Antarctic Geothermal Heat Flow, Crustal Conductivity and Heat Production Inferred From Seismological Data

Geothermal heat flow is a key parameter in governing ice dynamics, via its influence on basal melt and sliding, englacial rheology, and erosion. It is expected to exhibit significant lateral variability across Antarctica. Despite this, surface heat flow derived from Earth's interior remains one of the most poorly constrained parameters controlling ice sheet evolution. To obtain a continent‐wide map of Antarctic heat supply at regional‐scale resolution, we estimate upper mantle thermomechanical structure directly from VS. Until now, direct inferences of Antarctic heat supply have assumed constant crustal composition. Here, we explore a range of crustal conductivity and radiogenic heat production values by fitting thermodynamically self‐consistent geotherms to their seismically inferred counterparts. Independent estimates of crustal conductivity derived from VP are integrated to break an observed trade‐off between crustal parameters, allowing us to infer Antarctic geothermal heat flow and its associated uncertainty.


Introduction
Heat derived from Earth's interior, and supplied to its surface, is a crucial component of ice sheet basal conditions.The supply of thermal energy to the ice sheet-solid Earth interface can influence basal melt and sliding, englacial rheology, and erosion, and is therefore a key factor in governing ice dynamics (Burton-Johnson et al., 2020;Larour et al., 2012).Not only are ice dynamics highly sensitive to the supply of geothermal heat, the latter is expected to vary significantly across Antarctica (e.g., Shen et al., 2020).The result is that a good understanding of the pattern and amplitude of heat supply into the base of the Antarctic Ice Sheet is a requirement for accurately modeling its evolution.
To quantify heat supply we refer to geothermal heat flow (GHF), q s , pertaining to the amount of thermal energy supplied across Earth's surface, per unit area and time (units mW m 2 ).Since thermal conduction is the dominant mechanism of heat transfer in Earth's crust, Fourier's law of conduction is used to relate q s to Earth's temperature structure, (2) Here, k is thermal conductivity, T is temperature, z is a locally vertical depth co-ordinate, and z 0 is located at the surface.Theoretically, then, Equation 1gives us a pathway to estimating q s , via measurements of laterally varying thermomechanical structure.Indeed, local estimates of Antarctic GHF have been made using observations of temperature and depth from gravity-driven probes in unconsolidated sediment and boreholes drilled into ice or bedrock.However, such measurements can only be used to infer point estimates of GHF.
To obtain continental scale maps of GHF in Antarctica suitable for ice sheet modeling, geophysical methods are an extremely valuable tool.A number of methods based on magnetic, gravity or seismic data have been employed in the past (e.g., An et al., 2015;Haeger et al., 2022;Martos et al., 2017).Whilst useful, such methods have suffered from a range of data-and modeling-derived issues.For example, sparsity of data and a lack of sensitivity to short-wavelength structure has led to poor spatial resolution of inferred GHF models.Poor constraint on crustal parameters such as thermal conductivity and heat production has led to lateral variations being ignored, despite their potential to vary significantly, and the consequent impact of such variations on GHF.Difficulties in converting field observations into estimates of Earth's thermal structure, and the inference of only a single isotherm, has led to large uncertainty in GHF predictions.
A number of recent advances allow for the establishment of a novel approach to infer GHF from seismological data sets.First, the development of ANT-20, a wave-equation traveltime adjoint tomographic model, lays the groundwork for imaging Antarctic thermomechanical structure and henceforth GHF at regional-scale resolution (∼100 km) (Hazzard et al., 2023;Lloyd et al., 2020).Second, new geochemical analyses have improved our understanding of the likely range of key crustal parameters governing heat supply, their relationship with composition, and to what extent they can be inferred from geophysical data (Jennings et al., 2019;Sammon et al., 2022).Third, the emergence of physics-based parameterizations of mantle rock properties, constrained via laboratory experiments, has opened the door to converting seismic velocities directly into temperature (Faul & Jackson, 2005;Yabe & Hiraga, 2020;Yamauchi & Takei, 2016).In addition, methods to calibrate these parameterizations based on a range of geophysical data constraints have allowed us to reduce uncertainty in such conversions (Hazzard et al., 2023;Richards et al., 2020).Here, we harness the aforementioned advances to produce a new model of Antarctic GHF and its associated uncertainty, based on a new approach integrating both shear-(V S ) and compressional-(V P ) wave velocity data.

Methods
Our approach to estimating GHF across Antarctica is motivated by the desire to infer geothermal structure in as direct a fashion as possible, without relying on empirical comparisons to GHF estimates derived from geologically distinct continental environments.Central to this approach is the idea of constraining the relationship between temperature and depth, T(z), across a range of depth slices, rather than relying on a single isotherm.Therefore, we make use of V S data, which is especially sensitive to geothermal structure throughout the shallow upper mantle.Since crustal composition also plays a key role in determining heat supply, via variations in thermal conductivity and heat production, we seek to constrain these parameters within our modeling framework.To do so, we bring in information from V P data, which provides sensitivity to lateral variations in SiO 2 % content and therefore crustal conductivity.By fitting steady-state geothermal profiles to V S -derived counterparts, and looking at how the misfit between the two varies as a function of crustal heat production, we are able to co-constrain conductivity, heat production and geothermal heat flow in a thermodynamically self-consistent fashion.This framework serves as the basis for providing reasonable inferences of q s .

Inferring Thermal Structure From Seismic Data
The sensitivity of V S to temperature (T ) derives from the effect that temperature has on the viscoelastic properties of mantle rock.To reliably parameterize the V S (T ) relationship, we adopt the approach of Hazzard et al. (2023), who calibrated the anelasticity parameterization of Yamauchi and Takei (2016) against a suite of Antarctic geophysical data constraints (see Text S1 in Supporting Information S1 for details).Having established a method for relating seismic velocity and temperature, we can select a geographic location {θ, ϕ} (longitude, θ, latitude, ϕ) within the spatial footprint of the chosen tomographic model ANT-20, and convert the corresponding radial velocity structure V S (z) into an inferred geotherm T(z) (Figure 1a, black cross-hairs).

Fitting Geothermal Profiles
Due to the likely presence of noise and artifacts in the underlying seismic data, as well as the potential for unmodelled compositional seismic velocity variation, we avoid estimating q s directly from our seismically inferred geotherms.Instead, we fit steady-state, thermodynamically self-consistent geotherms to them.To prepare the V S -derived geotherms for fitting, we remove crustal velocities, as well as anomalously slow velocities beneath the Mohorovičić discontinuity (Moho) which may be associated with errors in the assumed crustal thickness.We interpolate the resulting geotherms on a 1 km depth interval (see Text S1 in Supporting Information S1 for details; Figure 1a, red dashed line).
We fit the geotherms according to a modified version of the procedure laid out in McKenzie et al. (2005).This procedure involves iteratively updating the Moho GHF, and mechanical boundary layer thickness, until the misfit between modeled and V S -derived geotherms is minimized.Once an optimal geotherm has been arrived at (Figure 1a, black solid line), q s can be calculated according to the surface temperature gradient and associated thermal conductivity.

Parameterizing Mantle Structure
In addition to providing a seismically inferred geotherm to the fitting procedure, we must also provide a suitable parameterization for thermal conductivity, k (W m 1 K 1 ), and heat production, h* (μW m 3 ), in the mantle and crust.
In the mantle, we calculate conductivity according to the temperature-and pressure-dependent parameterization of Korenaga and Korenaga (2016).We have adapted this parameterization to assume a grain size of 0.1 cm, relevant to the calculation of radiative thermal conductivity.We refer to this parameterization as k = k m (T, P).In accordance with the relatively low-abundance of heat-producing elements in the upper mantle, we assume a mantle heat production h* = 0.0 μW m 3 .We set constant-pressure heat capacity to C P = 1187 J kg 1 K 1 , and thermal expansivity to α = 3 × 10 5 K 1 , in our assumptions of adiabatic mantle properties.We assume a mantle kinematic viscosity of ν = 9 × 10 16 m 2 s 1 .

Parameterizing Crustal Structure
To parameterize thermal conductivity in the crust, we make use of the following parameterization (Goes et al., 2020), which we refer to as k = k c (k 0 , T, P), In this equation, the factors β = 0.1, and n = 6.4-2.3 ln(k 0 ), and k 0 is the reference crustal conductivity at atmospheric conditions (P = 0 GPa, T = 25°C).Note that this parameterization was misprinted in the original text of Goes et al. (2020); we have clarified with the authors that the expression above is the correct version.
To parameterize heat production, we divide the crust into two layers of equal depth.We assume a uniformly distributed heat production throughout each layer, set to h * = h * cu in the upper crust, and h* = 0.3 μW m 3 in the lower crust.We have adopted this simple parameterization to avoid imposing precise details of the depthdependence of h* a priori, which are not known.When the upper crustal heat production is set to h * cu =1.0 μW m 3 , our parameterization is consistent with globally averaged heat production values obtained from a comprehensive analysis of crustal geochemistry and seismic velocity (Sammon et al., 2022).

Sampling Crustal Parameters to Optimize GHF
Reference thermal conductivity, k 0 , and upper crustal heat production, h * cu , are treated as laterally variable parameters in our model, so as to account for the influence of crustal composition on geothermal structure.Both parameters could exhibit lateral variability within the approximate ranges k 0 ∼ 1.0-4.0W m 1 K 1 and h * cu ∼ 0.0 to 6.0 μW m 3 (Hasterok & Chapman, 2011;Jennings et al., 2019;Lösing et al., 2020;Sammon et al., 2022).Such variations can have a significant impact on q s .For example, we found that for a typical V Sderived input geotherm, varying k 0 and h * cu within the aforementioned ranges results in surface GHF variations of q s ∼ 20-170 mW m 2 .The lowest (highest) inferred q s occurs when both k 0 and h * cu are minimized (maximized).We can rationalize this observation by considering the dependence of q s on each crustal parameter in turn (see Text S2 in Supporting Information S1 for details).
In order to optimize our predictions of GHF at each location, we co-vary k 0 and h * cu , and evaluate the least-squared misfit between V S -inferred and fitted geotherms as a function of the two free parameters (Figure 2).If the misfit space at each location were to exhibit a global minimum, this would allow for simultaneous extraction of bestfitting k 0 , h * cu and q s .However, we find that k 0 and h * cu trade off significantly with one another.This trade-off can be visualized by holding k 0 constant and varying h * cu , and vice versa, and observing the similarity in fitted geotherms (Figure 2, panels a-b).Of course, this similarity is also borne out in the misfit space, where we see valley-like minima (Figure 2c).Since q s trades-off positively with both k 0 and h * cu , it is vital to be able to locate where in the valley of the misfit space the so-called true solution lies.To resolve this issue and break the observed trade-off, we require additional information, which we obtain by utilizing an independent geophysical constraint on k 0 .

10.1029/2023GL106274
To gain insight into laterally varying crustal conductivity, we draw on a model of crustal V P (km s 1 , Figure 1b).We use the same V P model as was assumed in ANT-20, for consistency with our chosen crustal thickness model.Jennings et al. (2019) relate V P to k 0 via laboratory measurements on igneous rocks spanning a wide range of compositions.They found that SiO 2 is the dominant control on thermal conductivity.By making use of the empirical relationship, as provided by Jennings et al. (2019), we estimate Antarctic crustal conductivity by averaging crustal V P (in km s 1 ) at each continental location, and converting it into k 0 (Figure 1c).In addition, we utilize the spread in V P data within the crust at each location, along with the k 0 (V P ) fitting residual ϵ = 0.31 W m 1 K 1 , to estimate an uncertainty in our predicted conductivity (Figure 1d).
Since we now have access to independent predictions of k 0 (θ, ϕ) derived from V P data, we can locate physically plausible regions of k 0 -space.We start by sampling a value of k 0 from a Gaussian distribution at each location, according to where μ(k 0 ) is given by the empirical prediction of Equation 4, and 0 ) is given by the uncertainty associated with this prediction (Figure 1).For each sampled value of k 0 , we extract the corresponding best fitting value of h * cu , as well as the q s associated with this combination of crustal parameters.By repeating this sampling procedure, we build up a distribution of k 0 , h * cu and q s .We summarize these distributions at each location using a mean and standard deviation, providing us with Antarctic GHF predictions along with an estimate of their uncertainty.

Antarctic GHF Estimates
Resulting estimates of Antarctic GHF are shown in Figure 3.To distinguish between West and East Antarctica, we utilize the satellite-mapped drainage network of Zwally and Giovinetto (2011).Our results indicate high q s in West Antarctica, where heat supply into the base of the Antarctic Ice Sheet is estimated to vary between 60 and 130 mW m 2 , and is on average 97 ± 14 mW m 2 (median, and median absolute deviation, respectively).Such GHF values are significantly higher than the global continental average, q s = 67 ± 47 mW m 2 (as inferred from gravity-driven probe and borehole temperature-depth data), and are in fact intermediate between the former and the global average over continental rift zones, q s = 114 ± 94 mW m 2 (Lucazeau, 2019).This result is consistent with recent tectonic activity, evidence for Cenozoic magmatism, and inferences of a thermal anomaly beneath West Antarctica (Ball et al., 2021;Barletta et al., 2018;Hazzard et al., 2023).The distribution of q s values within the aforementioned range is relatively uniform, implying significant lateral heterogeneity across West Antarctica.Maximum q s is inferred at the continental perimeter in the Amundsen Sea region, and in the northern Antarctic Peninsula.
In East Antarctica, our results indicate q s in the range 20-120 mW m 2 .Note that the presence of abovecontinental-average GHF values within this range is indicative of the fact that not all of our defined East Antarctic region is underlain by cold, cratonic material.However, the distribution of inferred GHF is heavily skewed toward lower values, which is borne out in the spatial average 30 ± 8 mW m 2 .Such low values are consistent with globally averaged GHF estimates in continental regions of Archean age, q s = 46 ± 21 mW m 2 (Lucazeau, 2019).
For the most part, the spatial pattern of GHF uncertainty, σ(q s ), is similar to that of the GHF prediction itself, μ(q s ).The ratio of these two predictions, σ(q s )/μ(q s ), is on average 16 ± 10 % over the Antarctic continent.Elevated proportional uncertainty in GHF structure is estimated in Coats Land and Dronning Maud Land in East Antarctica, in parallel with anomalously high uncertainty in heat production.The least-squared misfit between inferred and modeled geotherm is relatively insensitive to the choice of heat production here, reducing our ability to constrain this parameter and hence q s .Anomalously low q s uncertainty (σ(q s ) < 10 mW m 2 ) is estimated at the Amundsen Sea Embayment and Ross Ice Shelf, as well as along the grounding line between these two regions.These areas are characterized by high inferred GHF in the region of 100-130 mW m 2 .The uncertainty here is artificially low owing to the inferred heat production lying at the top of the parameter sweep range, h * cu = 6.0 μW m 3 (see Text S3 in Supporting Information S1 for maps of inferred h * cu ).Since the seismically inferred geotherm here is systematically hotter than the modeled profile, the inferred value of h * cu is insensitive to variations in crustal thermal conductivity, and thus exhibits no variation.We refrain from increasing the upper limit of our parameter sweep in response to this issue, as this would not be an appropriate resolution, since h * cu values in excess of 6.0 μW m 3 are inconsistent with the range of physically plausible values based on continental geology (Artemieva et al., 2017;Sammon et al., 2022), and unreasonable increases in h * cu would be required to attempt to fit the inferred geotherm.Instead, we suggest that the reason for our findings is due to our assumption of a steadystate geotherm.While this assumption is a reasonable approximation across most of Antarctica, it may be less   (a-h) Geophysical GHF inferences: HR24-inferred directly from V S and V P (this study); HR23-inferred directly from V S (Hazzard et al., 2023); A15-inferred directly from V S (An et al., 2015); H22-inferred via joint seismic and gravity inversion (Haeger et al., 2022); SR04-inferred empirically via V S (Shapiro & Ritzwoller, 2004); S20-inferred empirically via V S (Shen et al., 2020); FM05-inferred from magnetic anomaly data (Maule et al., 2005); M17-inferred from magnetic anomaly data (Martos et al., 2017).GHF inferences derived from gravity-driven probes and boreholes overlain as colored capsules/circles.Capsules used where 2+ local data points available (colored by lowest-average-highest local estimate from bottom-middle-top).Circles used where 1 local data point available.Note that HR24 has been extended into the oceanic domain to allow more complete comparison with local data.In the oceanic domain we assume k 0 = 2.6 W m 1 K 1 and h * cu = 0.0 μW m 3 , in keeping with oceanic crustal composition (Grose & Afonso, 2013;Richards et al., 2018).(i-p) Relationship between geophysically and locally inferred GHF (Section 3. accurate in regions recently affected by intraplate basaltic magmatism or episodes of rifting (e.g., Alexander Island offshore Antarctic Peninsula, Marie Byrd Land and the Victoria Land Basin; LeMasurier, 2008;Sauli et al., 2021).Indeed, by locally modeling time-dependent thermal evolution following lithospheric thinning, we improve fit to V S -derived temperature in these regions and find that optimal transient geotherms require less extreme h * cu values than steady-state equivalents (see Text S4 in Supporting Information S1 for transient geotherm modeling).Nevertheless, predicted q s is near-identical for the these two different model assumptions, indicating that, while our steady-state-based prediction likely overestimates h * cu , our q s estimates remain valid.Note, however, that uncertainty on q s is likely higher than predicted in these locations, since the low uncertainty is likely an artifact of the 6.0 μW m 3 upper limit we impose on upper crustal heat production.

Comparison With Previous Studies
A comparison of our GHF model with those from previous studies utilizing a range of approaches is presented in Figure 4. Consistent across all studies, we observe a long-wavelength pattern of elevated heat supply in West Antarctica, and more uniformly low heat supply in East Antarctica.However, short-wavelength (∼1, 000 10, 000 km) structure differs significantly between models (both in terms of spatial pattern, and amplitude), reflecting the range of data sets and modeling assumptions used to construct them.In particular, our model (HR24, Figure 4) spans a significantly greater range (110 mW m 2 ) than its comparators, with the exception of the two magnetic studies Maule et al. (2005) and Martos et al. (2017), which exhibit exceedingly high peak GHF values of 190 mW m 2 and 240 mW m 2 respectively.The higher amplitude of GHF variations in this study compared to most models can be explained by our incorporation of laterally heterogeneous crustal composition.In East Antarctica we infer below average crustal heat production, and in West Antarctica we see the opposite; the combined effect of which is to broaden the range of inferred q s .As compared to a directly analogous model assuming constant k 0 = 2.5 W m 1 K 1 and h * cu = 1.0 μW m 3 (HR23, Figure 4), we predict a 30% increase in maximum Antarctic q s , and a 50% reduction in minimum Antarctic q s (Hazzard et al., 2023).

Comparison With Local Data
Despite the sparsity of Antarctic GHF estimates derived from in situ temperature probe observations in boreholes and unconsolidated sediment, these data can be utilized to independently assess geophysically informed models of q s .It is important to treat in situ inferences carefully, since they are representative of localized temperature structure, and are potentially susceptible to contamination by thermal signals caused by frictional heating at the base of the ice sheet, hydrological circulation, and local topography (Colgan et al., 2021;Shen et al., 2020).In addition, limited lateral resolution in our chosen V S model will smooth out GHF variations on spatial scales smaller than ∼100 km, diminishing our ability to accurately compare to local estimates.Therefore, we collect local GHF estimates from gravity-driven probes and boreholes into regions of dimension 100 km, and compare locally and geophysically inferred GHF values in each region (Figure 4).Accounting for data uncertainty in the resulting data sets, our model produces the highest Pearson's correlation coefficient, r = 0.49 ± 0.07, the lowest root-mean-square deviation, RMS = 29 ± 3 mW m 2 , and a range of GHF values most consistent with local data (see Text S5 in Supporting Information S1 for details of quantitative model comparison).We note that two GHF models frequently used in ice sheet modeling studies, SR04 (r = 0.16 ± 0.18, RMS = 66 ± 9 mW m 2 ) and FM05 (r = 0.03 ± 0.17, RMS = 43 ± 5 mW m 2 ) (Maule et al., 2005;Shapiro & Ritzwoller, 2004), perform particularly poorly against independent data as compared to HR24.

Methodological Appraisal
There are a few reasons why our modeling approach may allow us to arrive at estimates of GHF more consistent with independent data than previous studies.First, the use of a geophysically constrained parameterization of mantle viscoelasticity enables us to map V S structure directly into temperature over a range of upper mantle depth slices.This stands in contrast to other studies, such as those based on magnetic data, where only a single isotherm associated with the Curie depth is constrained (Martos et al., 2017;Maule et al., 2005).As a result, more reliable estimates of the geothermal gradient can be made.Second, the incorporation of crustal V P information provides us with sensitivity to lateral variations in thermal conductivity, a parameter which affects q s both directly via its presence in Equation 1, and to a lesser extent, indirectly via its effect on the geothermal gradient.Third, by combining insights drawn from V S and V P data together with thermodynamic models of geothermal structure, we are able to constrain variations in crustal heat production.This stands in contrast to previous studies making use of Geophysical Research Letters 10.1029/2023GL106274 steady-state geotherm modeling, which have assumed constant composition (An et al., 2015;Haeger et al., 2022;Hazzard et al., 2023).In addition, methods based on empirical comparison of seismic data between continents are unable to account for differences in crustal composition between target and comparison sites (Shapiro & Ritzwoller, 2004;Shen et al., 2020).Therefore, whilst their inferred q s uncertainty may implicitly capture variations in heat supply associated with crustal composition, their estimates of q s itself will be agnostic to such variations.

Outstanding Challenges
Although the GHF modeling framework presented herein provides a powerful method to infer GHF from seismological data, a number of outstanding challenges remain.Chief amongst them is our inability to reliably infer temperature structure from V S at depths shallower than the Moho.We have mitigated this issue in three ways: by assuming a temperature of 0°C at the crystalline basement, excising anomalous seismic data associated with crustal bleeding, and fitting seismically inferred geotherms using thermodynamically self-consistent models of shallow thermal structure.However, given improved constraints on crustal temperature structure (at vertical resolution of ∼25 km or higher), it would be possible to generate more reliable predictions of surface geothermal gradient.Such constraints may also help in resolving relative contributions to GHF derived from transient-state geotherms versus crustal heat production.Pn-waves are a type of compressional wave guided along the mantle lid, providing sensitivity to Moho temperature structure.Therefore, a high resolution, continental scale model of Antarctic Pn-velocity (V Pn ) would be extremely valuable.Fortunately, this may be on the horizon, with the recent development of a V Pn model of central West Antarctica (Lucas et al., 2021).In general, deployment of additional broadband seismic stations in Antarctica would help to improve the accuracy and spatial resolution of velocity models used to infer geothermal structure.
Second, we rely on a parameterization of geochemical data pertaining to the relationship between k 0 and V P in order to estimate lateral variations in crustal thermal conductivity (Jennings et al., 2019).This parameterization inherently assumes that conductivity is sensitive only to silicate content.Further, it assumes that synthetic V P estimates from thermodynamic calculations on a range of mineral assemblages are accurate, and match up to velocities predicted from real data (Behn & Kelemen, 2003).In reality, systematic errors in modeled V P associated with the choice of regularization or starting model will be propagated into systematic errors in predicted k 0 .In addition, artifacts in V P structure caused by data sparsity and the ill-posed nature of the seismic inversion problem may cause us to improperly estimate k 0 at certain locations.Therefore, further validation of methods used to estimate k 0 (V P ) are needed.
Finally, the relative sparsity of Antarctic GHF estimates from gravity-driven probes and boreholes presents a clear challenge in assessing the quality of geophysical predictions.A significant expansion of this data set is needed to address the question: what is the most reliable geophysical method for estimating continental GHF?In addition, multiple boreholes at each field sampling region are needed, in order to properly account for localized variations in GHF associated with geology, hydrothermal circulation, and topography (Burton-Johnson et al., 2020).Promisingly, the Rapid Access Ice Drill (RAID) project seeks to address the lack of local data by drilling down to the deepest portions of the Antarctic Ice Sheet (Goodge & Severinghaus, 2016).

Conclusions
We have presented a novel modeling framework for estimating GHF from seismological data, incorporating lateral variations in crustal composition.We find that our geophysical inferences of heat supply are in better agreement with local estimates than previous studies, implying that crustal conductivity and heat production act as significant controls on Antarctic heat flow.Our models of Antarctic conductivity, heat production, and GHF provide improved constraints on Antarctic sub-glacial geology and thermal conditions, critical for use in ice sheet modeling studies.

Figure 1 .
Figure 1.Parameterizing Earth structure.(a) Temperature-depth data points inferred from V S (black cross-hairs) interpolated prior to fitting (red dashed line).Steady-state geotherm fitted to seismic data (black line), subject to depth-dependent thermodynamic constraints within the upper crust (0 ≤ z ≤ z 1 ), lower crust (z 1 < z ≤ z 2 ), and mantle (z 2 < z).All depths referenced with respect to the crystalline basement.(b) Average crustal V P across Antarctica.(c) Crustal conductivity (k 0 ) estimated from V P (Equation4).(d) Uncertainty in k 0 based on spread in crustal V P and k 0 (V P ) residual (Section 2.5).

Figure 4 .
Figure 4. GHF Model Comparison.(a-h)Geophysical GHF inferences: HR24-inferred directly from V S and V P (this study); HR23-inferred directly from V S(Hazzard et al., 2023); A15-inferred directly from V S(An et al., 2015); H22-inferred via joint seismic and gravity inversion(Haeger et al., 2022); SR04-inferred empirically via V S(Shapiro & Ritzwoller, 2004); S20-inferred empirically via V S(Shen et al., 2020); FM05-inferred from magnetic anomaly data(Maule et al., 2005); M17-inferred from magnetic anomaly data(Martos et al., 2017).GHF inferences derived from gravity-driven probes and boreholes overlain as colored capsules/circles.Capsules used where 2+ local data points available (colored by lowest-average-highest local estimate from bottom-middle-top).Circles used where 1 local data point available.Note that HR24 has been extended into the oceanic domain to allow more complete comparison with local data.In the oceanic domain we assume k 0 = 2.6 W m 1 K 1 and h * cu = 0.0 μW m 3 , in keeping with oceanic crustal composition(Grose & Afonso, 2013;Richards et al., 2018).(i-p) Relationship between geophysically and locally inferred GHF (Section 3.3), same studies as (a-h).Data points and associated error bars show the mean and range of local/geophysical GHF values at each location, respectively.Statistics summarizing local-geophysical agreement are: r = Pearson's r-value correlation coefficient; RMS = root-mean-square deviation (values reported in the form a ± b [c], where a = median, b = median absolute deviation, c = value calculated ignoring data uncertainty, see Text S5 in Supporting Information S1 for details of analysis).Gray data points correspond to locations where only one local GHF inference is available (i.e., circles in panels (a-h)) and are not included in model statistics.
Figure 4. GHF Model Comparison.(a-h)Geophysical GHF inferences: HR24-inferred directly from V S and V P (this study); HR23-inferred directly from V S(Hazzard et al., 2023); A15-inferred directly from V S(An et al., 2015); H22-inferred via joint seismic and gravity inversion(Haeger et al., 2022); SR04-inferred empirically via V S(Shapiro & Ritzwoller, 2004); S20-inferred empirically via V S(Shen et al., 2020); FM05-inferred from magnetic anomaly data(Maule et al., 2005); M17-inferred from magnetic anomaly data(Martos et al., 2017).GHF inferences derived from gravity-driven probes and boreholes overlain as colored capsules/circles.Capsules used where 2+ local data points available (colored by lowest-average-highest local estimate from bottom-middle-top).Circles used where 1 local data point available.Note that HR24 has been extended into the oceanic domain to allow more complete comparison with local data.In the oceanic domain we assume k 0 = 2.6 W m 1 K 1 and h * cu = 0.0 μW m 3 , in keeping with oceanic crustal composition(Grose & Afonso, 2013;Richards et al., 2018).(i-p) Relationship between geophysically and locally inferred GHF (Section 3.3), same studies as (a-h).Data points and associated error bars show the mean and range of local/geophysical GHF values at each location, respectively.Statistics summarizing local-geophysical agreement are: r = Pearson's r-value correlation coefficient; RMS = root-mean-square deviation (values reported in the form a ± b [c], where a = median, b = median absolute deviation, c = value calculated ignoring data uncertainty, see Text S5 in Supporting Information S1 for details of analysis).Gray data points correspond to locations where only one local GHF inference is available (i.e., circles in panels (a-h)) and are not included in model statistics.