We use the airborne geophysical data from the ICECAP-I and EAGLE/ICECAP-II surveys from 2008–2009 through to 2016–2018 seasons including magnetics, gravity, and radio-echo sounding (RES) bed topography data, supplemented by Bedmap3 bed topography point data . The ICECAP project collected data over East Antarctica using a Basler BT-67 aircraft (C-JKB) equipped with a Geometrics 823A magnetometer, and depending on the campaign, a LaCoste & Romberg (L&R) BGM-3 (early campaigns) or a Canadian Micro Gravity (CMG) GT-1A (later campaigns) gravimeter, HiCARS and later HiCARS-2 RES systems, and Riegl LD90-3800 HiP-LR Laser Altimeter. Surveys were conducted at varying aircraft heights, typically ranging from approximately 1.5 km up to ∼ 4 km ellipsoidal heights, and at average speeds around 80–90 m s⁻¹, with survey lines variably spaced from 10 to 50 km apart. Coverage is moderate, with close data around the grounding line, but major data gaps in the inland region (Fig. ).

ICECAP airborne gravity data have cross-over residuals typically in the range of 1 to 3 mGal after line-levelling . RES data typically carry 10 to 30 m uncertainty under good bed returns, increasing locally up to ∼ 50 m in areas of weak or multi-path echoes, steep bed slopes, or strong clutter . reprocessed the magnetic data with a median crossover error of 5 nT. We discarded all ICECAP data flagged with aviation turns.

On 7 January 2024, we collected nine ground-based gravity measurements along a ∼ 14 km transect across the Denman Glacier (Fig. a, spacing ≈ 1.7 km) to recover short-wavelength anomalies. For this, we used a Scintrex CG-5 Autograv (resolution 0.001 mGal; typical station repeatability of 5 µGal under stable conditions; long-term drift below 0.02 mGal d⁻¹; ), with daily base ties at Bunger Hills and loop closures including the Casey absolute site to control drift.

Field readings from the CG-5 (yraw) were first tied to an absolute reference by calibrating against the Casey Station fundamental value gfund = 982 380.48867 mGal (Lon: 110.5226, Lat: -66.2820, height: 19 m, positional error: 3 m, gravity error: 30 µGal). We modeled the instrument drift by fitting a baseline f(t) to repeated measurements of the base station at Casey and three different stations at Bunger Hills and evaluating this baseline at each observation time ti (linear interpolation between base ties, Fig. ). The interpolated baseline ybase(ti)=f(ti) represents the predicted CG-5 reading due solely to drift at time ti. We then applied a time-dependent offset C(ti)=gfund−ybase(ti) to each reading to obtain the absolute observed gravity 1gobs(ti)=yraw(ti)+C(ti).

Station coordinates were determined from dual-frequency Trimble GNSS. Rover trajectories were post-processed kinematically (PPK) in Emlid Studio v1.5 ; the local PPK network was tied to an AUSPOS (ITRF2014) solution . On the Glacier, we positioned one GNSS Antenna at a mid-line base (Lon: 99.4622, Lat: -67.1976, height: 804.817 m ellipsoidal) for ∼ 7 h. We used the ellipsoidal heights to provide the vertical control needed for accurate normal-gravity/free-air corrections.

We then computed the normal gravity γ(Φ,h) on the WGS84 reference ellipsoid at each station's geodetic latitude Φ and ellipsoidal height he using Boule's closed-form normal-gravity implementation . This already includes the free-air term, so no separate FA correction is added. Finally, we formed the free-air anomaly as 2Δg=gobs-γ(Φ,he)+gp+gtidal, where gtidal is a recomputed solid-Earth tide using a python library by , based on , replacing any tide the instrument applied. gp is the atmospheric-pressure correction of 0.3 µGal hPa⁻¹ applied to the station pressure anomaly relative to a campaign reference (Bunger Hills archive mean in February was near 981.14 hPa; ; for January no data was available).

To bring the ICECAP airborne and our ground-based gravity measurements onto a consistent datum, we estimated and applied constant (DC) shifts relative to the most recent Antarctic Gravity Anomaly Grid (AntGG) compilation . We used the 5 km resolution AntGG2021 product, which represents a major update of the earlier AntGG2016 release . AntGG2021 integrates airborne and terrestrial gravity observations (including ICECAP data) into a continent-wide homogenized compilation making it a suitable reference field. For each dataset, we compared the observations to the AntGG2021 gravity disturbance field by upward-continuing AntGG2021 from the surface to the ICECAP observation height using the workflow described in Sect. . For the ground-based transect, no upward continuation was required, as the data are already at (near-)surface elevation. In both cases, the mean difference was calculated and applied as a constant shift. These shifts were then applied to ICECAP (11 mGal) and ground-based (14 mGal) gravity disturbances to align them with the AntGG2021 reference frame. Along the ground-based transect, however, a significant local mismatch between the ICECAP airborne gravity and both the AntGG2021 reference field, and the ground-based observations persisted after application of the regional correction. Therefore, for the profile comparison shown in Fig. , an additional local adjustment of 26 mGal was applied to the ICECAP data in this limited area to ensure consistency with the AntGG2021 field at the local flight altitude and to facilitate comparison with the ground-based measurements. This local correction was only applied along the transect and not to the wider airborne dataset.

Both ICECAP and ground-based datasets report free-air gravity anomalies relative to the ellipsoid. Keeping the geodetic convention , we refer to these quantities throughout as gravity disturbances (Δg). To isolate signals associated with near-surface mass anomalies, we remove the isostatic Moho contribution giso (Fig. e) from both datasets. The isostatic correction is based on Airy compensation of the rock-equivalent topography (using BedMachine v3 ), obtained by compressing the ice column to a rock density of ρrock=2750 kg m⁻³ (based on the median density of collected in-situ rock samples from the Denman Terrestrial Campaign and previous field trips; ; Fig. h). We assume a crust–mantle density contrast of 400 kg m⁻³ and a reference Moho depth of 40 km, consistent with . The gravity effect of the resulting Moho relief is forward-modeled using the adaptive cuboids method of and evaluated at the respective observation heights of the airborne and ground-based gravity datasets. This procedure approximates the long-wavelength mass variations expected under near-isostatic equilibrium, thereby isolating deeper contributions to the gravity field. While the true Moho may deviate locally from the Airy prediction, this does not significantly affect the long-wavelength component emphasized here. The resulting isostatically corrected gravity disturbance is given by Δgiso(x)=Δg(x)-giso(x). The correction was applied separately to the original ICECAP and ground-based point observations. For each observation, giso was evaluated at its original horizontal coordinates and observation height and subtracted from the corresponding gravity disturbance.

To enable consistent comparison and inversion, we resampled the BedMachine topography onto reference grids at 1 and 2 km resolution for a high-resolution Denman Trough and lower-resolution regional inversion, respectively. Continuous fields were resampled using block-median reduction, while categorical fields were assigned by nearest-neighbour interpolation. We followed , and upward-continued the corrected ICECAP observations to a uniform observation height of 3.5 km above the WGS84 ellipsoid using gradient-boosted equivalent sources, as implemented in the open-source Python package Harmonica . We use optimized parameters by cross-validation for damping λ∈{0.1,1,100} and source-depth d∈{1,2,3} km with the best solution at λ=0.1 and d=1 km. The upward-continued gravity was then evaluated directly at the nodes of the resampled BedMachine reference grids, and cells farther than 2 km from the nearest original observation were masked. This conservative masking ensures that only values directly supported by observations are retained, avoiding artifacts from equivalent-source extrapolation and preventing the inversion from fitting unconstrained regions or producing overly smooth results. The radar bed picks were gridded onto the same reference grids using a 2D spatial binning approach. Point coordinates were assigned to grid cells whose boundaries were computed from the BedMachine Easting and Northing edges, and the mean bedrock altitude within each cell was computed to produce a rasterized field that was used to condition the inversion.

Next, the corrected ground-based gravity data are incorporated. The observation grid height was set to measured ice surface for the ground-based data. The nearest grid cells along the ground transect were explicitly identified using a nearest-neighbour search with a maximum distance threshold of 800 m. For each ground observation, the corresponding grid value in the upward-continued airborne gravity field was identified, and the transect gravity value and its associated observation height were added. This ensured that the nine ground gravity measurements were retained explicitly in the inversion dataset.

Our goal is to remove non–terrain contributions from the gravity observations so that the inversion is driven primarily by the terrain effect of unresolved bed geometry within the inversion domain. We therefore (i) forward–model and subtract the known terrain effect from the isostatically corrected gravity disturbance to obtain a non–terrain disturbance; (ii) estimate its long-wavelength component by fitting a smooth trend to selected conditioning observations with reliable, radar-based topographic control; (iii) subtract the fitted trend from the non-terrain disturbance, transform these residuals to normal scores and estimate their spatial covariance; (iv) simulate an ensemble of spatially correlated residual fields and add these back to the trend to obtain plausible non–terrain distubances; and (v) subtract each non–terrain field from the isostatically corrected gravity disturbance to obtain the ensemble of target terrain effects used for inversion (Fig. ). In particular, the separation of long-wavelength non-terrain gravity contributions from the shorter-wavelength terrain signal is conceptually similar to the DC-shift approach of and the constraint-point regionalization approach of . However, the regional field is estimated differently in the following steps.

To infer subglacial topography and its uncertainty in the Denman Glacier region, we employ a Markov Chain Monte Carlo (MCMC) approach following , which iteratively adjusts a model of the subglacial bed to minimize discrepancies between observed and modeled gravity disturbances.

We initialize the process by using bedrock topography (h0) based on BedMachine plus a smooth Gaussian random perturbation. Gravitational predictions are then again computed using the forward model that integrates gravitational effects of prisms derived from the generated topography (Sect. ). Here, we use the constant ρrock=2750 kg m⁻³.

At each iteration, we make a small, local change to the bed (Fig. ). We pick a random cell inside the inversion mask, form a b×b stencil around it, and add a zero-mean Gaussian patch only within that stencil: δh∼N0,s(v)2K,s(v)≡v3,Kij=exp⁡-‖pi-pj‖2dc+εδij, where pi,j are stencil index coordinates (in grid-cell units). The matrix K sets the spatial correlation in the patch; dc controls how smooth/broad it is (larger dc meaning smoother, broader), and ε is a tiny nugget for numerical stability. The scale s sets the proposal amplitude (derived from the perturbation strength v). We add δh to the current bed inside the stencil; outside, the bed is unchanged. The parameters we used in the inversion are listed in Table .

By progressing from large to small update stencils, the multiscale scheme fits the long-wavelength geometry early and incrementally adds finer detail, reconciling the model with the coarse airborne ICECAP coverage and the heterogeneous radar and ground-gravity constraints.

Proposals are clipped to remain physically plausible (e.g., below the ice surface by a small buffer to account for uncertainties). For efficiency, we recompute forward gravity gpred only at observation points within 10 km of the updated patch and insert this change into the full prediction.

Acceptance uses a Metropolis criterion based on a joint loss L(h), that combines gravity and radar bed picks (within the updated patch), by prescribed uncertainties. For a bed field h and a proposal h′=h+δh, we define L(h)=χg2(h)+μχh2(h), with χg2(h)=∑i∈Iggitarget-gipred(h)σg2,χh2(h)=∑k∈Ihhk-hkradarσh2. Here Ig indexes all gravity stations and Ih indexes radar–controlled bed cells inside the updated block. hradar is the bed elevation from radar, and σg and σh are the adopted data uncertainties, which we set to σg=1.5 mGal and σh=30 m, in the range of expected uncertainties (Sect. ). μ is a dimensionless weight controlling the gravity–vs–radar trade-off, which is set to 1. In this formulation, the gravity and radar terms enter the likelihood with equal prominence per unit misfit, meaning that any imbalance in uncertainty estimates (e.g., underestimated radar noise or spatially variable gravity errors) could shift the inversion towards favouring one dataset over the other.

The Metropolis acceptance probability is α=min⁡1,exp⁡-12L(h′)-L(h). A random drawing from a uniform distribution decides whether the updated model is accepted. Accepted proposals replace the current state (h′→h), otherwise the previous state is retained. Iterating this procedure yields a Markov chain of bed realizations that are jointly consistent with the gravity data and, when enabled, the radar constraints. To quantify sensitivity to stochastic choices and to obtain uncertainty bounds, we repeat the full inversion for each target terrain effect gtarget, yielding 100 regional and 50 local bed realizations. Each repetition uses an independent random seed for both the conditional Gaussian-field initialization and the block–proposal sequence.

Because the MCMC framework introduces stochastic bed perturbations throughout the inversion mask, small-scale bed undulations in areas far from gravity observations are poorly constrained and should therefore be interpreted cautiously. To quantify this uncertainty, we compute the ensemble standard deviation of accepted bed realizations (Fig. a) and use it as a measure of spatial model variability. This uncertainty estimate provides a quantitative assessment of the reliability of the inferred bed geometry. At the same time, the stochastic framework permits more geologically realistic spatial variability than would be obtained from purely smooth interpolation products.

First, we invert the regional Denman Glacier region at 2 km resolution. The resulting topography with the lowest remaining gravity residual is then used as the initial condition for the second, higher-resolution inversion focused on the Denman Trough with the ground-based gravity measurements. This second run is performed at 1 km resolution. The representative “best-fit” models, shown in Sect. , correspond to the realisations with the lowest RMS gravity misfit.

To consistently merge the local and regional “best-fit” results, a distance-weighted edge-blending approach was applied. First, a smoothed version of each field using a Gaussian filter (σ=3) to provide stable values for transition zones is generated. Then, the boundary between the local and regional domains using a narrow mask is identified and expanded with a binary dilation to define an “edge zone”. For every grid point, the Euclidean distance to this edge is computed and a weight map is constructed that tapers linearly from 1 at the boundary to 0 at distances of ≥10 grid cells. This weight controls how much of the smoothed field is incorporated near the transition. The original bed is retained in the interior, while a gradual blend towards the smoothed regional field occurs only within the defined edge width. The final merged bed grid is therefore seamless, avoiding artificial steps or discontinuities between the two independently derived topographies.

After selecting the best-fit bed model, we refine the background rock density field to account for the remaining gravity misfit. During this forward modeling step, grid cells containing radar picks are assigned the observed radar-derived bed elevation so that the gravity calculation honours the known topography locally. This replacement is applied only for the density refinement and does not modify the final inversion result. Potential cell-scale discontinuities are mitigated by the smooth spatial sensitivity of the gravity response and the regularization applied during the density estimation. The rock volume is represented by right-rectangular prisms from the local bed down to a fixed reference depth of 20 km . Using a linear relationship between cell densities and the vertical gravity at the observation points, we assemble a sensitivity matrix by perturbing each prism in turn with a unit density and recording its gravity effect at all stations. This matrix maps any density change to a predicted gravity change.

We form gravity residuals as observed minus predicted for the chosen bed. To avoid imprinting track-scale noise and very short wavelengths into the density update, we separate a smooth, long-wavelength component of the residuals using Gaussian smoothing in the observation plane (here, σ=5 km) and use only this component for the update. The density increment is then estimated with a damped least-squares inversion (zero-order Tikhonov, solved with LSMR using a small damping factor α=10-2) and added to the prior to obtain the updated rock density field. The damping factor was chosen to stabilize the inversion while allowing geologically plausible amplitudes; smaller values produced unstable, noise-amplifying updates, whereas larger values suppressed meaningful structure.

To complement interpretation, we estimated the depth to magnetic sources (DMS) via Euler deconvolution, following the method of using the same workflow as in . DMS meaning the shallowest depth at which rocks possess sufficient magnetization to produce the observed magnetic anomalies. Notably, DMS is a magnetic parameter and need not coincide with the physical top of crystalline or metamorphic basement: for example, an exposed basement unit may be underlain by more strongly magnetized strata that dominate the signal. We derived DMS from ICECAP airborne magnetic data (; reprocessed by ), using a conservative parameterization that trades spatial resolution for stability and is appropriate for resolving moderately deep sources (see Sect.  of the Appendix).

Gravity inversions are inherently non-unique: an infinite family of density–depth combinations can reproduce the same anomaly, and solutions are further blurred by measurement errors, terrain corrections, and upward continuation that suppresses short wavelengths e.g.. This ambiguity is especially acute beneath thick ice where direct constraints are sparse, as in Denman Glacier .

To mitigate this, we used SGS to generate an ensemble of plausible terrain effects, exploring a range of realizations rather than relying on a single deterministic solution. This incorporates structural uncertainty, reduces overfitting bias, and highlights features that persist across realizations. In practice, however, when a strong regional, non-terrain disturbance is present, mis-estimation of that field dominates the error . In such cases, adding well-placed constraints is more effective than modest noise reductions or additional re-flights . In our inversion, Monte Carlo uncertainty maps consistently flag high-error zones, guiding where new constraints or targeted (re-)flights will most improve the solution.

Along the Denman trough, steep flanks introduce trade-offs between density contrast and interface geometry that can translate into kilometer-scale variations in inferred depth. With the one-layer ice-bedrock contrast formulation used here, the modeled gravity low can absorb both residual terrain effect and genuine geological signal; it should therefore be viewed as a composite response rather than a uniquely resolved basement surface. Where trough geology departs from surrounding radar-constrained regions, the inversion lacks leverage to isolate the geological component, and a unique depth solution is not expected. Additional independent constraints will be required to separate these contributions. A longer ground-based gravity profile with overlap into areas of existing radar bed picks would help constrain the geological component more robustly. Incorporating magnetotelluric and/or seismic information would help refining the estimates and deepen our understanding of the subsurface geology.

The joint misfit combines gravity and radar constraints through prescribed uncertainties (σg and σh) and a dimensionless weighting factor μ (Sect. ). In our baseline formulation we set μ=1, ensuring that the two datasets contribute to the likelihood strictly according to their assumed uncertainties. This allows the inversion to converge toward bed geometries that are statistically consistent with the stated error structure, without introducing additional subjective weighting. Because gravity and radar misfits therefore enter the likelihood on equal footing per unit of normalised misfit, any mis-specification of σg or σh would implicitly shift the balance between the datasets. Our approach reflects a deliberate choice to let the inferred geometry be governed by the reported uncertainties rather than by manual tuning.

The sensitivity of the final results to the initial condition is low. First, we re-draw the Gaussian perturbation for every MCMC realization, ensuring that the ensemble does not inherit structure from any single starting model. Second, the magnitude of the perturbation is selected to be in a similar range of systematic differences between BedMachine and Bedmap3 in this region, preventing the sampler from being biased toward either compilation. As a consequence, the inversion explores a broad portion of the model space, and the posterior ensemble is dominated by the gravitational misfit rather than by the specific choice of initial bed geometry. This yields solutions that are effectively independent of the initial condition while still allowing the method to converge toward geologically and dynamically plausible structures.

The geometry revealed by the gravity-derived beds reinforces the susceptibility of Denman Glacier to Marine Ice Sheet Instability (MISI). In a marine setting, grounding line stability is strongly dependent on the underlying bed geometry . As a result, if the grounding line retreats onto a deeper, inland-sloping bed, buoyancy forces increase while ice flow accelerates, promoting a positive feedback loop of unstable retreat. The Denman Trough's steep and potentially retrograde geometry (Fig. ) is therefore of particular concern, as such configurations can promote MISI under certain combinations of atmospheric forcing and basal conditions e.g.,. However, along- and across-trough ridges (pinning points) could temporarily stabilize the grounding line by increasing basal/side drag and promoting local back-stress, once these highs are passed, instability can resume. While the presence or absence of MISI cannot be inferred from geometry alone, our results provide physically realistic basal boundary conditions that can be tested within ice sheet models to assess the susceptibility of this sector to future retreat and its possible contribution to long-term mass loss from the East Antarctic Ice Sheet.

Our probabilistic inversion differs from in both, data basis and physical assumptions. Rather than relying on mass conservation and ice-dynamical constraints, our method uses gravity. This produces a complementary estimate of bed geometry that reflects the integrated mass distribution beneath the ice sheet, only weakly constrained by ice flow dynamics. The two approaches therefore illuminate different aspects of the system. quantify how much bed geometry can vary while remaining dynamically consistent with present-day ice flow, but it inherits limitations where surface velocity gradients are small. Our gravity-based ensemble, by contrast, is unaffected by ice dynamics and instead reflects the deeper mass distribution. As a result, it tends to predict more compartmentalised, rugged trough geometries, including multiple local depressions within the broader Denman basin. These differences suggest that the dynamical constraint of mass conservation alone does not fully capture the complexity of the subglacial landscape in this region, and that complementary geophysical constraints such as gravity are essential for identifying plausible structural configurations. Taken together, their combined perspectives emphasize the need for ensemble-based modeling that incorporates both ice-dynamic and solid-Earth constraints when assessing basin geometry, grounding line sensitivity, and future retreat scenarios.

While Euler deconvolution provides a rapid estimate of magnetic source depths, it has several limitations. The method is sensitive to the magnitude of susceptibility contrasts; weakly magnetized rocks may yield weak anomalies that are difficult to interpret. Depth estimates depend critically on the assumed structural index, and misinterpretations can arise if the true source geometry differs from the model. In addition, the method amplifies data noise through the calculation of spatial derivatives, and its resolution is inherently limited by the flight altitude and the depth to magnetic sources. Remanent magnetization and the choice of window size further influence solution stability and accuracy, particularly in regions of deep or complex geology such as the Denman Trough.

The ICECAP magnetic data were acquired at an average flight height of approximately 2 km relative to the WGS84 ellipsoid. Over the Denman region, where the ice surface itself lies roughly 1–2 km above the ellipsoid, this corresponds to an effective height of approximately 0.5–1 km above the ice surface. Consequently, the minimum resolvable magnetic wavelengths range from about 1–3 km . At suggested trough depths of 3–6 km beneath the ice surface, the source-to-sensor distances imply that only magnetic anomalies with wavelengths larger than approximately 6–18 km are well resolved, favoring the detection of broader geometries rather than fine-scale basement features (Fig. ).