure minerals occurring in ultramafic rocks. In such thermal conditions, H2 could be still produced at a low rate, at a depth lower than 6 km, near the gas seepage zone, and the optimum depth for its production would be at 10-12 km.

Possible H2 bubbling at depth
Once produced by fluid-rock interaction processes (oxidation) at depth, H2 can migrate as a dissolved component. The solubility of H2 in aqueous solutions is rather low and drops when T and P decrease when approaching the surface (Fig. 7d). The possible mechanism of H2 discharge, concentrating, and transport upward to the lower T-P where H2 is less reactive is solution boiling, i.e. formation of vapor phase coexisting with the liquid phase. The concentrations of H2 in vapors are many orders of magnitude higher than that in the liquid (Bazarkina et al., 2020). At the same time, rock permeability is much higher for gases-rich vapors than for salt-rich liquids. Bubble formation is a function of T, P, total salinity, and gas saturation. Thus, during fluid ascend upward to the lower T-P, gas bubbles formation is favorable (Fig. 7d). Periodicity of H2 emission at the surface reported by Prinzhofer et al. (2019) could be related to the kinetics of fluid-rock interaction at depth, further time-dependent bubble accumulation, and the final periodical ejections similar to those described in geysers.

Draining fault system in the São Francisco Basin
Deep faults serve as significant channels for deep fluids to ascend into and through the crust and the 3 He/ 4 He ratio can be used to estimate the flow rate of mantle fluids through the fault zones (Kennedy et al., 1997 [54]). Since the 3 He/ 4 He signature seems to be of crustal origin in the São Francisco basin (Flude et al., 2019 [17]), the migration path followed by the H2 mostly crosses the sedimentary cover without major changes of the ratio value. This weak interaction with the Bambuí sequences could be due to a high flow rate value along the faults. This could be possible if the faults form direct drains from the basement to the surface assuming a sufficiently high value of permeability.
Several interpretations of the available seismic data have been proposed for the fault systems basin is characterized by a system of major NW-SE faults. One could expect that the deep-rooted faults in the graben structures (Precambrian sequence), which have been reactivated during the Neoproterozoic Macaúbas basin-cycle, could cross most of the sedimentary formation. As a major fault system, they may control the drainage at all depth and delineate some morphological features observed on satellite imagery and digital elevation models (Reis et al., 2017b [43]). If these faults cross different geological layers, mainly shales, sandstones and limestones, their permeability values should range from 10 -19 -10 -15 m 2 if the fluid is not over-pressurized (Donzé et al., 2020 [55]). In case of over-pressurization but below a destabilization of the fault, the permeability could range from 10 -15 m 2 to 10 -13 m 2 . In terms of hydraulic conductivity for the water carrying the gas and neglecting the contribution of temperature, this corresponds to values ranging from 10 -8 m/s to 10 -6 m/s. This means that in the fastest case, the fluid could take less than 50 years to migrate across 1500 m of a shale layer.

Possible temporary shallow zones of H2 accumulation
The pressure variation observed at 1 m depth in the São Francisco basin (Prinzhofer et al., 2019 [15]), with a momentary increase in H2 pressure could indicate that the H2 systems are active. There is only a small temperature window where H2 may remain stable over a long time. This window corresponds to a T range where abiotic redox reactions such as thermochemical sulfate reduction or carbonate reduction (e.g. Fisher Tropsh type reaction) are slow (Truche et al., 2009 [56]), and where bacteria are inactive. Such a T range can be roughly approximated to be 100-200 °C. Since these temperature conditions are not met at shallow depth, H2 will probably not survive to long residence time. Despite this fact, previous studies of H2 seepages often indicate that the hydrogen systems are active, and transient accumulations of hydrogen at relatively shallow depth can be observed (Prinzhofer et al., 2018 [14], Goebel et al., 1984 [28]; Guélard et al., 2017 [26]). These observations may suggest a constant recharge of the aquifers by H2 flowing from deeper levels of the basin.
The circular depression where H2 seepage is observed (Figure 2b) could be related to a sinkhole structure resulting from a chemical dissolution process at depth. If so, these depressions will contain standing water connected with a ground-water reservoir contained in karst (De Carvalho et al., 2014 [57]). The presence of resistive carbonate and calcareous rocks was inferred from ~320 m to ~480 m followed by a layer of intercalated shales and sandstones (Solon et al., 2015 [20]). This carbonate layer which corresponds to the Lagoa do Jacaré carbonate layer, exhibits a potential karst system according to the outcrops located East of the São Francisco Basin (Dos Santos et al., 2018 [58]). Assuming a karst system at depth, this could imply a high level of porosity favorable for a massive storage volume of an aquifer. Since karst features are controlled by structural heterogeneities, such as faults and fractures, which influence fluid flow, they can provide preferential pathways for geofluids with the development of secondary porosity. This could agree with the fact that the circular depressions where H2 is venting are aligned along a major fault (Cathles & Prinzhofer, 2020 [16]).

Putting it all together: A potential H2 system within the São Francisco basin
The first key point is related to potential source areas, e.g. the presence of iron-rich rocks. The presence of Archean greenstone belts containing ultramafic rocks represents excellent H2-producing zones either via serpentinization, or water radiolysis. Magnetic ( Figure 4) and Bouguer ( Figure 5) anomalies are compatible with the presence of ultramafic rock producing H2. Temperature conditions also seem favorable for the serpentinization process: with a temperature gradient of 25°C/km (Alexandrino et al., 2008 [49]), the optimum range of temperature would be expected at a depth of 10 km, with possible lower rate processes at a shallower depth.
The second key point is the structural/tectonic context and the presence of faults deeply rooted in the basements capable of draining a potential deep and scattered source. All interpretations of the seismic profile of the zone of interest, suggest the presence of deep faults following the graben structures Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 July 2020 doi:10.20944/preprints202007.0571.v1 ( Figure 3): they can be able to drain hydrogen produced at depth where the Pressure-Temperature conditions are optimal. Some interpretations suggest that some of these faults could cross the entire sedimentary sequence (Coelho et al., 2008 [40]), producing gas seepages directly at the surface. Some others predict that these faults could reach some potential shallow carbonated reservoirs (Romeiro-Silva & Zalán, 2005 [24]). These deep faults could also only reach the unconformity zone which composes the boundary between the sedimentary basin and basement (Alkmim & Martins-Neto, 2012 [41]).
The third key point concerns the storage areas (i.e. reservoirs) of H2 at depth. As mentioned previously, the interface between the basement rocks and the sedimentary layers could represent a potential zone of accumulation. The interface is composed of the Macaúbas and the Espinhaço formations. The Macaúbas sequence is made up of sandstones, pelites, diamictites, carbonates, basic volcanic rocks, and metamorphosed banded iron formations (Alkmim et al., 2012 [41]) whereas the Espinhaço formation is a quartz-arenite dominated package. The presence of the Paranoá-Upper Espinhaço quartzite, which is tectonically uplifted, can facilitate the occurrence of sandstone reservoirs with appreciable permeability and porosity. Thus, potential reservoir rocks could be found among siliciclastics of the Macaúbas-Paranoá Megasequence (Solon et al., 2015 [20]).
An interesting characteristic of the deep topography is that the seepage zone H2G is located near the apex of the basement rock in the central part of the basin (see Figure 3). As the H2 charged fluid reaches the Macaúbas/Espinhaço formations, it migrates along the unconformity toward this highest point before escaping to the surface in the green seepage zone (Figure 2). On its way to the surface, H2 can also be temporarily trapped in the Sete Lagoas formation and at a shallower depth, inside Lagoa do Jacaré formation. The permeability value of the Sete Lagoas Larst aquifer formation is estimated to range between 10 -14 m 2 and 10 -9 m 2 (Galvão et al., 2015 [59]). As for the Lagoa do Jacaré formation very low permeability and porosity values were found in the Petrobras well 1-RF-1-MG. The presence of faults, possibly connecting all these reservoirs with the surface could explain the apparent structural control on the distribution of the known gas seepages (Curto et al., 2012 [19]). Nevertheless, the presence of sinkholes in the H2G seepage area suggests the existence of a shallow local karst formation, which could constitute a temporary reservoir for H2.
Thus, surface seepages may be either in connection with the source rock or with intermediate leaking reservoirs since these two configurations are present in this area. A summary of H2 migration from sources to seeps in the São Francisco basin is presented in Figure 7.

Discussing the H2 production from radiolysis and hydration reactions in the São Francisco Basin
Combining the H2 production rate from water radiolysis and hydration reaction assessed in the previous sections, we obtain an estimate of 1.02 to 6.48 × 10 9 mol.yr -1 H2 production i.e. 2,000 to 13,000 tons.yr -1 (Table 3). Prinzhofer et al. (2019 [15]) estimated the local flux rate in the H2G seepage zone (Figure 2b) to be around 7000 and 178,000 m 3 per day. At a temperature of 21°C and a pressure of 1 atm, these values correspond to 584 and 14,850 kg per day, respectively. Extrapolating these values for a year, the H2 flux would be around 213 to 5400 tons.yr -1 (Table 3). In comparison, on the Mid-Atlantic Ridge (MAR), the total H2 discharge at the Rainbow hydrothermal field is estimated to be ~10 8 moles H2 per year, i.e. 202 tons.yr -1 (Charlou et al., 2010) (Table 3). At a larger scale, the H2 flux from all high-temperature basaltic vents along the MAR has been estimated at ~10 9 ─10 10 mol.yr -1 , whereas the H2 flux from high-temperature ultramafic vents along the Mid-Oceanic Ridge (MOR) has been estimated at ~10 10 ─10 11 mol.yr -1 (  [31]) for the Precambrian continental lithosphere, the maximum H2 production rate from the basement rocks of the São Francisco Basin is only 2.4 times higher than the production of only one sinkhole of 500 m in diameter (H2G zone). This latter H2 venting site would represent in itself from 0.5 to 1.5% of the global estimated H2 production from the Precambrian continental Lithosphere. This Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 July 2020 doi:10.20944/preprints202007.0571.v1 sinkhole alone is also supposed to produce more H2 (up to 25 times) than the entire Rainbow hydrothermal field. Therefore, the currently documented very high fluxes of H2 escaping out of the H2G structure are inconsistent with the newly developed H2 production models or with the estimations made for some major sub-seafloor hydrothermal vents. They either question the validity of these models or the measurement methodology.