DeepEarth: Multimodal Insights into Earth’s Interior

• DeepEarth is an umbrella term for diverse methods that infer Earth’s deep interior using indirect observables like neutrino oscillations, gravimetric signals, and electromagnetic responses.
• It integrates techniques such as atmospheric-neutrino tomography, geoneutrino heat measurements, and satellite gravimetry to assess density, composition, and dynamic processes in inaccessible regions.
• Advancements include computational models and machine learning approaches that fuse heterogeneous geophysical data to complement traditional seismology and geochemistry.

DeepEarth is a research label applied to several technically distinct programs concerned with the Earth’s deep interior, deep subsurface, or planetary-scale Earth representation. In the literature cited here, it denotes, among other things, atmospheric-neutrino oscillation tomography of the whole Earth, geoneutrino constraints on mantle radiogenic heat, gravimetric and electromagnetic probing of deep structure, chemically centered reinterpretations of the core–mantle system, and machine-learning models that encode global or subsurface Earth structure in latent space (Chattopadhyay, 30 Jan 2026, Kumaran et al., 2021, Mandea et al., 2020, Darnet et al., 2024, Herndon, 2011, Legel et al., 7 Mar 2026). The term is therefore not a single standardized method; it is an umbrella for approaches that seek information unavailable from direct sampling and that are often complementary to seismology, gravimetry, and geochemistry.

1. Scope of the term in current research

In the cited literature, “DeepEarth” or closely related phrasing is used for both observational and computational programs. Some usages target the entire planet, especially the mantle and core, whereas others focus on the first kilometers of the crust or on global spatiotemporal Earth data fields.

Usage in the cited literature	Primary observable or representation	Representative objective
Atmospheric-neutrino DeepEarth	Oscillation matter effects	Earth mass and layer densities
Geoneutrino deep-Earth studies	$\bar{\nu}_e$ from U and Th decay	Mantle radiogenic heat
Gravimetric / EM deep-Earth imaging	GRACE residual gravity; CSEM / DCIP	CMB dynamics; deep conductive crust
Computational DeepEarth	4D embeddings, transformers, synthetic geology	Planetary-scale or subsurface inference

The unifying feature is indirect inference from observables that respond to deep structure, composition, or dynamics. In neutrino-based work, the relevant field is electron density $N_e(r)$, not merely bulk density. In GRACE-based work, the signal is time-variable gravity after removal of dominant surface contributions. In subsurface machine learning, the latent object is a learned prior over heterogeneous observations or categorical geological volumes rather than a direct physical measurement (Chattopadhyay et al., 26 Feb 2025, Kumaran et al., 2021, Mandea et al., 2020, Mazumder et al., 2 Sep 2025).

2. Atmospheric-neutrino DeepEarth

In IceCube DeepCore, “DeepEarth” denotes the use of atmospheric neutrino oscillations as a probe of Earth’s interior. The key dependence is

$N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$

so matter effects in flavor evolution constrain electron density, and, under assumptions on electron fraction $Y_e$, constrain mass density $\rho(r)$. The matter potential is

$V(x) = \sqrt{2}\,G_F\,N_e(x),$

or, in the alternative formulation used in the DeepCore sensitivity paper,

$$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$

At energies of a few to tens of GeV and baselines up to the Earth’s diameter, MSW resonance and mantle–core–mantle parametric resonance imprint density-dependent structure in the $(E_\nu,\cos\theta_z)$ oscillogram (Chattopadhyay, 30 Jan 2026, Chattopadhyay et al., 26 Feb 2025).

The detector context is specific. IceCube instruments one cubic kilometer of Antarctic ice with 86 strings and 5,160 DOMs, while DeepCore is a denser low-energy sub-array of 15 strings optimized for GeV-scale neutrinos. The cited analyses use reconstructed atmospheric neutrinos in the 3–100 GeV range, with effective thresholds of 5 GeV for the matter-effect and mass analyses, 20 logarithmic energy bins, 20 zenith bins over $\cos\theta_z \in [-1,0]$, and 3 PID bins from a CNN-based classifier separating cascade-like, mixed, and track-like events. The simulation sample corresponds to 9.3 years of DeepCore-equivalent exposure, with event reweighting over oscillation parameters, fluxes, cross sections, detector systematics, and Earth-density parameters (Chattopadhyay et al., 26 Feb 2025).

Two parameterizations are central. For a neutrino-only Earth-mass measurement, the 12-layer PREM profile is scaled by a single factor $\alpha$,

$N_e(r)$0

For correlated layer-density studies, PREM is reduced to five averaged layers—inner core, outer core, inner mantle, middle mantle, and outer mantle—with a common core scaling $N_e(r)$1, separate inner and middle mantle scalings, fixed outer-mantle density, and external constraints that total mass and moment of inertia remain consistent with geophysics. In the simplified parameterization, the admissible family is effectively one-dimensional and can be expressed in terms of $N_e(r)$2 (Chattopadhyay, 30 Jan 2026).

The statistical framework is standard forward folding into reconstructed space using Asimov data sets and a binned Poisson likelihood with nuisance-parameter pulls. The work distinguishes non-nested tests—PREM matter effects versus vacuum oscillations, and layered Earth versus uniform-density Earth—from nested fits for $N_e(r)$3 or $N_e(r)$4, for which Wilks’ theorem is invoked. With 9.3 years of DeepCore-equivalent simulated data, the matter-effect sensitivity depends on $N_e(r)$5 and, for $N_e(r)$6, is about $N_e(r)$7 for normal ordering and about $N_e(r)$8 for inverted ordering. The layered-versus-homogeneous test gives about $N_e(r)$9 for normal ordering and about $N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$0 for inverted ordering. The Earth-mass likelihood curve is centered at $N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$1; the conference summary does not print exact uncertainties, but the figure implies $N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$2-level sensitivity or better. For correlated layer densities, neutrino data narrow the locus allowed by mass and moment-of-inertia constraints alone (Chattopadhyay et al., 26 Feb 2025, Chattopadhyay, 30 Jan 2026).

The IceCube Upgrade is expected to sharpen this program. The Upgrade adds seven very densely instrumented strings, a fiducial volume of about 2 Mton, a threshold down to $N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$3 GeV, and improved calibration and resolution. In the cited sensitivity study, 3 years of Upgrade data combined with 12 years of DeepCore data produce noticeably narrower likelihood curves for both $N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$4 and the correlated core–mantle density parameter $N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$5 (Chattopadhyay, 30 Jan 2026).

3. Geoneutrino DeepEarth and the mantle heat budget

A second neutrino-based DeepEarth program uses geoneutrinos, $N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$6 emitted in the decay chains of $N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$7, $N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$8, $N_e(r) = Y_e(r)\,\frac{\rho(r)}{m_N},$9, and $Y_e$0. Because each decay chain has a fixed, well-known ratio between radiogenic heat and emitted antineutrinos, geoneutrino measurements directly probe radiogenic heat production in the deep Earth. Borexino emphasizes that geoneutrinos are the only direct probe of radiogenic heat generation at depth, especially in the mantle, where composition and U–Th inventory are poorly constrained (Kumaran et al., 2021).

Borexino detects geoneutrinos by inverse beta decay,

$Y_e$1

with a kinematic threshold of 1.8 MeV. As a result, the detector is sensitive to $Y_e$2 and $Y_e$3 geoneutrinos but not to $Y_e$4 and $Y_e$5. The 2020 analysis used data from December 9, 2007 to April 28, 2019, totaling 3262.74 days of live time and an exposure of $Y_e$6 protons $Y_e$7 year, with detection efficiency $Y_e$8. Results are reported in TNU, with $Y_e$9 defined as 1 detected antineutrino event per year in a detector with $\rho(r)$0 free protons and 100% detection efficiency (Kumaran et al., 2021).

The total geoneutrino signal is reported as

$\rho(r)$1

corresponding to a total relative precision of about 19%. Geological modeling gives a bulk-lithosphere contribution at LNGS of

$\rho(r)$2

Subtracting the lithosphere-constrained component yields a mantle signal

$\rho(r)$3

and the null hypothesis $\rho(r)$4 is excluded at 99.0% confidence level. Under a homogeneous-mantle assumption and mantle Th/U mass ratio of 3.7, Borexino derives lower limits at 90% C.L. of uranium abundance $\rho(r)$5 ppb and thorium abundance $\rho(r)$6 ppb in the mantle (Kumaran et al., 2021).

These fluxes are translated into heat-budget quantities. Borexino reports mantle radiogenic heat from U+Th of

$\rho(r)$7

lithospheric radiogenic heat

$\rho(r)$8

and, after including $\rho(r)$9 through the assumption that K contributes 18% of the total mantle radiogenic heat, total Earth radiogenic heat

$V(x) = \sqrt{2}\,G_F\,N_e(x),$0

Relative to a total surface heat flow of $V(x) = \sqrt{2}\,G_F\,N_e(x),$1, this implies a convective Urey ratio of

$V(x) = \sqrt{2}\,G_F\,N_e(x),$2

and an 85% probability that radioactive decays produce more than half of the total terrestrial heat. In this geoneutrino-based DeepEarth framing, the observable is not density structure but the distribution of heat-producing elements in the bulk silicate Earth (Kumaran et al., 2021).

The same Borexino analysis also constrains a hypothetical deep georeactor. Under a U-fission spectrum, the 95% C.L. limits are $V(x) = \sqrt{2}\,G_F\,N_e(x),$3 TW at 2900 km, $V(x) = \sqrt{2}\,G_F\,N_e(x),$4 TW at 6371 km, and $V(x) = \sqrt{2}\,G_F\,N_e(x),$5 TW at 9842 km. These limits are framed as strong constraints on multi-terawatt natural fission reactors in the core or at the core–mantle boundary (Kumaran et al., 2021).

4. Gravimetric, electromagnetic, and phase-space approaches to the deep Earth

Outside neutrino physics, DeepEarth-style inference also uses satellite gravimetry, controlled-source electromagnetics, induced polarization, and pressure–temperature phase-space modeling. In the GRACEFUL program, monthly GRACE gravity fields from January 2003 to December 2015, built as an ensemble mean of CSR, GFZ, JPL, TUG, and GRGS solutions and corrected for geocenter motion, $V(x) = \sqrt{2}\,G_F\,N_e(x),$6, and GIA, are stripped of atmosphere, ocean, hydrology, land-ice, and GIA contributions to define a residual gravity field. After truncation to degree and order 8 and comparison with CHAOS-6 secular acceleration at virtual observatories on a $V(x) = \sqrt{2}\,G_F\,N_e(x),$7 grid, singular-value decomposition isolates a dominant common mode between gravity and geomagnetism. The residual signal has amplitudes of hundreds of nGal in gravity and a few tens of nT/yr$V(x) = \sqrt{2}\,G_F\,N_e(x),$8 in magnetic secular acceleration, with sub-decadal variability consistent with rapid core-flow or CMB processes (Mandea et al., 2020).

At crustal scales, the SEEMS DEEP project uses the phrase “DeepEarth regime” for deep electrical and electromagnetic imaging in highly resistive crystalline crust. At the Koillismaa Layered Intrusion Complex, the acquisition used 25 galvanic transmitter dipoles of about 1 km length and 115 autonomous receivers over more than $V(x) = \sqrt{2}\,G_F\,N_e(x),$9–$$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$0, with square-wave injection at 0.0625, 0.125, 0.5, 2, 8, 32, 128, and 512 Hz. From the same time series the project extracted ERT, phase/IP, and CSEM responses, then inverted them in 3D with pyGIMLi and custEM. The ERT–IP model reached a depth of investigation of about 2.5 km and resolved a deep phase anomaly of about $$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$1 mrad beginning below $$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$2 m depth. In multifrequency CSEM, resetting all resistivities below 2 km depth to 10,000 $$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$3m increased the RMS misfit from 1.73 to 4.51, which the paper interprets as evidence of genuine sensitivity below 2 km. The conductive and chargeable body correlates with the ultramafic intrusion and with a borehole interval at $$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$4 m showing anomalous electrical and chargeability properties (Darnet et al., 2024).

A different deep-Earth framing appears in pressure–temperature phase-space studies of water and the biosphere. By representing the atmosphere, surface, oceans, crust, mantle, and core in $$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$5–$$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$6 space and overlaying the stability field of liquid water, Jones and Lineweaver locate the deepest terrestrial liquid water at $$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$7 and $$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$8 bar, corresponding to a depth of $$V_\text{CC} \approx \pm 7.6 \times Y_e \times 10^{-14} \left[\frac{\rho}{\mathrm{g/cm}^3}\right] \mathrm{eV}.$$9 km. They estimate that about 3.5% of Earth’s volume lies above 75 km depth, that only about 12% of the Earth–liquid-water overlap in $(E_\nu,\cos\theta_z)$0–$(E_\nu,\cos\theta_z)$1 space is inhabited by life under current biosphere limits, and that at least 1% of the volume of liquid water on Earth is uninhabited (Jones et al., 2010). This extends DeepEarth from structure and dynamics to the geometry of the deep hydrosphere and biosphere.

5. Chemical reinterpretations and alternative deep-Earth paradigms

Some literature uses DeepEarth in a chemically centered sense that explicitly departs from mainstream mantle-convection and core-composition models. In Herndon’s 2011 papers, the deep Earth below 660 km is modeled as compositionally analogous to the Abee enstatite chondrite. Quantitative mass-ratio comparisons are presented between the lower mantle and core on one side and Abee’s silicate and alloy fractions on the other. In this framework, the inner core is identified as a nickel–silicide phase, Dʺ as a layer of sulfide “core-floaters” composed of CaS and MgS, and the ULVZ as predominantly CaS. The argument relies on close matches such as lower mantle mass / total core mass of 1.49 for Earth versus 1.43 for Abee, inner core mass / total core mass of 0.052 for Earth versus 0.052 for theoretical Ni$(E_\nu,\cos\theta_z)$2Si, and ULVZ mass / total core mass of about 0.012 for both Earth and CaS in Abee-like enstatites (Herndon, 2011, Herndon, 2011).

The same program extends to planetary formation and geodynamics. Herndon proposes that Earth initially formed as a Jupiter-like gas giant, with a massive primordial gas envelope compressing the rocky kernel to approximately 64% of its present radius. After removal of the gas during a T-Tauri phase, Earth is argued to have undergone whole-Earth decompression dynamics, generating primary decompression cracks identified with the global mid-ocean ridge system and secondary decompression cracks identified with submarine trenches. In this picture, oceanic basalt moves by gravitational creep and infills secondary cracks, so plate-tectonic observations are reinterpreted without mantle convection (Herndon, 2011).

A central component of this alternative paradigm is a deep nuclear georeactor. Because uranium is inferred to partition into the metallic core under highly reducing conditions, it is proposed to segregate to the planetary center and form a fissioning sub-core surrounded by a convecting shell of radioactive waste products. Herndon identifies this small central system, rather than the outer core, as the seat of the geodynamo and as a source of heat for hotspot volcanism. The papers explicitly frame these ideas as alternatives to “physics-only” models and call for high-pressure studies of the elastic properties and stability of CaS and MgS at CMB conditions (Herndon, 2011, Herndon, 2011).

6. Computational DeepEarth: 4D world models, synthetic geology, and multimodal foundation models

A distinct computational usage appears in the 2026 paper titled “DeepEarth,” where the term names a self-supervised multi-modal world model built around Earth4D, a planetary-scale 4D space-time positional encoder. Earth4D decomposes $(E_\nu,\cos\theta_z)$3 into four 3D multi-resolution hash grids—xyz, xyt, yzt, and xzt—with 24 levels per grid and 2D features per level, yielding a 192-dimensional embedding from $(E_\nu,\cos\theta_z)$4. In the default configuration, each level has capacity $(E_\nu,\cos\theta_z)$5, the full encoder contains about 724M trainable parameters, and training uses about 11 GB of GPU memory. Learned hash probing substantially improves performance over standard hash encoding: on the Globe-LFMC 2.0 benchmark, Earth4D with learned probing, using only $(E_\nu,\cos\theta_z)$6 and a species embedding, achieves MAE 11.7 pp, RMSE 18.7 pp, and $(E_\nu,\cos\theta_z)$7, surpassing the Galileo baseline with MAE 12.6, RMSE 18.9, and $(E_\nu,\cos\theta_z)$8 despite using fewer modalities (Legel et al., 7 Mar 2026).

The same broad agenda appears in “Synthetic Geology,” which targets the first few kilometers of the Earth’s subsurface by learning a generative prior over voxelated geological volumes. A Geomodel is defined as

$(E_\nu,\cos\theta_z)$9

with transformations $\cos\theta_z \in [-1,0]$0 acting through displacement fields and depositions $\cos\theta_z \in [-1,0]$1 overwriting voxel classes in geologically motivated windows. Histories are compositions of these operators, and a flow-matching model learns the distribution of resulting 3D categorical fields after embedding them into a continuous space. Sampling is then conditioned on surface geology and boreholes, and the authors propose the learned model as an AI-based regularizer for inverse problems in resource exploration, hazard assessment, and geotechnical engineering (Ghyselincks et al., 11 Jun 2025).

Transparent Earth extends the foundation-model formulation to heterogeneous subsurface modalities. It uses a transformer-based encoder–decoder with geospatial positional encodings

$\cos\theta_z \in [-1,0]$2

text-derived modality embeddings from the E5 model, and Perceiver-style cross-attention into latent arrays. The system currently includes eight modalities—stress angle, strain angle, sediment thickness, mantle temperature, tectonic plates, fault type, basin type, and basin age—and supports in-context learning from arbitrary subsets of observations or from no observations at all. On validation data, the model reduces errors in predicting stress angle by more than a factor of three, and performance improves systematically from 3M to 243M parameters (Mazumder et al., 2 Sep 2025).

These computational programs are not direct measurements of the deep Earth. They are learned priors or world models over multimodal geospatial data. A plausible implication is that “DeepEarth” has acquired, in machine-learning usage, a second meaning: not only inference about the deep interior, but also foundation-model representations of Earth structure across space, depth, and time (Legel et al., 7 Mar 2026, Ghyselincks et al., 11 Jun 2025, Mazumder et al., 2 Sep 2025).

7. Complementarity, limitations, and research trajectory

Across these usages, DeepEarth is defined less by a single instrument than by complementarity to established methods. Atmospheric-neutrino tomography is sensitive to $\cos\theta_z \in [-1,0]$3, not directly to seismic velocity or gravitational potential; geoneutrinos measure radiogenic-element inventories rather than density; GRACE residuals respond to mass redistribution and boundary deformation; EM methods respond to resistivity and chargeability; and foundation models operate on statistical structure in heterogeneous observations (Chattopadhyay, 30 Jan 2026, Kumaran et al., 2021, Mandea et al., 2020, Darnet et al., 2024, Mazumder et al., 2 Sep 2025).

The limitations are correspondingly method-specific. In IceCube DeepCore, the dominant constraints are atmospheric-flux uncertainties, cross-section systematics, detector calibration, oscillation-parameter degeneracies, and finite energy–angle resolution; current sensitivities remain at the $\cos\theta_z \in [-1,0]$4–$\cos\theta_z \in [-1,0]$5 level for matter-effect and layered-Earth tests in 9.3-year Asimov studies, and traditional seismology and gravimetry remain much more precise for bulk density structure (Chattopadhyay et al., 26 Feb 2025). In Borexino, mantle inference depends on lithosphere subtraction, reactor-background modeling, and assumptions on Th/U and K contributions (Kumaran et al., 2021). In GRACE, the difficulty is separation of small deep signals from dominant atmosphere–ocean–hydrology–ice variability and model dependence in GIA correction (Mandea et al., 2020). In deep EM imaging, transmitter coupling in resistive ground, sparse receiver spacing, spontaneous-potential removal, and inversion non-uniqueness limit resolution at depth (Darnet et al., 2024). In machine-learning formulations, domain shift, data sparsity, computational cost, and the absence of explicit physical constraints remain central issues (Legel et al., 7 Mar 2026, Ghyselincks et al., 11 Jun 2025, Mazumder et al., 2 Sep 2025).

The overall trajectory is toward integration. The neutrino literature explicitly anticipates synergy across IceCube DeepCore, the IceCube Upgrade, ORCA, ARCA, Hyper-Kamiokande, and related atmospheric-neutrino experiments for composition-sensitive density inference (Chattopadhyay, 30 Jan 2026). Geoneutrino work calls for multi-site detectors such as SNO+, JUNO, JINPING, and HanoHano to separate crust and mantle more cleanly (Kumaran et al., 2021). GRACEFUL links gravimetry, geomagnetism, and Earth rotation for joint inference on core flow (Mandea et al., 2020). SEEMS DEEP is already organized as a seismic–EM program (Darnet et al., 2024). Transparent Earth and Synthetic Geology explicitly aim to serve as priors or integrators for heterogeneous observations (Ghyselincks et al., 11 Jun 2025, Mazumder et al., 2 Sep 2025).

In that sense, DeepEarth is best understood as a family of inference programs directed at inaccessible parts of the planet. In one branch, the Earth is a long-baseline oscillation medium; in another, it is a source of radiogenic antineutrinos; in another, a dynamical mass distribution sensed by satellites; in another, a deep conductive crust interrogated by galvanic and electromagnetic sources; and in another, a latent multimodal object reconstructed by foundation models. The shared scientific problem is the same: extracting information about structure, composition, and dynamics from indirect observables that remain informative where direct sampling ends.