# The low permeability of the Earth's Precambrian crust

Grant Ferguson, Jennifer Mcintosh, Oliver Warr, Barbara Sherwood Lollar

► To cite this version:

Grant Ferguson, Jennifer Mcintosh, Oliver Warr, Barbara Sherwood Lollar. The low permeability of the Earth's Precambrian crust. Communications Earth & Environment, 2023, 4, 363, p. 1-14. 10.1038/s43247-023-00968-2. insu-04462241

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# The low permeability of the Earth's Precambrian crust

Grant Ferguson, Jennifer Mcintosh, Oliver Warr, Barbara Sherwood Lollar

► To cite this version:

Grant Ferguson, Jennifer Mcintosh, Oliver Warr, Barbara Sherwood Lollar. The low permeability of the Earth's Precambrian crust. Communications Earth & Environment, 2023, 4, 363, p. 1-14. 10.1038/s43247-023-00968-2. insu-04462241

HAL Id: insu-04462241

https://insu.hal.science/insu-04462241v1

Submitted on 17 Feb 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# The low permeability of the Earth's Precambrian crust

Grant Ferguson<fnref n="1" />,²,³,<fnref n="4" />✉, Jennifer McIntosh<fnref n="1" />,², Oliver Warr<fnref n="1" />,⁵ & Barbara Sherwood Lollar⁶,⁷

The large volume of deep groundwater in the Precambrian crust has only recently been understood to be relatively hydrogeologically isolated from the rest of the hydrologic cycle. The paucity of permeability measurements in Precambrian crust below 1.3 km is a barrier to modeling fluid flow and solute transport in these low porosity and permeability deep environments. Whether permeability-depth relationships derived from measurements shallower than 1.3 km can be extended to greater depths in unclear. Similarly, application of a widely-used permeability-depth relationship from prograde metamorphic and geothermal systems to deep Precambrian rocks may not be appropriate. Here, we constrain permeabilities for Precambrian crust to depths of 3.3 km based on fluid residence times estimated from noble gas analyses. Our analysis shows no statistically significant relationship between permeability and depth where only samples below 1 km are considered, challenging previous assumptions of exponential decay. Additionally, we show that estimated permeabilities at depths >1 km are at least an order of magnitude lower than some previous estimates and possibly much lower. As a consequence, water and solute fluxes at these depths will be extremely limited, imposing important controls on elemental cycling, distribution of subsurface microbial life and connections with the near-surface water cycle.

<footnote n="1">¹Department of Civil, Geological and Environmental Engineering, University of Saskatchewan, Saskatoon, Canada. ²Department of Hydrology and Atmospheric Sciences, University of Arizona, Tucson, USA. ³School of Environment and Sustainability, University of Saskatchewan, Saskatoon, Canada.</footnote>

<footnote n="4">⁴Global Institute for Water Security, University of Saskatchewan, Saskatoon, Canada. ⁵Department of Earth and Environmental Sciences, University of Ottawa, Ottawa, Canada. ⁶Department of Earth Sciences, University of Toronto, Toronto, Canada. ⁷Institut de Physique du Globe de Paris (IPGP), Université Paris Cité, Paris, France. ✉email: grant.ferguson@usask.ca</footnote>
<figure><img src="image_2.png" /></figure>

# The low permeability of the Earth's Precambrian crust

Grant Ferguson<fnref n="1" />,²,³,<fnref n="4" />✉, Jennifer McIntosh<fnref n="1" />,², Oliver Warr<fnref n="1" />,⁵ & Barbara Sherwood Lollar⁶,⁷

The large volume of deep groundwater in the Precambrian crust has only recently been understood to be relatively hydrogeologically isolated from the rest of the hydrologic cycle. The paucity of permeability measurements in Precambrian crust below 1.3 km is a barrier to modeling fluid flow and solute transport in these low porosity and permeability deep environments. Whether permeability-depth relationships derived from measurements shallower than 1.3 km can be extended to greater depths in unclear. Similarly, application of a widely-used permeability-depth relationship from prograde metamorphic and geothermal systems to deep Precambrian rocks may not be appropriate. Here, we constrain permeabilities for Precambrian crust to depths of 3.3 km based on fluid residence times estimated from noble gas analyses. Our analysis shows no statistically significant relationship between permeability and depth where only samples below 1 km are considered, challenging previous assumptions of exponential decay. Additionally, we show that estimated permeabilities at depths >1 km are at least an order of magnitude lower than some previous estimates and possibly much lower. As a consequence, water and solute fluxes at these depths will be extremely limited, imposing important controls on elemental cycling, distribution of subsurface microbial life and connections with the near-surface water cycle.

<footnote n="1">¹Department of Civil, Geological and Environmental Engineering, University of Saskatchewan, Saskatoon, Canada. ²Department of Hydrology and Atmospheric Sciences, University of Arizona, Tucson, USA. ³School of Environment and Sustainability, University of Saskatchewan, Saskatoon, Canada.</footnote>

<footnote n="4">⁴Global Institute for Water Security, University of Saskatchewan, Saskatoon, Canada. ⁵Department of Earth and Environmental Sciences, University of Ottawa, Ottawa, Canada. ⁶Department of Earth Sciences, University of Toronto, Toronto, Canada. ⁷Institut de Physique du Globe de Paris (IPGP), Université Paris Cité, Paris, France. ✉email: grant.ferguson@usask.ca</footnote>
Precambrian crust, which makes up ~72% of the Earth's continents by area¹, has been estimated to host between ~8.5 and 13 million km³ of groundwater²,³. This deep store of mostly saline fluids accounts for 20 to 30% of total continental groundwater. Estimates of groundwater residence times in Precambrian rocks (Figs. 1 and 2a), can exceed 1 billion years²,⁴⁻⁶, with the longest residence times found in Archean age rocks. These deep and ancient groundwaters are estimated to contain a substantial portion of the Earth's biomass, with microbial activity found to depths of up to 2-3 km⁷⁻¹². The degree of hydrogeologic —and associated geochemical—isolation from near-surface environments exerts control on the habitability, abundance, and diversity of subsurface microbial life⁶,⁹,¹¹⁻¹³. At these depths, life is isolated from the photosphere and increasingly dependent on chemosynthesis. The supply of electron donors and acceptors exerts and important control on subsurface microbial activity¹¹, which is influenced by permeability.

The crystalline rocks of the Earth's Precambrian crust are inherently a low permeability hydrogeologic regime where fluid flow occurs primarily via fractures. Despite representing a significant proportion of the crust globally (Fig. 1), detailed permeability measurements are few, particularly in deep (>1 km) crystalline rock¹⁴⁻¹⁷. Permeability values are necessary to constrain fluid and solute fluxes in the crust, to define the degree of interconnectivity that might occur between subsurface biomes, and to provide insights into the distribution and connectivity of fracture networks in deep Precambrian rock.

## Previous permeability-depth relationships

Permeability typically decreases with depth due to tectonic stresses, compaction, diagenesis and weathering¹⁴,¹⁸,¹⁹ and permeability-depth relationships have been derived for a variety of environments using various approaches (Table 1). A prime example of such a relationship was generated using data from geothermal and metamorphic environments¹⁵,²⁰ (Fig. 2b), which extended down to depths of 40 km, including the 10 km thickness of brittle crust nearest to the ground surface. Permeabilities of geothermal systems were estimated by determining the amount of fluid flow required to produce enough advection to replicate observed temperature distributions. In contrast, in metamorphic systems, permeabilities were estimated using the time-integrated fluid flux required to produce the observed amount of mineralization. The resulting permeability-depth relationship for geothermal and metamorphic systems has been widely applied to

studies of generic regional flow systems²¹, geomechanics of the crust²², circulation of deep meteoric fluids²³, biogeochemical cycles²⁴ and, following scaling for gravity, Martian hydrogeology²⁵.

Ingebritsen and Manning²⁰ noted that stable tectonic crystalline rock settings ('cratons') where a significant proportion of the world's oldest rocks, including those of Archean age, are located, are likely to have even lower permeability values than the models they developed for areas of tectonic or magmatic activity would predict. We note that there are exceptions to cratons being stable, such as the Precambrian basement in the Yellowstone region, where the Wyoming Craton appears to have become more permeable due to magmatic activity²⁶. More recent studies, based on compilations and regression analysis of permeability estimates from a range of in situ and laboratory hydraulic testing techniques, support the idea of lower permeability values in stable crystalline rock¹⁴ and batholiths down to depths of 1.3 km (Fig. 2b). Evaluating whether those relationships hold at greater depths is difficult with only one hydraulic test beyond a depth of 1.3 km available in those databases; a value of 10⁻¹⁹ m² measured over a depth interval of 4.3–9.0 km in the Kola Superdeep Borehole in Russia²⁷.

These previous attempts to estimate permeability are inadequate to understand the past behaviour of fluids in Precambrian rocks. Numerical models have used a wide range of permeability values for these settings, from as low as 10⁻²¹ for Atikokan, Canada²⁸ to 10⁻¹⁶ m² for Fennoscandia²⁹. A continental-scale simulation of the Canadian Shield that used a value of 10⁻¹⁷ m² predicted residence times of 800 ka at a depth of 3.7 km near Kidd Creek, Canada for the mid Pleistocene Epoch and much younger ages under current conditions following flushing during inflow of subglacial meltwater³⁰. These values are inconsistent with residence times of 400–1700 Ma estimated from noble gas measurements²,⁴, suggesting that the permeabilities used in the model were far too high.

## Constraining permeability with residence time estimates

To constrain the permeability of stable crystalline rocks beyond 1.3 km, we carried out a novel approach to estimate in situ permeabilities by incorporating noble gas-based residence times of groundwaters in Precambrian rocks at depths from the ground surface to 3.3 km²,⁴,⁵,³¹ (Fig. 2a). Radiogenic noble gases, such as ⁴He and ⁴⁰Ar, are produced due to radiogenic reactions in the crust and accumulate in groundwaters³²⁻³⁴. From measured

<figure><img src="image_3.png" /><figcaption>**Fig. 1** Global distribution of Archean cratons (exposed and buried)⁸¹ and Proterozoic rock⁸². Locations of noble gas-derived residence time data used to estimate permeabilities in this study²,⁴,³¹,³⁶⁻⁴³ are shown within these geologic regions⁸².</figcaption></figure>
Precambrian crust, which makes up ~72% of the Earth's continents by area¹, has been estimated to host between ~8.5 and 13 million km³ of groundwater²,³. This deep store of mostly saline fluids accounts for 20 to 30% of total continental groundwater. Estimates of groundwater residence times in Precambrian rocks (Figs. 1 and 2a), can exceed 1 billion years²,⁴⁻⁶, with the longest residence times found in Archean age rocks. These deep and ancient groundwaters are estimated to contain a substantial portion of the Earth's biomass, with microbial activity found to depths of up to 2-3 km⁷⁻¹². The degree of hydrogeologic —and associated geochemical—isolation from near-surface environments exerts control on the habitability, abundance, and diversity of subsurface microbial life⁶,⁹,¹¹⁻¹³. At these depths, life is isolated from the photosphere and increasingly dependent on chemosynthesis. The supply of electron donors and acceptors exerts and important control on subsurface microbial activity¹¹, which is influenced by permeability.

The crystalline rocks of the Earth's Precambrian crust are inherently a low permeability hydrogeologic regime where fluid flow occurs primarily via fractures. Despite representing a significant proportion of the crust globally (Fig. 1), detailed permeability measurements are few, particularly in deep (>1 km) crystalline rock¹⁴⁻¹⁷. Permeability values are necessary to constrain fluid and solute fluxes in the crust, to define the degree of interconnectivity that might occur between subsurface biomes, and to provide insights into the distribution and connectivity of fracture networks in deep Precambrian rock.

## Previous permeability-depth relationships

Permeability typically decreases with depth due to tectonic stresses, compaction, diagenesis and weathering¹⁴,¹⁸,¹⁹ and permeability-depth relationships have been derived for a variety of environments using various approaches (Table 1). A prime example of such a relationship was generated using data from geothermal and metamorphic environments¹⁵,²⁰ (Fig. 2b), which extended down to depths of 40 km, including the 10 km thickness of brittle crust nearest to the ground surface. Permeabilities of geothermal systems were estimated by determining the amount of fluid flow required to produce enough advection to replicate observed temperature distributions. In contrast, in metamorphic systems, permeabilities were estimated using the time-integrated fluid flux required to produce the observed amount of mineralization. The resulting permeability-depth relationship for geothermal and metamorphic systems has been widely applied to

studies of generic regional flow systems²¹, geomechanics of the crust²², circulation of deep meteoric fluids²³, biogeochemical cycles²⁴ and, following scaling for gravity, Martian hydrogeology²⁵.

Ingebritsen and Manning²⁰ noted that stable tectonic crystalline rock settings ('cratons') where a significant proportion of the world's oldest rocks, including those of Archean age, are located, are likely to have even lower permeability values than the models they developed for areas of tectonic or magmatic activity would predict. We note that there are exceptions to cratons being stable, such as the Precambrian basement in the Yellowstone region, where the Wyoming Craton appears to have become more permeable due to magmatic activity²⁶. More recent studies, based on compilations and regression analysis of permeability estimates from a range of in situ and laboratory hydraulic testing techniques, support the idea of lower permeability values in stable crystalline rock¹⁴ and batholiths down to depths of 1.3 km (Fig. 2b). Evaluating whether those relationships hold at greater depths is difficult with only one hydraulic test beyond a depth of 1.3 km available in those databases; a value of 10⁻¹⁹ m² measured over a depth interval of 4.3–9.0 km in the Kola Superdeep Borehole in Russia²⁷.

These previous attempts to estimate permeability are inadequate to understand the past behaviour of fluids in Precambrian rocks. Numerical models have used a wide range of permeability values for these settings, from as low as 10⁻²¹ for Atikokan, Canada²⁸ to 10⁻¹⁶ m² for Fennoscandia²⁹. A continental-scale simulation of the Canadian Shield that used a value of 10⁻¹⁷ m² predicted residence times of 800 ka at a depth of 3.7 km near Kidd Creek, Canada for the mid Pleistocene Epoch and much younger ages under current conditions following flushing during inflow of subglacial meltwater³⁰. These values are inconsistent with residence times of 400–1700 Ma estimated from noble gas measurements²,⁴, suggesting that the permeabilities used in the model were far too high.

## Constraining permeability with residence time estimates

To constrain the permeability of stable crystalline rocks beyond 1.3 km, we carried out a novel approach to estimate in situ permeabilities by incorporating noble gas-based residence times of groundwaters in Precambrian rocks at depths from the ground surface to 3.3 km²,⁴,⁵,³¹ (Fig. 2a). Radiogenic noble gases, such as ⁴He and ⁴⁰Ar, are produced due to radiogenic reactions in the crust and accumulate in groundwaters³²⁻³⁴. From measured

<figure><img src="image_3.png" /><figcaption>**Fig. 1** Global distribution of Archean cratons (exposed and buried)⁸¹ and Proterozoic rock⁸². Locations of noble gas-derived residence time data used to estimate permeabilities in this study²,⁴,³¹,³⁶⁻⁴³ are shown within these geologic regions⁸².</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Fig. 2** Residence times estimated from noble gases provide constraints on the distribution of permeability with depth. a Fracture water residence times estimated from noble gas analyses from Warr et al.⁵ and references therein show an increase with depth. b Permeability estimates from groundwater residence times are lower than those expected from Ingebritsen and Manning's²⁰ permeability-depth relationship and those for stable provinces found by Achtziger-Zupančić et al.¹⁴ but higher than the relationship found by Snowdon et al.¹⁶. Error bars in both figures are based on the minimum and maximum residence times where provided by previous studies.</figcaption></figure>

<table><caption>**Table 1** Permeability-depth relationships derived from previous studies.</caption><thead><tr><th>Environment</th><th>Permeability-depth relationship</th><th>Method</th><th>Maximum depth (km)</th></tr></thead><tbody><tr><td>Prograde metamorphic<sup>15,20</sup></td><td>log k = -14 - 3.2 log z</td><td>Geothermal and metamorphic analysis</td><td>28.4</td></tr><tr><td>Tectonically active continental crust (dynamic)<sup>66</sup></td><td>log k = -11.5 - 3.2 log z</td><td>Metamorphic and seismic analysis</td><td>38</td></tr><tr><td>Upper crust<sup>80</sup></td><td>log k = -25.4 + 13.9(1 + z)<sup>-0.25</sup></td><td>Various</td><td>5</td></tr><tr><td>Crystalline rock (various environments)<sup>14</sup></td><td>log k = -16.26 - 1.53 log z</td><td>Hydraulic testing</td><td>1.0 (measurements below 1.0 km not used in regression)</td></tr><tr><td>Stable shields and platforms<sup>14</sup></td><td>log k = -16.12 - 1.35 log z</td><td>Hydraulic testing</td><td>1.0</td></tr><tr><td>Canadian Shield (equivalent porous medium)</td><td>log k = -21 + (5.55/[1 + (z/0.151)<sup>4.2</sup>]<sup>0.1919</sup></td><td>Hydraulic testing</td><td>1.3 (22 measurements below 1 km)</td></tr></tbody></table>

concentrations of uranium, thorium, and potassium, rates of production of these noble gases can be determined. Combining these with measured concentrations of the noble gases in the groundwater phase can provide effective means to estimate residence times beyond those provided by unstable radioisotopes such as ³H, ¹⁴C and ⁸¹Kr³⁵. Analysis of the noble gas content of fracture fluids sampled from Canada, Fennoscandia and South Africa have revealed mean fluid residence times ranging from a few thousand to over one billion years²,⁴,³¹,³⁶⁻⁴³.

The maximum distance groundwater can travel since exposure to the atmosphere is limited by the size of topography-driven flow systems, which is defined by distance between recharge and discharge points as determined by the distribution of hydraulic head. We estimate permeabilities by applying the working assumption that the flow system size provides an upper constraint to permeability because water found within a regional system will have travelled a smaller distance than the maximum flowline length and is defined by hydraulic divides. In many cases, the distance travelled will be considerably smaller, particularly where other mechanisms of emplacement, such as burial or tectonics, were involved. While some continental-scale groundwater models have predicted hydraulic divides that indicate the presence of flow systems extending over 100 s of km in Precambrian rock²⁹,⁴⁴, these are at odds with smaller scale models that have incorporated

more geological complexity and local site geologic and hydrogeologic details. Groundwater models produced for Whiteshell⁴⁵,⁴⁶ and Atikokan⁴⁷ in the Canadian Shield, Foresmark⁴⁸,⁴⁹ and Okiluoto⁵⁰ in the Fennoscandian Shield, and Moab Khotsong, South Africa⁵¹ have all found that local topography and surface water bodies along with geologic structures exert strong controls on the hydraulic divides that delineate groundwater flow systems. Flow system extents were typically on the order of 10–25 km and similar in size to HydroBASINS level 12 catchment size⁵², which we use to estimate the size of topography-driven flow systems at sites where noble gases have been analysed (see “Methods” section).

We acknowledge that the flow system geometries may have varied over time due to deposition and erosion of sediments overlying cratons⁵³, along with folding and faulting⁴. However, the Precambrian rocks themselves have been subject to slow erosion rates over much of their history, suggesting that flow system size may not have changed dramatically for long periods of time⁵⁴. Samples taken from these systems will have travelled less than the full length of the system. Forces other than topographic-relief may also be important (e.g. compaction, tectonic stresses, dewatering reactions, free convection), but those drivers are generally less important and limited in both time and space in terms of developing hydraulic gradients⁵⁵. We estimate
<figure><img src="image_4.png" /><figcaption>**Fig. 2** Residence times estimated from noble gases provide constraints on the distribution of permeability with depth. a Fracture water residence times estimated from noble gas analyses from Warr et al.⁵ and references therein show an increase with depth. b Permeability estimates from groundwater residence times are lower than those expected from Ingebritsen and Manning's²⁰ permeability-depth relationship and those for stable provinces found by Achtziger-Zupančić et al.¹⁴ but higher than the relationship found by Snowdon et al.¹⁶. Error bars in both figures are based on the minimum and maximum residence times where provided by previous studies.</figcaption></figure>

<table><caption>**Table 1** Permeability-depth relationships derived from previous studies.</caption><thead><tr><th>Environment</th><th>Permeability-depth relationship</th><th>Method</th><th>Maximum depth (km)</th></tr></thead><tbody><tr><td>Prograde metamorphic<sup>15,20</sup></td><td>log k = -14 - 3.2 log z</td><td>Geothermal and metamorphic analysis</td><td>28.4</td></tr><tr><td>Tectonically active continental crust (dynamic)<sup>66</sup></td><td>log k = -11.5 - 3.2 log z</td><td>Metamorphic and seismic analysis</td><td>38</td></tr><tr><td>Upper crust<sup>80</sup></td><td>log k = -25.4 + 13.9(1 + z)<sup>-0.25</sup></td><td>Various</td><td>5</td></tr><tr><td>Crystalline rock (various environments)<sup>14</sup></td><td>log k = -16.26 - 1.53 log z</td><td>Hydraulic testing</td><td>1.0 (measurements below 1.0 km not used in regression)</td></tr><tr><td>Stable shields and platforms<sup>14</sup></td><td>log k = -16.12 - 1.35 log z</td><td>Hydraulic testing</td><td>1.0</td></tr><tr><td>Canadian Shield (equivalent porous medium)</td><td>log k = -21 + (5.55/[1 + (z/0.151)<sup>4.2</sup>]<sup>0.1919</sup></td><td>Hydraulic testing</td><td>1.3 (22 measurements below 1 km)</td></tr></tbody></table>

concentrations of uranium, thorium, and potassium, rates of production of these noble gases can be determined. Combining these with measured concentrations of the noble gases in the groundwater phase can provide effective means to estimate residence times beyond those provided by unstable radioisotopes such as ³H, ¹⁴C and ⁸¹Kr³⁵. Analysis of the noble gas content of fracture fluids sampled from Canada, Fennoscandia and South Africa have revealed mean fluid residence times ranging from a few thousand to over one billion years²,⁴,³¹,³⁶⁻⁴³.

The maximum distance groundwater can travel since exposure to the atmosphere is limited by the size of topography-driven flow systems, which is defined by distance between recharge and discharge points as determined by the distribution of hydraulic head. We estimate permeabilities by applying the working assumption that the flow system size provides an upper constraint to permeability because water found within a regional system will have travelled a smaller distance than the maximum flowline length and is defined by hydraulic divides. In many cases, the distance travelled will be considerably smaller, particularly where other mechanisms of emplacement, such as burial or tectonics, were involved. While some continental-scale groundwater models have predicted hydraulic divides that indicate the presence of flow systems extending over 100 s of km in Precambrian rock²⁹,⁴⁴, these are at odds with smaller scale models that have incorporated

more geological complexity and local site geologic and hydrogeologic details. Groundwater models produced for Whiteshell⁴⁵,⁴⁶ and Atikokan⁴⁷ in the Canadian Shield, Foresmark⁴⁸,⁴⁹ and Okiluoto⁵⁰ in the Fennoscandian Shield, and Moab Khotsong, South Africa⁵¹ have all found that local topography and surface water bodies along with geologic structures exert strong controls on the hydraulic divides that delineate groundwater flow systems. Flow system extents were typically on the order of 10–25 km and similar in size to HydroBASINS level 12 catchment size⁵², which we use to estimate the size of topography-driven flow systems at sites where noble gases have been analysed (see “Methods” section).

We acknowledge that the flow system geometries may have varied over time due to deposition and erosion of sediments overlying cratons⁵³, along with folding and faulting⁴. However, the Precambrian rocks themselves have been subject to slow erosion rates over much of their history, suggesting that flow system size may not have changed dramatically for long periods of time⁵⁴. Samples taken from these systems will have travelled less than the full length of the system. Forces other than topographic-relief may also be important (e.g. compaction, tectonic stresses, dewatering reactions, free convection), but those drivers are generally less important and limited in both time and space in terms of developing hydraulic gradients⁵⁵. We estimate
<figure><img src="image_5.png" /><figcaption>Fig. 3 The permeability estimates in this study are consistent with the conceptual model of an upper zone characterized by decreasing permeability with depth that contains lower TDS, higher Eh waters with stable water isotope (δ²H and δ¹⁸O) values that plot near the Global Meteoric Water Line (GMWL)⁸³; and a lower zone characterized by low permeability without a strong relationship with depth that contains higher TDS, lower Eh waters that plot to the left of the GMWL. The upper zone hosts protobacteria-dominated communities, while the lower zone tends to contain Firmicutes-dominated communities¹⁰,³⁶.</figcaption></figure>

permeabilities by assuming that these fluids have travelled <14.7–30.0 km based on the dimensions of catchments in Precambrian rocks, which are similar to flow system dimensions used in previous analysis of permeabilities in metamorphic and geothermal environments¹⁵ (see “Methods” section). This distance provides an upper bound for flow system size in Precambrian rocks, where flow systems will likely be shorter and could be driven by factors other than topography.

The permeabilities estimated from the noble gas residence times have the following relationship with depth (Fig. 2):

$$ \log k = -17.07 - 1.44 \log z \quad (1) $$

where k is permeability in m² and z is depth in km. This linear regression has an R² value of 0.579, which is significant at a p-value of 0.001. The vast majority of the locations examined here are from Archean settings, with only one sample from Sweden and one from Finland both in Proterozoic rock. Whether Archean cratons and other Precambrian rocks of Proterozoic age that reflect a broader range of structural features, such as rifts, accretionary complexes, and/or metasediments, have significantly different permeability-depth relationships is beyond the scope of this paper, as permeability measurements or estimates for a diverse global set of Proterozoic settings are even fewer than for the Archean systems.

Equation [1] produces permeability values that are over 2 orders of magnitude lower than the Ingebritsen and Manning (1999) curve at a depth of 3 km. Our log k estimates would increase by 2.0 if either hydraulic gradients were decreased by approximately two orders of magnitude or flow systems were increased by an equal amount. These higher permeabilities are unlikely because longer flowlines are uncommon in Precambrian rock due to the limited geologic continuity and the hydraulic gradients of 4.7 × 10⁻⁴ to 1.4 × 10⁻³ used here are below or near the global median value of 1.3 × 10⁻²⁵. It is plausible these noble gas samples were collected in systems that had higher hydraulic gradients in the geologic past, perhaps approaching 0.1⁵⁶, which would result in a decrease in our estimated permeabilities by approximately an order of magnitude. There is also considerable evidence that solute transport in deep Precambrian rock is dominated by diffusion⁶,⁵⁷,⁵⁸, which indicates that permeabilities <10⁻²⁰ m² are common⁵⁹ (Fig. 2).

This study suggests that permeabilities are at least one order of magnitude lower than those predicted by the regression of in situ

hydraulic tests compiled by Achtziger-Zupancic et al.¹⁴ (Table 1) for stable crust (i.e. cratons). Those tests likely had support volumes on length scales of a few m up to a few 100 m⁶⁰ and may not reflect the effect of discontinuities in the fracture network on solute transport that would affect groundwater ages. In order for the permeabilities found here to match those found from hydraulic testing, flow system lengths would need to increase by an order of magnitude, which is inconsistent with detailed studies of the regional scale flow systems in cratons²⁸,⁴⁵,⁴⁷⁻⁵¹. These results could also be achieved if porosity was increased to ~10%, which is inconsistent with measurements for cratons⁵⁸, or if hydraulic gradients were reduced by an order of magnitude. However, it should also be noted that the median log k for depths >1 km in the Achtziger-Zupancic et al.¹⁴ database is ~19.0, which is similar to those found in the analysis presented here. Data at those depths were not considered in the regression analysis for cratons and shields in that study.

It is instructive to compare the results obtained here with those for batholiths (large masses of relatively homogeneous intrusive igneous rock)¹⁶ (Table 1; Fig. 2), which likely reflect the lower-end of permeability relative to Precambrian rock as a whole. The upper limit of permeabilities estimated here are approximately two orders of magnitude greater than those predicted by a relationship proposed for the equivalent porous media values for batholiths. The higher permeabilities appear to be plausible given that environments considered here include settings that with higher degrees of fracturing such as ore deposits⁴,⁴², areas within impact structures²,⁶ and fracture zones within batholiths¹⁶. Reducing flow system lengths to ~100 m could bring the estimates here into closer agreement with the relationship for batholiths. However, if the flow system lengths used here are approximately correct, unrealistically low porosity (~0.01%)⁶¹ or excessively high hydraulic gradients, approaching 1, would need to be present.

Permeability is elevated in the upper 1 km in Precambrian rock, which supports the concept that enhanced permeability in shallow (<1 km) crystalline rocks is largely a function of weathering⁶²,⁶³ along with unloading and tectonics (Fig. 3). This shallow zone to ~1 km also corresponds to the approximate depth where meteoric and paleometeoric waters are typically found to penetrate in the Canadian Shield, Fennoscandian Shield and Witwatersrand Basin⁵,²³. Groundwater flow is more active in the upper 1 km and limited by permeability at greater depths.
<figure><img src="image_5.png" /><figcaption>Fig. 3 The permeability estimates in this study are consistent with the conceptual model of an upper zone characterized by decreasing permeability with depth that contains lower TDS, higher Eh waters with stable water isotope (δ²H and δ¹⁸O) values that plot near the Global Meteoric Water Line (GMWL)⁸³; and a lower zone characterized by low permeability without a strong relationship with depth that contains higher TDS, lower Eh waters that plot to the left of the GMWL. The upper zone hosts protobacteria-dominated communities, while the lower zone tends to contain Firmicutes-dominated communities¹⁰,³⁶.</figcaption></figure>

permeabilities by assuming that these fluids have travelled <14.7–30.0 km based on the dimensions of catchments in Precambrian rocks, which are similar to flow system dimensions used in previous analysis of permeabilities in metamorphic and geothermal environments¹⁵ (see “Methods” section). This distance provides an upper bound for flow system size in Precambrian rocks, where flow systems will likely be shorter and could be driven by factors other than topography.

The permeabilities estimated from the noble gas residence times have the following relationship with depth (Fig. 2):

$$ \log k = -17.07 - 1.44 \log z \quad (1) $$

where k is permeability in m² and z is depth in km. This linear regression has an R² value of 0.579, which is significant at a p-value of 0.001. The vast majority of the locations examined here are from Archean settings, with only one sample from Sweden and one from Finland both in Proterozoic rock. Whether Archean cratons and other Precambrian rocks of Proterozoic age that reflect a broader range of structural features, such as rifts, accretionary complexes, and/or metasediments, have significantly different permeability-depth relationships is beyond the scope of this paper, as permeability measurements or estimates for a diverse global set of Proterozoic settings are even fewer than for the Archean systems.

Equation [1] produces permeability values that are over 2 orders of magnitude lower than the Ingebritsen and Manning (1999) curve at a depth of 3 km. Our log k estimates would increase by 2.0 if either hydraulic gradients were decreased by approximately two orders of magnitude or flow systems were increased by an equal amount. These higher permeabilities are unlikely because longer flowlines are uncommon in Precambrian rock due to the limited geologic continuity and the hydraulic gradients of 4.7 × 10⁻⁴ to 1.4 × 10⁻³ used here are below or near the global median value of 1.3 × 10⁻²⁵. It is plausible these noble gas samples were collected in systems that had higher hydraulic gradients in the geologic past, perhaps approaching 0.1⁵⁶, which would result in a decrease in our estimated permeabilities by approximately an order of magnitude. There is also considerable evidence that solute transport in deep Precambrian rock is dominated by diffusion⁶,⁵⁷,⁵⁸, which indicates that permeabilities <10⁻²⁰ m² are common⁵⁹ (Fig. 2).

This study suggests that permeabilities are at least one order of magnitude lower than those predicted by the regression of in situ

hydraulic tests compiled by Achtziger-Zupancic et al.¹⁴ (Table 1) for stable crust (i.e. cratons). Those tests likely had support volumes on length scales of a few m up to a few 100 m⁶⁰ and may not reflect the effect of discontinuities in the fracture network on solute transport that would affect groundwater ages. In order for the permeabilities found here to match those found from hydraulic testing, flow system lengths would need to increase by an order of magnitude, which is inconsistent with detailed studies of the regional scale flow systems in cratons²⁸,⁴⁵,⁴⁷⁻⁵¹. These results could also be achieved if porosity was increased to ~10%, which is inconsistent with measurements for cratons⁵⁸, or if hydraulic gradients were reduced by an order of magnitude. However, it should also be noted that the median log k for depths >1 km in the Achtziger-Zupancic et al.¹⁴ database is ~19.0, which is similar to those found in the analysis presented here. Data at those depths were not considered in the regression analysis for cratons and shields in that study.

It is instructive to compare the results obtained here with those for batholiths (large masses of relatively homogeneous intrusive igneous rock)¹⁶ (Table 1; Fig. 2), which likely reflect the lower-end of permeability relative to Precambrian rock as a whole. The upper limit of permeabilities estimated here are approximately two orders of magnitude greater than those predicted by a relationship proposed for the equivalent porous media values for batholiths. The higher permeabilities appear to be plausible given that environments considered here include settings that with higher degrees of fracturing such as ore deposits⁴,⁴², areas within impact structures²,⁶ and fracture zones within batholiths¹⁶. Reducing flow system lengths to ~100 m could bring the estimates here into closer agreement with the relationship for batholiths. However, if the flow system lengths used here are approximately correct, unrealistically low porosity (~0.01%)⁶¹ or excessively high hydraulic gradients, approaching 1, would need to be present.

Permeability is elevated in the upper 1 km in Precambrian rock, which supports the concept that enhanced permeability in shallow (<1 km) crystalline rocks is largely a function of weathering⁶²,⁶³ along with unloading and tectonics (Fig. 3). This shallow zone to ~1 km also corresponds to the approximate depth where meteoric and paleometeoric waters are typically found to penetrate in the Canadian Shield, Fennoscandian Shield and Witwatersrand Basin⁵,²³. Groundwater flow is more active in the upper 1 km and limited by permeability at greater depths.
Likely the most important outcome of this exercise is when
only data deeper than this 1 km zone is considered, there is no
significant correlation between estimated permeability and depth
(log k and log z, respectively) at the *p* = 0.1 level. Permeability
below 10 km has also been shown to have a weak relationship
with depth, although that has attributable due to its position
below the brittle-ductile transition²⁰ and does not explain the lack
of relationship between 1.0 and 3.3 km. In sedimentary envir-
onments, permeabilities generally decrease from the ground
surface to depths of several km due to compaction and
diagenesis¹⁹,⁶⁴ but a similar trend is not obvious in Precambrian
rock below 1 km. Any trends related to geomechanical and geo-
chemical processes that are a simple function of depth could be
overwhelmed by the long and often complex burial and exhu-
mation histories of Precambrian rocks⁵³. The apparent increase
in permeability from Canada to Fennoscandia to South Africa
hints at the importance of differences in the geological histories of
these settings that promise to be important issues for future
studies. The presence of younger groundwaters at depth in the
Witwatersrand Basin, and in the Sudbury Impact Crater on the
Canadian Shield, may be the result of the high degree of frac-
turing related to the impact events forming both basins²,⁶. The
widespread presence of paleometeoric waters at depth in the
Fennoscandian Shield⁶⁵ suggests the presence of interconnected
fracture networks and elevated permeability. There is also the
possibility that these fluids were emplaced in the past when
permeabilities were elevated¹⁷,⁶⁶, which would make current
permeabilities lower than those estimated here.

These estimated permeability values overestimate actual values
because the transit distances of groundwater in Precambrian rock
are likely substantially less than the full length of the topography-
driven flow system and associated flow system lengths used here
(Fig. 3). Sleep and Zoback⁶⁷ proposed that 1 km long flow sys-
tems in fractured Precambrian rock could support sufficient
geochemical fluxes to sustain microbial activity. If this length was
used rather than full flow system length, estimated permeabilities
would be approximately an order of magnitude lower than the
upper estimates presented here, reinforcing the overall conclu-
sion. The noble gas analyses determine the period of hydro-
geologic isolation from atmospheric recharge events, but it is
important to note that these fracture fluids are the net product of
groundwater circulation, original syn-depositional fluids, and
subsequent fluid history and water-rock reaction⁴,⁵. Hence burial,
negative buoyancy, and tectonic forcing may have been important
mechanisms that would result in shorter transit distances and
lower permeability estimates, as would the inherently hydro-
geologically discontinuous nature of sparsely fractured rock.

The overall coherence between the He-Ne-Ar-Xe derived noble
gas residence times at each site support a model of hydrogeologic
isolation². However, Warr et al.⁶ recently demonstrated that these
settings actually represent a spectrum from being fully isolated to
fully open to diffusive transport. At sufficiently low diffusion
coefficients (10⁻¹⁵ m²/s), there will be no appreciable loss of any
noble gases⁵⁷. At slightly higher diffusion coefficients, noticeable
diffusive transport of He and Ne will occur, while Ar, Kr, and
Xe are retained⁶,⁵⁷. Relating these low rates of diffusion to per-
meability is not straightforward. While laboratory testing of core
samples has found correlations between permeability and diffu-
sion coefficients⁶⁸⁻⁷⁰, there is no universally agreed upon rela-
tionship between these two parameters. The lowest diffusion
coefficients found in the laboratory studies were a few orders of
magnitude higher than those required to prevent differential
diffusion of noble gases and suggest permeabilities <10⁻²¹ m².
For porosities and hydraulic gradients similar to those estimated
in this study, fluids could migrate distances up to a few 100 m
over a time period of a billion years, keeping them isolated from

the surface. If the relationships found by Kuva et al.⁶⁹ holds for
lower diffusion coefficients, bulk permeabilities in Precambrian
crust could be as low as 10⁻²⁵ m². The focus in these studies is on
diffusive transport, as advective transport would be limited to
distances of a few cm over billion-year time scales at these low
permeabilities. Manning and Ingebritsen¹⁵ suggested a transition
between diffusion-dominated environments and advection-
dominated environments occurs at a permeability of 10⁻²⁰ m².

The permeabilities estimated here, along with previous findings
on diffusion rates of noble gases, bring into question the results of
prior numerical simulations of groundwater flow in Precambrian
rock at depths >1 km. Simulations that used higher permeabilities
will have overestimated flow rates and underestimated residence
times, potentially by a few orders of magnitude.

Permeability and life in the deep subsurface

Studies of the deep subsurface biosphere have to date suggested
there is evidence for a depth component associated with micro-
bial communities, with Proteobacteria-dominated communities at
shallower depths of ~1 km¹⁰, while Firmicutes-dominated com-
munities are thought to be more common at depths >1 km. This
pattern has been observed in South Africa¹⁰,³⁶,⁷¹ and
Fennoscandia⁷²,⁷³, while patterns in Canada are not yet apparent
due to a sample bias to date towards very deep sites alone. These
biome boundaries correspond to a general geochemical transition,
with changes observed in total dissolved solids (TDS), redox
conditions (Eh) and a general transition from meteoric and
paleometeoric waters to shield-type brines with δ²H and δ¹⁸O
values that plot to the left of the global meteoric water line
(GMWL)⁵,³⁷,⁷⁴. This shift in stable water isotope values at depths
>1 km is the result of water-rock reactions, including oxygen
isotopic exchange between waters associated with hydrothermal/
metamorphic activity and the host rocks over very long (Ma+) time
periods⁵,⁷⁵. The position of this transition zone approxi-
mately corresponds to the transition from the upper more
permeable zone of the Precambrian crust to lower permeability
environments at depth (Fig. 3). The reduced permeability at these
depths restricts fluid and solute fluxes and transport is likely
dominated by diffusion on a regional scale, and fracture-
controlled fluid flow only locally⁷⁶,⁷⁷. These lower fluxes can
affect cycling and migration of elements in the subsurface related
to microbial life (e.g. CHNOPS) and have been proposed to exert
an important control on the distribution and composition of
microbial communities⁷⁴,⁷⁶,⁷⁸.

Conclusions

Residence times estimated from noble gas analyses of deep
groundwaters suggest that the permeability of Precambrian crust
in stable cratons is at least ~2 orders of magnitude lower than
previous estimates from prograde metamorphic and geothermal
environments and an order of magnitude lower than a relation-
ship based on hydraulic tests in the upper 1 km of Precambrian
crust¹⁴ and possibly approaching values measured in batholiths¹⁶.
Importantly, permeability estimates based on noble gas data
measured between 1.0 and 3.3 km no longer show a statistically
significant correlation with depth. The limited diffusion rates in
these environments imply that the permeabilities are likely even
lower than those estimated here, and considerably more depen-
dent on lithologic setting and local geological history, including
events such as impact fracturing, than previously considered.

The low permeabilities of Precambrian rock suggest that
microbiological processes in this deep biosphere are more likely
to be limited by fluid and solute fluxes and more dependent on
diffusive transport than they are in other environments. As a
consequence, microbial communities at depths in Precambrian
Likely the most important outcome of this exercise is when
only data deeper than this 1 km zone is considered, there is no
significant correlation between estimated permeability and depth
(log k and log z, respectively) at the *p* = 0.1 level. Permeability
below 10 km has also been shown to have a weak relationship
with depth, although that has attributable due to its position
below the brittle-ductile transition²⁰ and does not explain the lack
of relationship between 1.0 and 3.3 km. In sedimentary envir-
onments, permeabilities generally decrease from the ground
surface to depths of several km due to compaction and
diagenesis¹⁹,⁶⁴ but a similar trend is not obvious in Precambrian
rock below 1 km. Any trends related to geomechanical and geo-
chemical processes that are a simple function of depth could be
overwhelmed by the long and often complex burial and exhu-
mation histories of Precambrian rocks⁵³. The apparent increase
in permeability from Canada to Fennoscandia to South Africa
hints at the importance of differences in the geological histories of
these settings that promise to be important issues for future
studies. The presence of younger groundwaters at depth in the
Witwatersrand Basin, and in the Sudbury Impact Crater on the
Canadian Shield, may be the result of the high degree of frac-
turing related to the impact events forming both basins²,⁶. The
widespread presence of paleometeoric waters at depth in the
Fennoscandian Shield⁶⁵ suggests the presence of interconnected
fracture networks and elevated permeability. There is also the
possibility that these fluids were emplaced in the past when
permeabilities were elevated¹⁷,⁶⁶, which would make current
permeabilities lower than those estimated here.

These estimated permeability values overestimate actual values
because the transit distances of groundwater in Precambrian rock
are likely substantially less than the full length of the topography-
driven flow system and associated flow system lengths used here
(Fig. 3). Sleep and Zoback⁶⁷ proposed that 1 km long flow sys-
tems in fractured Precambrian rock could support sufficient
geochemical fluxes to sustain microbial activity. If this length was
used rather than full flow system length, estimated permeabilities
would be approximately an order of magnitude lower than the
upper estimates presented here, reinforcing the overall conclu-
sion. The noble gas analyses determine the period of hydro-
geologic isolation from atmospheric recharge events, but it is
important to note that these fracture fluids are the net product of
groundwater circulation, original syn-depositional fluids, and
subsequent fluid history and water-rock reaction⁴,⁵. Hence burial,
negative buoyancy, and tectonic forcing may have been important
mechanisms that would result in shorter transit distances and
lower permeability estimates, as would the inherently hydro-
geologically discontinuous nature of sparsely fractured rock.

The overall coherence between the He-Ne-Ar-Xe derived noble
gas residence times at each site support a model of hydrogeologic
isolation². However, Warr et al.⁶ recently demonstrated that these
settings actually represent a spectrum from being fully isolated to
fully open to diffusive transport. At sufficiently low diffusion
coefficients (10⁻¹⁵ m²/s), there will be no appreciable loss of any
noble gases⁵⁷. At slightly higher diffusion coefficients, noticeable
diffusive transport of He and Ne will occur, while Ar, Kr, and
Xe are retained⁶,⁵⁷. Relating these low rates of diffusion to per-
meability is not straightforward. While laboratory testing of core
samples has found correlations between permeability and diffu-
sion coefficients⁶⁸⁻⁷⁰, there is no universally agreed upon rela-
tionship between these two parameters. The lowest diffusion
coefficients found in the laboratory studies were a few orders of
magnitude higher than those required to prevent differential
diffusion of noble gases and suggest permeabilities <10⁻²¹ m².
For porosities and hydraulic gradients similar to those estimated
in this study, fluids could migrate distances up to a few 100 m
over a time period of a billion years, keeping them isolated from

the surface. If the relationships found by Kuva et al.⁶⁹ holds for
lower diffusion coefficients, bulk permeabilities in Precambrian
crust could be as low as 10⁻²⁵ m². The focus in these studies is on
diffusive transport, as advective transport would be limited to
distances of a few cm over billion-year time scales at these low
permeabilities. Manning and Ingebritsen¹⁵ suggested a transition
between diffusion-dominated environments and advection-
dominated environments occurs at a permeability of 10⁻²⁰ m².

The permeabilities estimated here, along with previous findings
on diffusion rates of noble gases, bring into question the results of
prior numerical simulations of groundwater flow in Precambrian
rock at depths >1 km. Simulations that used higher permeabilities
will have overestimated flow rates and underestimated residence
times, potentially by a few orders of magnitude.

Permeability and life in the deep subsurface

Studies of the deep subsurface biosphere have to date suggested
there is evidence for a depth component associated with micro-
bial communities, with Proteobacteria-dominated communities at
shallower depths of ~1 km¹⁰, while Firmicutes-dominated com-
munities are thought to be more common at depths >1 km. This
pattern has been observed in South Africa¹⁰,³⁶,⁷¹ and
Fennoscandia⁷²,⁷³, while patterns in Canada are not yet apparent
due to a sample bias to date towards very deep sites alone. These
biome boundaries correspond to a general geochemical transition,
with changes observed in total dissolved solids (TDS), redox
conditions (Eh) and a general transition from meteoric and
paleometeoric waters to shield-type brines with δ²H and δ¹⁸O
values that plot to the left of the global meteoric water line
(GMWL)⁵,³⁷,⁷⁴. This shift in stable water isotope values at depths
>1 km is the result of water-rock reactions, including oxygen
isotopic exchange between waters associated with hydrothermal/
metamorphic activity and the host rocks over very long (Ma+) time
periods⁵,⁷⁵. The position of this transition zone approxi-
mately corresponds to the transition from the upper more
permeable zone of the Precambrian crust to lower permeability
environments at depth (Fig. 3). The reduced permeability at these
depths restricts fluid and solute fluxes and transport is likely
dominated by diffusion on a regional scale, and fracture-
controlled fluid flow only locally⁷⁶,⁷⁷. These lower fluxes can
affect cycling and migration of elements in the subsurface related
to microbial life (e.g. CHNOPS) and have been proposed to exert
an important control on the distribution and composition of
microbial communities⁷⁴,⁷⁶,⁷⁸.

Conclusions

Residence times estimated from noble gas analyses of deep
groundwaters suggest that the permeability of Precambrian crust
in stable cratons is at least ~2 orders of magnitude lower than
previous estimates from prograde metamorphic and geothermal
environments and an order of magnitude lower than a relation-
ship based on hydraulic tests in the upper 1 km of Precambrian
crust¹⁴ and possibly approaching values measured in batholiths¹⁶.
Importantly, permeability estimates based on noble gas data
measured between 1.0 and 3.3 km no longer show a statistically
significant correlation with depth. The limited diffusion rates in
these environments imply that the permeabilities are likely even
lower than those estimated here, and considerably more depen-
dent on lithologic setting and local geological history, including
events such as impact fracturing, than previously considered.

The low permeabilities of Precambrian rock suggest that
microbiological processes in this deep biosphere are more likely
to be limited by fluid and solute fluxes and more dependent on
diffusive transport than they are in other environments. As a
consequence, microbial communities at depths in Precambrian
rock will likely be more isolated than in other geological environments and, as a consequence, will be slower to respond (if at all) to changes in surface and near-surface Earth system processes.

## Methods

Groundwater residence time ($\tau$) is calculated with:

$$ \tau = \frac{L}{\frac{kpg}{\mu\eta} \nabla h} \qquad (2) $$

where $L$ is flow system length, $k$ is permeability, $\rho$ is fluid density, $\mu$ is viscosity, $\eta$ is porosity, and $\nabla h$ is the hydraulic gradient (Fig. 1). Here, we rearrange this equation to estimate permeability ($k$):

$$ k = \frac{L \nabla h \mu \eta}{\tau \rho g} \qquad (3) $$

$L$ was determined from the maximum length of the Hydro-BASINS level 12 polygons⁵² containing the sample site. This length was similar to flow system lengths found in detailed studies of the flow systems at a subset of the sample sites, including Whiteshell⁴⁵,⁴⁶, Okiluoto⁵⁰, Foresmark⁴⁸,⁴⁹ and Moab Khotsong⁵¹, which found that flow systems are affected by local topography and surface water bodies and bound by geological structures on scales of ~10–25 km. This length is also similar to previous treatment of flow system dimensions in metamorphic and geothermal environments¹⁵. Hydraulic gradients were estimated using $L$ from HydroBASINS and the minimum and maximum topographies for those polygons⁷⁹. We use the residence times, depths and porosities from various noble gas studies (Supplementary Data 1). Where porosities were not available in those studies, we use a porosity of 1% based on a number of previous studies that have reviewed porosity in Precambrian rocks²,³,¹⁷,⁵⁶,⁵⁸.

## Data availability

Noble gas and porosity data compiled in this study are available in Supplementary Data 1 and can be accessed at https://doi.org/10.6084/m9.fishgate.23713047.

Received: 11 January 2023; Accepted: 17 August 2023; Published online: 13 September 2023

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39. Lippmann-Pipke, J. et al. Neon identifies two billion year old fluid component in Kaapvaal Craton. *Chem. Geol.* **283**, 287–296 (2011).

40. Kietäväinen, R., Ahonen, L., Kukkonen, I. T., Niedermann, S. & Wiersberg, T. Noble gas residence times of saline waters within crystalline bedrock, Outokumpu Deep Drill Hole, Finland. *Geochim. Cosmochim. Acta* **145**, 159–174 (2014).
rock will likely be more isolated than in other geological environments and, as a consequence, will be slower to respond (if at all) to changes in surface and near-surface Earth system processes.

## Methods

Groundwater residence time ($\tau$) is calculated with:

$$ \tau = \frac{L}{\frac{kpg}{\mu\eta} \nabla h} \qquad (2) $$

where $L$ is flow system length, $k$ is permeability, $\rho$ is fluid density, $\mu$ is viscosity, $\eta$ is porosity, and $\nabla h$ is the hydraulic gradient (Fig. 1). Here, we rearrange this equation to estimate permeability ($k$):

$$ k = \frac{L \nabla h \mu \eta}{\tau \rho g} \qquad (3) $$

$L$ was determined from the maximum length of the HydroBASINS level 12 polygons⁵² containing the sample site. This length was similar to flow system lengths found in detailed studies of the flow systems at a subset of the sample sites, including Whiteshell⁴⁵,⁴⁶, Okiluoto⁵⁰, Foresmark⁴⁸,⁴⁹ and Moab Khotsong⁵¹, which found that flow systems are affected by local topography and surface water bodies and bound by geological structures on scales of ~10–25 km. This length is also similar to previous treatment of flow system dimensions in metamorphic and geothermal environments¹⁵. Hydraulic gradients were estimated using $L$ from HydroBASINS and the minimum and maximum topographies for those polygons⁷⁹. We use the residence times, depths and porosities from various noble gas studies (Supplementary Data 1). Where porosities were not available in those studies, we use a porosity of 1% based on a number of previous studies that have reviewed porosity in Precambrian rocks²,³,¹⁷,⁵⁶,⁵⁸.

## Data availability

Noble gas and porosity data compiled in this study are available in Supplementary Data 1 and can be accessed at https://doi.org/10.6084/m9.fishshare.23713047.

Received: 11 January 2023; Accepted: 17 August 2023; Published online: 13 September 2023

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## Acknowledgements

The authors are grateful for comments from three reviewers. Peter Higgins and Jeffrey McDonnell provided insightful feedback on earlier versions of this manuscript. This research was funded by a Natural Sciences and Engineering Research Council of Canada Discovery Grant to Ferguson, a Global Water Futures grant and a US National Science Foundation - Frontier Research in Earth Sciences (#2120733) to McIntosh and Ferguson. Research funding for B.S.L. and O.W. came from the Nuclear Waste Management Organisation (NWMO), with additional funding provided by the Natural Sciences and Engineering Research Council of Canada Discovery and NFREF grants awarded to B.S.L. B.S.L. is a Director of the CIFAR Earth 4D Subsurface Science and Exploration program and J.C.M. is a fellow of the same program.

## Author contributions

G.F. and J.C.M. conceived of this study and led the writing of this paper. Methodology was developed by G.F., who also performed calculations. Calculations were performed G.F. and data was compiled by G.F. and O.W. G.F., J.C.M., O.W. and B.S.L. contributed to writing and editing.

## Competing interests

All authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s43247-023-00968-2.

**Correspondence** and requests for materials should be addressed to Grant Ferguson.

**Peer review information** *Communications Earth & Environment* thanks David Bakaert, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editors: Teng Wang and Joe Aslin.

**Reprints and permission information** is available at http://www.nature.com/reprints

**Publisher's note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
41. Bottomley, D. J., Clark, I. D., Battye, N. & Kotzer, T. Geochemical and isotopic evidence for a genetic link between Canadian Shield brines, dolomitization in the Western Canada Sedimentary Basin, and Devonian calcium-chloridic seawater. *Can. J. Earth Sci.* **42**, 2059–2071 (2005).

42. Greene, S., Battye, N., Clark, I., Kotzer, T. & Bottomley, D. Canadian Shield brine from the Con Mine, Yellowknife, NT, Canada: Noble gas evidence for an evaporated Palaeozoic seawater origin mixed with glacial meltwater and Holocene recharge. *Geochim. Cosmochim. Acta* **72**, 4008–4019 (2008).

43. Trinchero, P., Delos, A., Molinero, J., Dentz, M. & Pitkänen, P. Understanding and modelling dissolved gas transport in the bedrock of three Fennoscandian sites. *J. Hydrol.*, **512**, 506–517 (2014).

44. Lemieux, J., Sudicky, E., Peltier, W. & Tarasov, L. Dynamics of groundwater recharge and seepage over the Canadian landscape during the Wisconsinian glaciation. *J. Geophys. Res., Earth Surface (2003–2012)* **113**, (2008).

45. Sykes, J. F., Normani, S. D., Jensen, M. R. & Sudicky, E. A. Regional-scale groundwater flow in a Canadian Shield setting. *Can. Geotech. J.* **46**, 813–827 (2009).

46. Ophori, D. U. et al. Revised model of regional groundwater flow in the Whiteshell Research Area. (1996).

47. Ophori, D. U. & Chan, T. Regional groundwater flow in the Atikokan Research Area: Model development and calibration (1996).

48. Hartley, L. & Joyce, S. Approaches and algorithms for groundwater flow modeling in support of site investigations and safety assessment of the Forsmark site, Sweden. *J. Hydrol.* **500**, 200–216 (2013).

49. Joyce, S., Hartley, L., Applegate, D., Hoek, J. & Jackson, P. Multi-scale groundwater flow modeling during temperate climate conditions for the safety assessment of the proposed high-level nuclear waste repository site at Forsmark, Sweden. *Hydrogeol. J.* **22**, 1233 (2014).

50. Blessent, D., Therrien, R. & Gable, C. W. Large-scale numerical simulation of groundwater flow and solute transport in discretely-fractured crystalline bedrock. *Adv. Water Resour.* **34**, 1539–1552 (2011).

51. Mengistu, H. A., Demlie, M. B., Abiye, T. A., Xu, Y. & Kanyere, T. Conceptual hydrogeological and numerical groundwater flow modelling around the Moab Khutsong deep gold mine, South Africa. *Groundwater Sustain. Dev.* **9**, 100266 (2019).

52. Lehner, B. & Grill, G. Global river hydrography and network routing: baseline data and new approaches to study the world's large river systems. *Hydrol. Process.* **27**, 2171–2186 (2013).

53. Drake, H. & Reiners, P. W. Thermochronologic perspectives on the deep-time evolution of the deep biosphere. *Proc. Natl Acad. Sci. USA* **118**, e2109609118 (2021).

54. Flowers, R. M., Bowring, S. A. & Reiners, P. W. Low long-term erosion rates and extreme continental stability documented by ancient (U-Th)/He dates. *Geology* **34**, 925–928 (2006).

55. Neuzil, C. E. Groundwater flow in low-permeability environments. *Water Resour. Res.* **22**, 1163–1195 (1986).

56. Gleeson, T., Befus, K. M., Jasechko, S., Luijendijk, E. & Cardenas, M. B. The global volume and distribution of modern groundwater. *Nat. Geosci.* **9**, 161–167 (2016).

57. Ballentine, C. J. & Burnard, P. G. Production, release and transport of noble gases in the continental crust. *Rev. Mineral. Geochem.* **47**, 481–538 (2002).

58. Sherwood Lollar, B., Onstott, T. C., Lacrampe-Couloume, G. & Ballentine, C. The contribution of the Precambrian continental lithosphere to global H₂ production. *Nature* **516**, 379–382 (2014).

59. Ingebritsen, S. E., Sanford, W. E. & Neuzil, C. Groundwater in Geologic Processes (Cambridge University Press, 2006).

60. Clauser, C. Permeability of crystalline rocks. *Eos, Trans. Am. Geophys. Union* **73**, 233–238 (1992).

61. Manning, C. E. Fluids of the lower crust: deep is different. *Annu. Rev. Earth Planet. Sci.* **46**, 67–97 (2018).

62. Lachassagne, P., Wyns, R. & Dewandel, B. The fracture permeability of hard rock aquifers is due neither to tectonics, nor to unloading, but to weathering processes. *Terra Nova* **23**, 145–161 (2011).

63. Lachassagne, P., Dewandel, B. & Wyns, R. Hydrogeology of weathered crystalline/hard-rock aquifers—guidelines for the operational survey and management of their groundwater resources. *Hydrogeol. J.* **29**, 2561–2594 (2021).

64. Bjorlykke, K. Relationships between depositional environments, burial history and rock properties. Some principal aspects of diagenetic process in sedimentary basins. *Sediment. Geol.* **301**, 1–14 (2014).

65. Osterholz, H. et al. Terrigenous dissolved organic matter persists in the energy-limited deep groundwaters of the Fennoscandian Shield. *Nat. Commun.* **13**, 4837 (2022).

66. Ingebritsen, S. E. & Manning, C. Permeability of the continental crust: dynamic variations inferred from seismicity and metamorphism. *Geofluids* **10**, 193–205 (2010).

67. Sleep, N. H. & Zoback, M. D. Did earthquakes keep the early crust habitable? *Astrobiology* **7**, 1023–1032 (2007).

68. Reimus, P. W. & Callahan, T. J. Matrix diffusion rates in fractured volcanic rocks at the Nevada Test Site: evidence for a dominant influence of effective fracture apertures. *Water Resour. Res.* **43**, W07421 (2007).

69. Kuva, J. et al. Gas phase measurements of porosity, diffusion coefficient, and permeability in rock samples from Olkiluoto bedrock, Finland. *Transport Porous Med.* **107**, 187–204 (2015).

70. Boving, T. B. & Grathwohl, P. Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity. *J. Contam. Hydrol.* **53**, 85–100 (2001).

71. Labonté, J. M. et al. Single cell genomics indicates horizontal gene transfer and viral infections in a deep subsurface Firmicutes population. *Front. Microbiol.* **6**, 349 (2015).

72. Itävaara, M. et al. Characterization of bacterial diversity to a depth of 1500 m in the Outokumpu deep borehole, Fennoscandian Shield. *FEMS Microbiol. Ecol.* **77**, 295–309 (2011).

73. Purkamo, L. et al. Microbial co-occurrence patterns in deep Precambrian bedrock fracture fluids. *Biogeosciences* **13**, 3091–3108 (2016).

74. Ward, J. A. et al. Microbial hydrocarbon gases in the Witwatersrand Basin, South Africa: implications for the deep biosphere. *Geochim. Cosmochim. Acta* **68**, 3239–3250 (2004).

75. Frape, S. K., Blyth, A., Blomqvist, R., McNutt, R. H. & Gascoyne, M. Deep fluids in the continents: II. Crystalline rocks. *Treatise Geochem.* **5**, 605 (2003).

76. Sherwood Lollar, B. et al. Unravelling abiogenic and biogenic sources of methane in the Earth's deep subsurface. *Chem. Geol.* **226**, 328–339 (2006).

77. Sherwood Lollar, B. et al. Hydrogeologic controls on episodic H2 release from Precambrian fractured rocks—energy for deep subsurface life on Earth and Mars. *Astrobiology* **7**, 971–986 (2007).

78. Simkus, D. N. et al. Variations in microbial carbon sources and cycling in the deep continental subsurface. *Geochim. Cosmochim. Acta* **173**, 264–283 (2016).

79. USGS. USGS 30 ARC-second Global Elevation Data, GTOPO30. https://doi.org/10.5065/A1Z4-EE71 (1997).

80. Kuang, X. & Jiao, J. J. An integrated permeability-depth model for Earth's crust. *Geophys. Res. Lett.* **41**, 7539–7545 (2014).

81. Hasterok, D. et al. New maps of global geological provinces and tectonic plates. *Earth-Sci. Rev.* **231**, 104069 (2022).

82. Chorlton, L. B. Generalized geology of the world: bedrock domains and major faults in GIS format. *Geological Survey of Canada, Open File 5529*, (2007).

83. Craig, H. Isotopic variations in meteoric waters. *Science* **133**, 1702–1703 (1961).

## Acknowledgements

The authors are grateful for comments from three reviewers. Peter Higgins and Jeffrey McDonnell provided insightful feedback on earlier versions of this manuscript. This research was funded by a Natural Sciences and Engineering Research Council of Canada Discovery Grant to Ferguson, a Global Water Futures grant and a US National Science Foundation - Frontier Research in Earth Sciences (#2120733) to McIntosh and Ferguson. Research funding for B.S.L. and O.W. came from the Nuclear Waste Management Organisation (NWMO), with additional funding provided by the Natural Sciences and Engineering Research Council of Canada Discovery and NFREF grants awarded to B.S.L. B.S.L. is a Director of the CIFAR Earth 4D Subsurface Science and Exploration program and J.C.M. is a fellow of the same program.

## Author contributions

G.F. and J.C.M. conceived of this study and led the writing of this paper. Methodology was developed by G.F., who also performed calculations. Calculations were performed G.F. and data was compiled by G.F. and O.W. G.F., J.C.M., O.W. and B.S.L. contributed to writing and editing.

## Competing interests

All authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s43247-023-00968-2.

**Correspondence** and requests for materials should be addressed to Grant Ferguson.

**Peer review information** *Communications Earth & Environment* thanks David Bakaert, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editors: Teng Wang and Joe Aslin.

**Reprints and permission information** is available at http://www.nature.com/reprints

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© The Author(s) 2023
<figure><img src="image_6.png" /></figure>

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

© The Author(s) 2023