Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Neutrino tomography of Earth


Cosmic-ray interactions with the atmosphere produce a flux of neutrinos in all directions with energies extending above the TeV scale1. The Earth is not a fully transparent medium for neutrinos with energies above a few TeV, as the neutrino–nucleon cross-section is large enough to make the absorption probability non-negligible2. Since absorption depends on energy and distance travelled, studying the distribution of the TeV atmospheric neutrinos passing through the Earth offers an opportunity to infer its density profile3,4,5,6,7. This has never been done, however, due to the lack of relevant data. Here we perform a neutrino-based tomography of the Earth using actual data—one-year of through-going muon atmospheric neutrino data collected by the IceCube telescope8. Using only weak interactions, in a way that is completely independent of gravitational measurements, we are able to determine the mass of the Earth and its core, its moment of inertia, and to establish that the core is denser than the mantle. Our results demonstrate the feasibility of this approach to study the Earth’s internal structure, which is complementary to traditional geophysics methods. Neutrino tomography could become more competitive as soon as more statistics is available, provided that the sources of systematic uncertainties are fully under control.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Zenith angular distribution of the atmospheric muon neutrino events in the IC86 sample.
Fig. 2: Ratio of the number of observed events in the IC86 sample to the number of expected events without including Earth attenuation.
Fig. 3: Fit of the density profile of the Earth with IC86 data.
Fig. 4: Earth measurements from neutrino tomography.

Similar content being viewed by others

Data availability

The IceCube data we consider in this paper are the same sample used by the collaboration to search for resonant matter effects induced by light sterile neutrinos8. The Monte Carlo results used to simulate the detector characteristics and all data are publicly available and can be downloaded from


  1. Gaisser, T. K. & Honda, M. Flux of atmospheric neutrinos. Ann. Rev. Nucl. Part. Sci. 52, 153–199 (2002).

    Article  ADS  Google Scholar 

  2. Gandhi, R., Quigg, C., Reno, M. H. & Sarcevic, I. Ultrahigh-energy neutrino interactions. Astropart. Phys. 5, 81–110 (1996).

    Article  ADS  Google Scholar 

  3. González-García, M. C., Halzen, F., Maltoni, M. & Tanaka, H. K. M. Radiography of Earth’s core and mantle with atmospheric neutrinos. Phys. Rev. Lett. 100, 061802 (2008).

  4. Borriello, E. et al. Sensitivity on Earth core and mantle densities using atmospheric neutrinos. J. Cosmol. Astropart. Phys. 0906, 030 (2009).

    Article  ADS  Google Scholar 

  5. Borriello, E. et al. Studies on neutrino Earth radiography. Earth Planets Space 62, 211–214 (2010).

  6. Takeuchi, N. Simulation of heterogeneity sections obtained by neutrino radiography. Earth Planets Space 62, 215–221 (2010).

    Article  ADS  Google Scholar 

  7. Romero, I. & Sampayo, O. A. About the Earth density and the neutrino interaction. Eur. Phys. J. C 71, 1696 (2011).

    Article  ADS  Google Scholar 

  8. Aartsen, M. G. et al. Searches for sterile neutrinos with the IceCube detector. Phys. Rev. Lett. 117, 071801 (2016).

    Article  ADS  Google Scholar 

  9. Bolt, B. A. The precision of density estimation deep in the Earth. Q. J. R. Astron. Soc. 32, 367–388 (1991).

    ADS  Google Scholar 

  10. Kennett, B. L. N. On the density distribution within the Earth. Geophys. J. Int. 132, 374–382 (1998).

    Article  ADS  Google Scholar 

  11. Masters, G. & Gubbins, D. On the resolution of density within the Earth. Phys. Earth Planet. Inter. 140, 159–167 (2003).

    Article  ADS  Google Scholar 

  12. de Wit, R., Käufl, P., Valentine, A. & Trampert, J. Bayesian inversion of free oscillations for Earth’s radial (an)elastic structure. Phys. Earth Planet. Inter. 237, 1–17 (2014).

    Article  ADS  Google Scholar 

  13. Williamson, E. & Adams, L. H. Density distribution in the Earth. J. Wash. Acad. Sci. 13, 413–428 (1923).

    Google Scholar 

  14. The USGS Earthquake Hazards Program (US Geological Survey, 2017);

  15. Bellini, G. et al. Observation of geo-neutrinos. Phys. Lett. B 687, 299–304 (2010).

    Article  ADS  Google Scholar 

  16. Gando, A. et al. Partial radiogenic heat model for Earth revealed by geoneutrino measurements. Nat. Geosci. 4, 647–651 (2011).

    Article  ADS  Google Scholar 

  17. Winter, W. Neutrino tomography: Learning about the Earth’s interior using the propagation of neutrinos. Earth Moon Planets 99, 285–307 (2006).

    Article  ADS  Google Scholar 

  18. Placci, A. & Zavattini, E. On the Possibility of Using High-Energy Neutrinos to Study the Earth’s Interior CERN Report (CERN, 1973);

  19. Volkova, L. V. & Zatsepin, G. T. On the problem of neutrino penetration though the Earth. Izv. Akad. Nauk SSSR Ser. Fiz. 38, 1060–1063 (1974).

    Google Scholar 

  20. Hoshina, K. & Tanaka, H. K. M. Neutrino radiography with IceCube neutrino observatory. Poster at the XXV International Conference on Neutrino Physics and Astrophysics, 3–9 June 2012, Kyoto (Japan) (2012).

  21. Dziewonski, A. M. & Anderson, D. L. Preliminary reference Earth model. Phys. Earth Planet. Inter. 25, 297–356 (1981).

    Article  ADS  Google Scholar 

  22. Luzum, B. et al. The IAU 2009 system of astronomical constants: the report of the IAU working group on numerical standards for fundamental astronomy. Celest. Mech. Dyn. Astron. 110, 293–304 (2011).

    Article  ADS  Google Scholar 

  23. USAO, USNO, HMNAO and UKHO The Astronomical Almanac (US Navy, 2017);

  24. Chen, W., Li, C. L., Ray, J., Shen, W. B. & Huang, C. L. Consistent estimates of the dynamic figure parameters of the Earth. J. Geod. 89, 179–188 (2015).

    Article  ADS  Google Scholar 

  25. Adrián-Martínez, S. et al. Letter of intent for KM3NeT 2.0. J. Phys. G 43, 084001 (2016).

  26. Gaisser, T. K., Stanev, T. & Tilav, S. Cosmic ray energy spectrum from measurements of air showers. Front. Phys. 8, 748–758 (2013).

    Article  Google Scholar 

  27. Ostapchenko, S. Monte Carlo treatment of hadronic interactions in enhanced Pomeron scheme: I. QGSJET-II model. Phys. Rev. D 83, 014018 (2011).

    Article  ADS  Google Scholar 

  28. Zatsepin, V. I. & Sokolskaya, N. V. Three component model of cosmic ray spectra from 100-GeV up to 100-PeV. Astron. Astrophys. 458, 1–5 (2006).

    Article  ADS  Google Scholar 

  29. Riehn, F., Engel, R., Fedynitch, A., Gaisser, T. K. & Stanev, T. A new version of the event generator Sibyll. PoS ICRC2015, 558 (2016).

    Google Scholar 

  30. Barr, G. D., Gaisser, T. K., Robbins, S. & Stanev, T. Uncertainties in atmospheric neutrino fluxes. Phys. Rev. D 74, 094009 (2006).

    Article  ADS  Google Scholar 

  31. Fedynitch, A., Becker Tjus, J. & Desiati, P. Influence of hadronic interaction models and the cosmic ray spectrum on the high energy atmospheric muon and neutrino flux. Phys. Rev. D 86, 114024 (2012).

    Article  ADS  Google Scholar 

  32. Aartsen, M. G. et al. Measurement of the multi-TeV neutrino cross section with IceCube using Earth absorption. Nature 551, 596–600 (2017).

    ADS  Google Scholar 

  33. Cooper-Sarkar, A., Mertsch, P. & Sarkar, S. The high energy neutrino cross-section in the Standard Model and its uncertainty. J. High Ener. Phys. 08, 042 (2011).

    Article  ADS  Google Scholar 

  34. Aaron, F. D. et al. Combined measurement and QCD analysis of the inclusive e + − p scattering cross sections at HERA. J. High Energy Phys. 01, 109 (2010).

  35. Bustamante, M. & Connolly, A. Measurement of the energy-dependent neutrino-nucleon cross section above 10 TeV using IceCube showers. Preprint at (2017).

  36. Argüelles Delgado, C. A., Salvado, J. & Weaver, C. N. A simple quantum integro-differential solver (SQuIDS). Comput. Phys. Commun. 196, 569–591 (2015).

    Article  ADS  Google Scholar 

  37. González-García, M. C., Halzen, F. & Maltoni, M. Physics reach of high-energy and high-statistics IceCube atmospheric neutrino data. Phys. Rev. D 71, 093010 (2005).

  38. Berezinsky, V. S., Gazizov, A. Z., Zatsepin, G. T. & Rozental, I. L. On penetration of high-energy neutrinos through Earth and a possibility of their detection by means of EAS. Sov. J. Nucl. Phys. 43, 406 (1986). [Yad. Fiz. 43, 637 (1986)].

  39. Halzen, F. & Saltzberg, D. Tau-neutrino appearance with a 1000 megaparsec baseline. Phys. Rev. Lett. 81, 4305–4308 (1998).

    Article  ADS  Google Scholar 

  40. Beacom, J. F., Crotty, P. & Kolb, E. W. Enhanced signal of astrophysical tau neutrinos propagating through Earth. Phys. Rev. D 66, 021302 (2002).

    Article  ADS  Google Scholar 

  41. Dembinski, H. P. et al. Data-driven model of the cosmic-ray flux and mass composition from 10 GeV to 1011 GeV. PoS ICRC2017, 533 (2017).

    ADS  Google Scholar 

  42. Riehn, F. et al. The hadronic interaction model SIBYLL 2.3c and Feynman scaling. PoS ICRC2017, 301 (2017).

    ADS  Google Scholar 

  43. Ostapchenko, S. LHC results and hadronic interaction models. Preprint at (2016).

  44. Aab, A. et al. Testing hadronic interactions at ultrahigh energies with air showers measured by the Pierre Auger Observatory. Phys. Rev. Lett. 117, 192001 (2016).

    Article  ADS  Google Scholar 

  45. Dedenko, L. G., Lukyashin, A. V., Roganova, T. M. & Fedorova, G. F. Testing of the VENUS 4.12, DPMJET 2.55, QGSJET II-03 and SIBYLL 2.3 hadronic interaction models via help of the atmospheric vertical muon spectra. EPJ Web Conf. 158, 06006 (2017).

    Article  Google Scholar 

  46. Dedenko, L. G., Lukyashin, A. V., Roganova, T. M. & Fedorova, G. F. Testing of the EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 hadronic interaction models via help of the atmospheric vertical muon spectra. J. Phys. Conf. Ser. 934, 012017 (2017).

    Article  Google Scholar 

  47. Pierog, T. Review of model predictions for extensive air showers. JPS Conf. Proc. 19, 011018 (2018).

    Google Scholar 

  48. Feroz, F. & Hobson, M. P. Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis. Mon. Not. R. Astron. Soc. 384, 449–463 (2008).

    Article  ADS  Google Scholar 

  49. Feroz, F., Hobson, M. P. & Bridges, M. MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics. Mon. Not. R. Astron. Soc. 398, 1601–1614 (2009).

    Article  ADS  Google Scholar 

  50. Feroz, F., Hobson, M. P., Cameron, E. & Pettitt, A. N. Importance nested sampling and the MultiNest algorithm. Preprint at (2013).

Download references


A.D. thanks G. Cultrera, D. Errandonea, A. Kavner, C. Piromallo and G. Soldati for useful discussions. A.D. and J.S. were supported by the Generalitat Valenciana under grant PROMETEO II/2014/050 and by the Spanish MINECO grants FPA2014-57816-P and FPA2017-85985-P. S.P.-R. is supported by the Generalitat Valenciana under grant PROMETEOII/2014/049, by the Spanish MINECO grants FPA2014-54459-P and FPA2017-84543-P, by a Ramón y Cajal contract, and also partially by the Portuguese FCT through the CFTP-FCT Unit 777 (PEst-OE/FIS/UI0777/2013). The authors also acknowledge support by the Spanish MINECO under grant SEV-2014-0398. J.S. is also supported by the Spanish MINECO grant FPA2016-76005-C2-1-P, María de Maetzu program grant MDM-2014-0367 of ICCUB and research grant 2017-SGR-929. All authors are supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreements No. 690575 and 674896.

Author information

Authors and Affiliations



The idea was conceived by A.D. The approach of the study was discussed by all authors. J.S. performed all the numerical calculations and prepared the figures. S.P.-R. wrote the text, with inputs from A.D. Bibliography selection was performed by A.D. and S.P.-R. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Sergio Palomares-Ruiz.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Donini, A., Palomares-Ruiz, S. & Salvado, J. Neutrino tomography of Earth. Nature Phys 15, 37–40 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing