1 Introduction

Improved knowledge of the Antarctic basal geothermal heat flux, q GHF , is important for sharpening our theoretical and numerical estimations of future ice sheet contribution to sea level rise. However, only a few direct in situ measurements have been conducted at the bottom of deep boreholes by Engelhardt [2004] and Fisher et al. [2015], due to the thick ice cover. Other inferences of geothermal heat flux come from tectonic correlation to surface wave maps [Shapiro and Ritzwoller, 2004], satellite magnetic data [Maule et al., 2005], or interpretations of ice penetrating radar [Schroeder et al., 2014]. While the important connection between heat and water has long been known to be critical to understanding processes beneath the Antarctic ice streams [e.g., Blankenship et al., 1986], a growing interest in the basal hydrologic conditions beneath West Antarctic Ice Sheet (WAIS) has been motivated by both the discovery of extensive subglacial water activity [e.g., Fricker et al., 2007; B. E. Smith et al., 2009; Creyts and Schoof, 2009; Siegfried et al., 2014; Fricker et al., 2016] and by the recognition that basal conditions are of major importance to the proper formulation of numerical simulations of ice sheet evolution in a warming climate [e.g., Nowicki et al., 2013].

Quantification of the thermodynamic state of the WAIS is essential for properly assessing the time scales and amplitudes of potential unstable collapse. Examination of the error and uncertainty caused by relatively poor characterization of the ice sheet thermodynamic and phase states is now under increased scrutiny, as any assessment of how future ice flow might change is related to the heat flux condition applied at the solid Earth‐ice interface [e.g., Rogozhina et al., 2012; Larour et al., 2012a]. A zeroth‐order problem is to attack the uncertainty in background heat flux at the bed.

Snow falling on an ice sheet provides continuous replenishment of a thick thermally insulating layer. As the ice temperature melting point decreases with pressure, the thicker the ice sheet, the easier it is for the geothermal heat flux to raise the basal temperature to the melting point. The sensitivity of basal melt to geothermal heat flux, q GHF , is revealed by the theory of Budd et al. [1984] for one‐dimensional flow lines. It emphasizes the linear relation between basal temperature and geothermal flux and predicts the presence of basal meltwater beneath most of the Antarctic ice sheet for q GHF ≥ 80 mW/m2. Most numerical models of the polar ice sheets assume the geothermal flux to be 42 ≤q GHF ≤ 65 mW/m2 [Siegert and Dowdeswell, 1996; Llubes et al., 2006], as pointed out by Rogozhina et al. [2012]. However, in West Antarctica, which experiences active Cenozoic volcanism and rift formation, the question of higher q GHF is especially important as geothermal heat flux exceeds 70 mW/m2 in analogue regions, such as the continental United States, west of the Rocky Mountain Ranges [Ramirez et al., 2016; Davies, 2013; Blackwell, 1989].

Pattyn [2010] has shown that more than half of the Antarctic ice sheet base reaches the pressure melting point and estimates the total continent‐wide basal meltwater production rate to be about 65 Gt/yr. Such a production rate is substantial, amounting to roughly 3% of the surface accumulation rate in Antarctica. Using lakes as an indicator of the presence of basal meltwater, similar to what was done by Siegert and Dowdeswell [1996], the analysis of Pattyn [2010] derived a modified geothermal heat flux map connected to the observations of Antarctic basal water conditions. However, this map lacks any new solid Earth information that can now be derived from the large‐scale broadband seismic stations that are currently imaging the mantle and crustal environment [e.g., Chaput et al., 2014; Emry et al., 2015; Lloyd et al., 2015; Heeszel et al., 2016]. The three‐dimensional (3‐D) seismic wave velocity structure derived from this new data provides new constraints on tectonic conditions under the ice sheet. Any ice sheet observation that confirms the presence of mantle plume conditions has profound implications for regional mantle properties beneath the WAIS. Mantle viscosity is exponentially temperature dependent, and the viscous response time to loading and unloading by ice is, also, governed by an exponential dependency on the viscosity. A hotter mantle, therefore, predicts drastically reduced time scales over which glacial isostatic adjustment stress relaxation occurs [e.g., Ivins et al., 2000].

The hypothesis of a deep mantle plume of sufficient heat transport to manifest Cretaceous to Holocene age volcanism and present‐day seismicity in West Antarctica dates to the 1980s. However, no seismic imaging provided support for a plume beneath Antarctica until surface wave mapping by Sieminski et al. [2003] and Montelli et al. [2006] mapped a slow structure in the top of the lower mantle beneath the western Ross Sea.

Central to the 3 km MBL uplift is a dome that contains 18 major high‐standing volcanoes of felsic alkaline and alkali basaltic chemistry. The majority of these volcanoes form linear chains that age toward the center of the province [Storey et al., 2013]. Late Cenozoic volcanism (28–35 Ma) may well be associated with a single active plume [LeMasurier and Rex, 1989; LeMasurier and Landis, 1996]. Alternatively, a longer‐lived and more broadly scaled mantle upwelling may have arrived to the lithospheric environment circa 100 Ma, with analysis of uranium and lead isotopic ratios supporting a separation from slab material that stagnated at the top of the lower mantle beneath Gondwana [Steinberger, 2000; Panter et al., 2006; Sutherland et al., 2010; Spasojevic et al., 2010].

Global seismic tomography, having inherently lower resolution, seems to support the broad‐scale, longer‐lived model, while more recent high‐resolution tomography resulting from the broadband seismic Antarctic Polar Earth Observing Network seems to support the single, younger, and more spatially focused model [e.g., Hansen et al., 2014; Accardo et al., 2014; An et al., 2015; Emry et al., 2015; Lloyd et al., 2015; Heeszel et al., 2016]. The seismic images reveal the pattern and amplitude of upper mantle anisotropy as well as lateral variability in shear and compressional wave velocity and, collectively, lend support for the hypothesis of a lower mantle plume origin as the cause of the more youthful MBL volcanism and geophysical structure. Compelling evidence of ongoing magmatic movement at lower crustal depths has been found recently in long‐period earthquakes [Lough et al., 2013], and these events indicate that the locus of activity has moved ∼55 km southward of the Quaternary eruptions of Mount Waesche in the Executive Committee Range (ECR, see Figure 1). The surface manifestations of continental plumes are approachable using simple models when the lithospheric plate has been nearly stationary over the past 30 Ma, as is the case with Antarctica [e.g., Gripp and Gordon, 2002]. As a consequence, we may be able to further test the hypothesis of a single‐focused plume by modeling its thermal interaction with the base of the ice sheet.

Figure 1 Open in figure viewer PowerPoint Modeled ice surface velocities overlaid on a Moderate Resolution Imaging Spectroradiometer Mosaic of Antarctica. Locations mark Marie Byrd Land (MBL), Ames Range (AR), Crary Mountains (CM), Executive Committee Range (ECR), Flood Range (FR), Mount Takahe (MT), Mount Waesche (MW), Toney Mountains (TM), and the Whillans Ice Stream Subglacial Access Research Drilling project drilling site (SLW). Black lines delineate the contour of the model domain and the three main basins: the Amundsen Basin, the Ross Basin, and the Coastal Basin. Grey lines indicate ice surface elevation every 250 m. Stars indicate active volcanoes, and white symbols represent the three locations where the plume experiments with varying mantle plume parameters (Plume FR, Plume ECR, and Plume SLW; see Table 1 ) are performed.

In this study, we conduct numerical modeling for simulating the interaction between the solid Earth mantle plume and the ice sheet thermal structure. While our focus is primarily on the MBL dome, it is also instructive to perform computations for an area around Subglacial Lake Whillans (SLW) where there is abundant evidence for basal water. Observations in both regions suggest the presence of magmatic activity and high geothermal flux. While there are measurements of geothermal heat flux near mantle plumes, these suffer from their spatial sparsity, often faced with difficult logistics in the deep ocean [e.g., Nyblade and Robinson, 1994]. Harris and McNutt [2007] show that there are significant sampling deficiencies in ocean floor heat flow studies that have targeted hotspots. These owe to the lack of sufficient spatial density combined with a heterogeneous fluid convective transport through the shallow crust. Studies at La Réunion [e.g., Bonneville et al., 1997] and Hawaii hotspot tracks, where spatial sampling is highest, tend, however, to show that the anomaly with respect to a background plate model is small, about 10 mW/m2. Jaupart et al. [2015] conclude that the heat supplied by the mantle plume hotspot in the oceanic lithospheric environment is suppressed by the fact that it locks deeply to the base of the lithosphere. Studies of continental flux where rising plumes meet a rheologically weaker lithosphere than beneath the ocean plates [e.g., Kohlstedt et al., 1995] reveal anomalies that are an order of magnitude larger. The most widely studied and data‐rich example is the Yellowstone hotspot. We therefore use an analytical mantle plume model parameterization that is capable of producing realistic spatial patterns of geothermal heat flux where observations are in abundance [e.g., DeNosaquo et al., 2009]. A complete discussion of the parameterization is presented in Appendices A–C.

The thermal regime of the 3‐D ice flow model is based on the enthalpy framework, an energy‐conserving formulation that allows modeling cold and temperate ice [Aschwanden et al., 2012], and includes thermal advection, diffusion, deformational heat, and basal heat flux. The location and extent of the mantle plume beneath the WAIS is only roughly inferred from seismic data. We therefore perform here a series of numerical experiments with varying plume location and intensity to characterize mantle plume‐related basal conditions in MBL and beneath the WAIS. We first summarize evidence supporting the presence of a mantle plume in West Antarctica and validation of the mantle plume parameterization. We then detail the ice sheet model as well as the experiments performed. We finally present and discuss our results and their implications for the presence of a mantle plume in West Antarctica.