# Gravity Spectra from the Density Distribution of Earth’s Uppermost 435 km

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## Abstract

The Earth masses reside in a near-hydrostatic equilibrium, while the deviations are, for example, manifested in the geoid, which is nowadays well determined by satellite gravimetry. Recent progress in estimating the density distribution of the Earth allows us to examine individual Earth layers and to directly see how the sum approaches the observed anomalous gravitational field. This study evaluates contributions from the crust and the upper mantle taken from the LITHO1.0 model and quantifies the gravitational spectra of the density structure to the depth of 435 km. This is done without isostatic adjustments to see what can be revealed with models like LITHO1.0 alone. At the resolution of 290 km (spherical harmonic degree 70), the crustal contribution starts to dominate over the upper mantle and at about 150 km (degree 130) the upper mantle contribution is nearly negligible. At the spatial resolution \(<150\,\hbox {km},\) the spectra behavior is driven by the crust, the mantle lid and the asthenosphere. The LITHO1.0 model was furthermore referenced by adding deeper Earth layers from ak135, and the gravity signal of the merged model was then compared with the observed satellite-only model GOCO05s. The largest differences are found over the tectonothermal cold and old (such as cratonic), and over warm and young areas (such as oceanic ridges). The misfit encountered comes from the mantle lid where a velocity–density relation helped to reduce the RMS error by 40%. Global residuals are also provided in terms of the gravitational gradients as they provide better spatial localization than gravity, and there is strong observational support from ESA’s satellite gradiometry mission GOCE down to the spatial resolution of 80–90 km.

## Keywords

Density distribution model Satellite Gravimetry Lithosphere Upper mantle GOCE Gravitational gradients## Notes

### Acknowledgements

The study is connected to the ESA STSE project “3D Earth - A Dynamic Living Planet” (https://www.3dearth.uni-kiel.de/en). We thank the Editor in Chief Michael J. Rycroft and anonymous reviewers for their helpful comments.

## References

- Afonso JC, Rawlinson N, Yang Y, Schutt DL, Jones AG, Fullea J, Griffin WL (2016) 3-D multiobservable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle: III. Thermochemical tomography in the Western-Central US. J Geophys Res Solid Earth 121(10):7337–7370CrossRefGoogle Scholar
- Anderson DL (2007) New theory of the earth. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Arfken GB, Weber HJ (2005) Mathematical methods for physicists international student edition. Academic press, CambridgeGoogle Scholar
- Artemieva IM (2006) Global \(1\times 1\) thermal model TC1 for the continental lithosphere: implications for lithosphere secular evolution. Tectonophysics 416(1):245–277CrossRefGoogle Scholar
- Auer L, Boschi L, Becker T, Nissen-Meyer T, Giardini D (2014) Savani: a variable resolution whole-mantle model of anisotropic shear velocity variations based on multiple data sets. J Geophys Res Solid Earth 119(4):3006–3034CrossRefGoogle Scholar
- Bertotti B, Farinella P, Vokrouhlicky D (2012) Physics of the solar system: dynamics and evolution, space physics, and spacetime structure, vol 293. Springer, BerlinGoogle Scholar
- Bird P (2003) An updated digital model of plate boundaries. Geochem Geophys Geosyst 4(3):Google Scholar
- Bouman J, Ebbing J, Meekes S, Fattah RA, Fuchs M, Gradmann S, Haagmans R, Lieb V, Schmidt M, Dettmering D et al (2015) GOCE gravity gradient data for lithospheric modeling. Int J Appl Earth Obs Geoinf 35:16–30CrossRefGoogle Scholar
- Bouman J, Ebbing J, Fuchs M, Sebera J, Lieb V, Szwillus W, Haagmans R, Novak P (2016) Satellite gravity gradient grids for geophysics. Sci Rep. https://doi.org/10.1038/srep21050 Google Scholar
- Chase CG (1979) Subduction, the geoid, and lower mantle convection. Nature 282:29CrossRefGoogle Scholar
- Cubells, J., Calsamiglia, A. (2010). Transitando por los espacios jurídico-penales: Discursos sociales e implicaciones para la intervención en casos de violencia hacia la mujer. Acciones e Investigaciones Sociales 28, 79-108Google Scholar
- De Pater I, Lissauer JJ (2015) Planetary sciences. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Denis C, Rogister Y, Amalvict M, Delire C, Denis AI, Munhoven G (1997) Hydrostatic flattening, core structure, and translational mode of the inner core. Phys Earth Planet Inter 99(3):195–206CrossRefGoogle Scholar
- Ebbing J, Braitenberg C, Wienecke S (2007) Insights into the lithospheric structure and tectonic setting of the Barents Sea region from isostatic considerations. Geophys J Int 171(3):1390–1403. https://doi.org/10.1111/j.1365-246X.2007.03602.x CrossRefGoogle Scholar
- Ebbing J, Bouman J, Fuchs M, Lieb V, Haagmans R, Meekes J, Fattah RA (2013) Advancements in satellite gravity gradient data for crustal studies. Lead Edge 32(8):900–906CrossRefGoogle Scholar
- Floberghagen R, Fehringer M, Lamarre D, Muzi D, Frommknecht B, Steiger C, Piñeiro J, Da Costa A (2011) Mission design, operation and exploitation of the gravity field and steady-state ocean circulation explorer mission. J Geodesy 85(11):749–758CrossRefGoogle Scholar
- Fukao Y, Obayashi M (2013) Subducted slabs stagnant above, penetrating through, and trapped below the 660 km discontinuity. J Geophys Res Solid Earth 118(11):5920–5938CrossRefGoogle Scholar
- Fullea J, Rodríguez-González J, Charco M, Martinec Z, Negredo A, Villaseñor A (2015) Perturbing effects of sub-lithospheric mass anomalies in GOCE gravity gradient and other gravity data modelling: application to the Atlantic-Mediterranean transition zone. Int J Appl Earth Obs Geoinf 35:54–69CrossRefGoogle Scholar
- Gruber T (2015) GOCE gravity field models-signal and error assessment. In: EGU general assembly conference abstracts, vol 17, p 1657Google Scholar
- Haagmans R (2000) A synthetic earth for use in geodesy. J Geodesy 74(7–8):503–511CrossRefGoogle Scholar
- Hager BH, Clayton RW, Richards MA, Comer RP, Dziewonski AM (1985) Lower mantle heterogeneity, dynamic topography and the geoid. Nature 313:541–545. https://doi.org/10.1038/313541a0 CrossRefGoogle Scholar
- van Hees GS (2000) Some elementary relations between mass distributions inside the earth and the geoid and gravity field. J Geodyn 29(1):111–123CrossRefGoogle Scholar
- Hildebrand FB (1987) Introduction to numerical analysis. Courier Corporation, North ChelmsfordGoogle Scholar
- James R, Kopal Z (1962) The equilibrium figures of the earth and the major planets. Icarus 1(1–6):442–454CrossRefGoogle Scholar
- Kaban M, Tesauro M, Cloetingh S (2010) An integrated gravity model for Europe’s crust and upper mantle. Earth Planet Sci Lett 296(3):195–209CrossRefGoogle Scholar
- Kaban MK, Schwintzer P, Artemieva IM, Mooney WD (2003) Density of the continental roots: compositional and thermal contributions. Earth Planet Sci Lett 209(1):53–69CrossRefGoogle Scholar
- Kaula WM (2000) Theory of satellite geodesy: applications of satellites to geodesy. Dover Publications, MineolaGoogle Scholar
- Kennett B, Engdahl E, Buland R (1995) Constraints on seismic velocities in the Earth from traveltimes. Geophys J Int 122(1):108–124CrossRefGoogle Scholar
- Laske G, Masters G, Ma Z, Pasyanos M (2013) Update on CRUST1. 0A 1-degree global model of Earth’s crust. Geophys Res Abstr 15:2658Google Scholar
- Li C, Van Der Hilst RD (2010) Structure of the upper mantle and transition zone beneath Southeast Asia from traveltime tomography. J Geophys Res Solid Earth 115(B7):Google Scholar
- Martinec Z (2014) Mass-density Green’s functions for the gravitational gradient tensor at different heights. Geophys J Int 196(3):1455–1465CrossRefGoogle Scholar
- Mayer-Guerr T (2015) The combined satellite gravity field model GOCO05s. In: EGU general assembly conference abstracts, vol 17, p 12364Google Scholar
- Montagner JP, Anderson DL (1989) Constrained reference mantle model. Phys Earth Planet Inter 58(2–3):205–227CrossRefGoogle Scholar
- Moritz H (2000) Geodetic reference system 1980. J Geodesy 74(1):128–133CrossRefGoogle Scholar
- Nolet G, Allen R, Zhao D (2007) Mantle plume tomography. Chem Geol 241(3):248–263CrossRefGoogle Scholar
- Panet I, Pajot-Métivier G, Greff-Lefftz M, Métivier L, Diament M, Mandea M (2014) Mapping the mass distribution of Earth’s mantle using satellite-derived gravity gradients. Nat Geosci 7(2):131–135CrossRefGoogle Scholar
- Pasyanos M (2017) Personal communicationGoogle Scholar
- Pasyanos ME, Masters TG, Laske G, Ma Z (2014) LITHO1.0: an updated crust and lithospheric model of the earth. J Geophys Res Solid Earth 119(3):2153–2173CrossRefGoogle Scholar
- Simmons NA, Forte AM, Boschi L, Grand SP (2010) GyPSuM: a joint tomographic model of mantle density and seismic wave speeds. J Geophys Res Solid Earth 115(B12):Google Scholar
- Simmons NA, Myers SC, Johannesson G, Matzel E (2012) LLNL-G3Dv3: Global P wave tomography model for improved regional and teleseismic travel time prediction. J Geophys Res Solid Earth 117(B10):Google Scholar
- Steinberger B, Becker TW (2016) A comparison of lithospheric thickness models. TectonophysicsGoogle Scholar
- Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: Mission overview and early results. Geophys Res Lett 31(9):Google Scholar
- Tenzer R, Hamayun K, Vajda P (2009) Global maps of the crust 2.0 crustal components stripped gravity disturbances. J Geophys Res Solid Earth 114(B5):b05408. https://doi.org/10.1029/2008JB006016 CrossRefGoogle Scholar
- Tenzer R, Novák P, Vajda P, Gladkikh V (2012) Spectral harmonic analysis and synthesis of Earth’s crust gravity field. Comput Geosci 16(1):193–207CrossRefGoogle Scholar
- Tenzer R, Chen W, Tsoulis D, Bagherbandi M, Sjöberg LE, Novák P, Jin S (2015) Analysis of the refined CRUST1.0 crustal model and its gravity field. Surv Geophys 36(1):139–165CrossRefGoogle Scholar
- Turcotte D, Schubert G (2002) Geodynamics, 2nd edn. Cambridge University Press, New YorkCrossRefGoogle Scholar
- van der Meijde M, Pail R, Bingham R, Floberghagen R (2015) GOCE data, models, and applications: a review. Int J Appl Earth Obs Geoinf 35:4–15CrossRefGoogle Scholar
- Vallado D, McClain W (2001) Fundamentals of astrodynamics and applications, space technology library. Kluwer Academic Publishers, Dordrecht, p 792Google Scholar
- Yegorova T, Pavlenkova G (2015) Velocity-density models of the earth’s crust and upper mantle from the quartz, craton, and kimberlite superlong seismic profiles. Izvestiya Phys Solid Earth 51(2):250CrossRefGoogle Scholar
- Zoback ML, Mooney WD (2003) Lithospheric buoyancy and continental intraplate stresses. Int Geol Rev 45(2):95–118CrossRefGoogle Scholar