PREM, Matter Effects, and Earth Tomography with Neutrinos

Neutrinos travelling through the Earth experience the matter effect — a coherent forward scattering on the electrons of the medium that modifies their effective masses and oscillation pattern. For low-energy or short-baseline experiments, this is a small perturbation. For long-baseline experiments at GeV and TeV energies, it can dominate the oscillation phenomenology. Either way, accurate predictions require a quantitative model of the Earth’s electron density along the neutrino’s path.

The standard reference is PREM — the Preliminary Reference Earth Model, published by Dziewonski and Anderson in 1981. PREM is a radial density profile derived from seismological data: the travel times of seismic waves through the Earth, integrated over many earthquake-station pairs, constrain the average density at each depth. The result is the canonical interior structure used by both geophysicists and particle physicists.

This post is about PREM, how it shapes neutrino oscillation in long-baseline experiments, and how neutrinos themselves are now beginning to provide an independent probe of the Earth’s interior.

The Earth interior

PREM divides the Earth into shells of progressively decreasing density from the centre outward.

The structure:

• Inner core: A solid iron-nickel sphere of radius approximately 1,220 km, density approximately 13 g/cm³, with electron mole fraction $Y_e\approx 0.47$.
• Outer core: A liquid iron-nickel-light-element shell from 1,220 to 3,486 km radius, density 10-12 g/cm³.
• Lower mantle: Solid silicate rock from 3,486 to 5,701 km radius, density 5 g/cm³.
• Upper mantle and transition zones: From 5,701 km to approximately 6,346 km (variable density 3.4-4.4 g/cm³).
• Crust: Outer 30 km, density 2.7 g/cm³.

For neutrino physics, the relevant quantity is the electron density: $n_e=\rho \cdot Y_e\cdot N_A$ where $\rho$ is the mass density, $Y_e$ is the electron mole fraction, and $N_A$ is Avogadro’s number. For Earth-mantle silicates, $Y_e\approx 0.5$. For the iron-rich core, $Y_e$ is slightly lower (around 0.47).

The matter potential — the energy that an electron neutrino feels in this medium relative to the muon or tau neutrino — is: $V_e=\sqrt{2}{G}_F{n}_e$

This is small in absolute terms (about $7\times 10^{-14}$ eV at the Earth’s mantle density), but for high-energy or long-baseline neutrinos it can dominate the oscillation phase.

Matter effect implications

The matter effect modifies the oscillation phenomenology in three ways:

MSW resonance. At a particular neutrino energy, the matter potential exactly compensates the vacuum mass-squared difference, producing a resonance. The resonance condition is: $E_{\nu }^{\text{res}}=\frac{\Delta m^2\cos 2\theta }{2V_e}$

For $\Delta m_{31}^2\approx 2.5\times 10^{-3}$ eV² and Earth-mantle density, the resonance for atmospheric neutrinos is at approximately $E_{\nu }\sim 6$ GeV. For solar-splitting parameters, the corresponding resonance is at much lower energies (consistent with the solar matter effect itself).

Ordering-dependent appearance. For long-baseline accelerator neutrinos in normal ordering, the matter effect enhances the ${\nu }_{\mu }\to {\nu }_e$ appearance probability (compared to vacuum). For inverted ordering, the matter effect suppresses it. The opposite is true for antineutrinos. This is the basis for the ordering-discrimination in NOvA and DUNE.

Modified oscillation amplitudes. The effective mixing angle in matter is shifted from the vacuum value: ${\sin }^{2}2{\theta }^{\text{matter}}=\frac{{\sin }^{2}2\theta }{(\cos 2\theta -2E{V}_e/\Delta m^2{)}^2+{\sin }^{2}2\theta }$

At the resonance, the effective mixing becomes maximal regardless of the vacuum value — this is the original MSW phenomenon and is the dominant effect in solar neutrino propagation.

For long-baseline accelerator experiments running at energies in the 1-3 GeV range, the matter effect is approximately a 10-30% modification of the appearance probability, depending on the ordering. For atmospheric or astrophysical neutrinos at higher energies passing through significant Earth chord, the effects can be much larger.

Long-baseline experiments and PREM

Modern long-baseline analyses use a layered Earth model with approximately 80 shells (a discretized PREM) to compute the oscillation probabilities.

T2K (J-PARC to Super-Kamiokande, 295 km) operates at energies around 0.6 GeV, where matter effects are small (a few percent modification).

NOvA (Fermilab to Soudan, 810 km) operates at peak energy 2 GeV, where matter effects are around 10% — already significant for the appearance measurement.

DUNE (Fermilab to South Dakota, 1300 km) will operate at 2-3 GeV, with substantial matter effects (around 30% modification of the appearance probability). DUNE’s longer baseline and higher matter potential give it the strongest single-experiment sensitivity to mass ordering.

For atmospheric neutrinos at IceCube and Super-Kamiokande, the relevant baselines range from ~10 km (downward-going from above) to ~12,800 km (upward-going through the Earth’s diameter). The matter effect modifies the oscillation pattern depending on the chord length, with the largest effects for nearly-vertical upward events.

Atmospheric measurements as Earth probes

The most exciting recent development is the use of atmospheric neutrinos to probe Earth’s interior structure. The idea: high-energy atmospheric neutrinos crossing the Earth at different zenith angles experience different chord lengths and density profiles. By measuring the modification of the oscillation pattern as a function of zenith angle, one can extract the integrated electron density along the neutrino’s path.

IceCube reported the first such measurement in 2018, using approximately one year of atmospheric data at 100 GeV-1 TeV energies. The result was consistent with PREM at the 30-50% level — limited by statistics but already a meaningful constraint.

By 2025, with several additional years of data and improved analyses, the constraints have tightened. IceCube’s atmospheric data now provides density measurements at the 15-20% level, comparable to seismic measurements in the deep Earth where the seismic constraints are weakest.

For comparison, seismology measures Earth structure to better than 1% in shallow layers but loses precision in the deep core where direct sampling is impossible. The neutrino measurement is complementary: weakest in shallow layers (because the chord through them is short) and strongest in the deep core.

A 2024 IceCube analysis specifically constrained the density of the inner core. The result was consistent with PREM but allowed a 10% lighter or 10% heavier core within 1σ. With another decade of running, this could tighten to 3-5%.

ORCA and the future

KM3NeT-ORCA, located in the Mediterranean off Toulon, is specifically designed for atmospheric-neutrino measurements at oscillation energies around 5-10 GeV. ORCA is partially deployed and accumulating data.

ORCA’s vertical reach allows measurements at intermediate chord lengths that IceCube does not access optimally. Combined ORCA-IceCube measurements over the next decade should provide the most stringent neutrino-tomography constraints on Earth structure.

PINGU (a proposed IceCube core-extension upgrade) would have similar sensitivity to ORCA but at the South Pole. Whether PINGU is built will depend on resource allocation to IceCube-Gen2 and other priorities; ORCA will deploy first.

By 2035, neutrino tomography is expected to provide constraints on the inner core density at the 1-2% level — competitive with seismology in this region. This will not replace seismology (which provides much richer information about elastic moduli, anisotropy, and so on) but will provide an independent cross-check.

Beyond density: composition probes

Neutrino tomography can also probe Earth’s chemical composition, specifically the electron mole fraction $Y_e$, which depends on the iron-versus-silicate ratio in different layers.

For the inner core, $Y_e$ is expected to be slightly lower than for the mantle (because iron has fewer electrons per nucleon than oxygen). The difference is small (about 5%) but measurable in principle with sufficient statistics.

This kind of composition information is hard to obtain from seismology alone. Neutrino measurements provide complementary information: they directly measure $n_e$, while seismology directly measures elastic moduli (which depend on a different combination of composition and structure).

A two-way conversation

The traditional flow has been: seismology measures Earth, gives PREM, particle physicists use PREM for oscillation analyses. The recent development is making this a two-way conversation: neutrinos measure Earth, providing independent constraints that can be used by geophysicists.

For most of physics history, the Earth has been a mere background for fundamental measurements. The new era is one where the Earth itself is a target — a natural laboratory whose interior structure can be probed through how neutrinos respond to it.

The matter effect, originally a complication to be subtracted from oscillation analyses, is now also a tool for probing the medium it operates in. PREM, originally a seismology product, is now also a particle-physics input. The connections between disciplines run both ways.

By 2035, neutrino tomography will be a routine cross-check on Earth’s interior structure. By 2050, with multi-decade exposures from successor experiments, it may provide constraints competitive with seismology in regions where both apply.

The Earth and the neutrino, two seemingly disparate subjects, are now one connected experimental programme. Each illuminates the other.