{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T02:27:44Z","timestamp":1768012064325,"version":"3.49.0"},"reference-count":42,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,12]],"date-time":"2023-01-12T00:00:00Z","timestamp":1673481600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The Afar and Ethiopian plateaus are in a dynamic uplift due to the mantle plume, therefore, considering the plume effect is necessary for any geophysical investigation including the estimation of lithospheric stress in this area. The Earth gravity models of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and lithospheric structure models can be applied to estimate the stress tensor inside the Ethiopian lithosphere. To do so, the boundary-value problem of elasticity is solved to derive a general solution for the displacement field in a thin elastic spherical shell representing the lithosphere. After that, general solutions for the elements of the strain tensor are derived from the displacement field, and finally the stress tensor from the strain tensor. The horizontal shear stresses due to mantle convection and the vertical stress due to the mantle plume are taken as the lower boundary value at the base of the lithosphere, and no stress at the upper boundary value of the lithospheric shell. The stress tensor and maximum stress directions are computed at the Moho boundary in three scenarios: considering horizontal shear stresses due to mantle convection, vertical stresses due to mantle plume, and their combination. The estimated maximum horizontal shear stresses\u2019 locations are consistent with tectonics and seismic activities in the study area. In addition, the maximum shear stress directions are highly correlated with the World Stress Map 2016, especially when the effect of the mantle plume is solely considered, indicating the stress in the study area mainly comes from the plume.<\/jats:p>","DOI":"10.3390\/rs15020462","type":"journal-article","created":{"date-parts":[[2023,1,12]],"date-time":"2023-01-12T06:25:57Z","timestamp":1673504757000},"page":"462","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Lithospheric Stress Due to Mantle Convection and Mantle Plume over East Africa from GOCE and Seismic Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6708-6505","authenticated-orcid":false,"given":"Andenet A.","family":"Gedamu","sequence":"first","affiliation":[{"name":"School of Civil and Environmental Engineering, Addis Ababa University, Addis Ababa P.O. Box 1176, Ethiopia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0067-8631","authenticated-orcid":false,"given":"Mehdi","family":"Eshagh","sequence":"additional","affiliation":[{"name":"Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran"},{"name":"Ethiopian Space Science and Geospatial Institute, Addis Ababa P.O. Box 597, Ethiopia"}]},{"given":"Tulu B.","family":"Bedada","sequence":"additional","affiliation":[{"name":"Ethiopian Space Science and Geospatial Institute, Addis Ababa P.O. Box 597, Ethiopia"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,12]]},"reference":[{"key":"ref_1","unstructured":"Teisseyre, R., Czechowski, L., and Leliwa-Kopysty\u0144ski, J.B.T.-D. (1993). 5\u2014The Evolving Earth and its Lithospheric Stresses. Physics and Evolution of the Earth\u2019s Interior, Elsevier."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"494","DOI":"10.3389\/feart.2021.700550","article-title":"Plume Versus Slab-Pull: Example from the Arabian Plate","volume":"9","author":"Aldaajani","year":"2021","journal-title":"Front. Earth Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/0031-9201(77)90010-3","article-title":"Convection pattern and stress system under the African plate","volume":"15","author":"Liu","year":"1977","journal-title":"Phys. Earth Planet. Inter."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1111\/j.1365-246X.1967.tb06253.x","article-title":"Flow in the Mantle Inferred from the Low Degree Harmonics of the Geopotential","volume":"14","author":"Runcorn","year":"1967","journal-title":"Geophys. J. Int."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6261","DOI":"10.1029\/JZ072i024p06261","article-title":"Some remarks on heat flow and gravity anomalies","volume":"72","author":"McKenzie","year":"1967","journal-title":"J. Geophys. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5267","DOI":"10.1029\/JB081i029p05267","article-title":"On global gravity anomalies and two-scale mantle convection","volume":"81","author":"Marsh","year":"1976","journal-title":"J. Geophys. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4843","DOI":"10.1029\/JB086iB06p04843","article-title":"A simple global model of plate dynamics and mantle convection","volume":"86","author":"Hager","year":"1981","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0031-9201(78)90018-3","article-title":"Mantle convection pattern and subcrustal stress field under Asia","volume":"16","author":"Liu","year":"1978","journal-title":"Phys. Earth Planet. Inter."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/0031-9201(82)90007-3","article-title":"The mantle convection pattern and force source mechanism of recent tectonic movement in China","volume":"28","year":"1982","journal-title":"Phys. Earth Planet. Inter."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/0031-9201(83)90102-4","article-title":"The global stress field in the lithosphere obtained from the satellite gravitational harmonics","volume":"31","author":"Fu","year":"1983","journal-title":"Phys. Earth Planet. Inter."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/0031-9201(83)90135-8","article-title":"A dynamical basis for crustal deformation and seismotectonic block movements in central Europe","volume":"32","author":"Liu","year":"1983","journal-title":"Phys. Earth Planet. Inter."},{"key":"ref_12","first-page":"47","article-title":"Plate Motions, Earth\u2019S Geoid Anomalies, and Mantle Convection","volume":"49","year":"1989","journal-title":"Slow Deform. Transm. Stress Earth"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/0031-9201(90)90271-X","article-title":"Global stress pattern constrained on deep mantle flow and tectonic features","volume":"60","author":"Fu","year":"1990","journal-title":"Phys. Earth Planet. Inter."},{"key":"ref_14","unstructured":"ESA (1999). Gravity Field and Steady-State Ocean Circulation Mission, ESA SP-1233(1), Report for Mission Selection of the Four Candidate Earth Explorer Missions, ESA Publications Division."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2391","DOI":"10.1007\/s00024-014-0847-2","article-title":"From Satellite Gradiometry Data to Subcrustal Stress Due to Mantle Convection","volume":"171","author":"Eshagh","year":"2014","journal-title":"Pure Appl. Geophys."},{"key":"ref_16","first-page":"317","article-title":"Local recovery of lithospheric stress tensor from GOCE gravitational tensor","volume":"209","author":"Eshagh","year":"2017","journal-title":"Geophys. J. Int."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1093\/gji\/ggaa313","article-title":"Lithospheric stress, strain and displacement changes from GRACE-FO time-variable gravity: Case study for Sar-e-Pol Zahab Earthquake 2018","volume":"223","author":"Eshagh","year":"2020","journal-title":"Geophys. J. Int."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"931","DOI":"10.2514\/1.A34326","article-title":"GRACE-FO: The Gravity Recovery and Climate Experiment Follow-On Mission","volume":"56","author":"Kornfeld","year":"2019","journal-title":"J. Spacecr. Rockets"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Eshagh, M. (2020). Satellite Gravimetry and the Solid Earth: Mathematical Foundations, Elsevier.","DOI":"10.1016\/B978-0-12-816936-0.00002-5"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6175","DOI":"10.1029\/JZ070i024p06175","article-title":"Gravity anomalies and convection currents: 1. A sphere and cylinder sinking beneath the surface of a viscous fluid","volume":"70","author":"Morgan","year":"1965","journal-title":"J. Geophys. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1002\/2015TC004000","article-title":"Long-term, deep-mantle support of the Ethiopia-Yemen Plateau","volume":"35","author":"Sembroni","year":"2016","journal-title":"Tectonics"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.tecto.2016.05.041","article-title":"Isostasy, flexure, and dynamic topography","volume":"683","author":"Gvirtzman","year":"2016","journal-title":"Tectonophysics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1016\/j.tecto.2018.07.007","article-title":"The World Stress Map database release 2016: Crustal stress pattern across scales","volume":"744","author":"Heidbach","year":"2018","journal-title":"Tectonophysics"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1932","DOI":"10.1002\/2014JB011724","article-title":"Mantle dynamics, isostasy, and the support of high terrain","volume":"120","author":"Molnar","year":"2015","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"104318","DOI":"10.1016\/j.jafrearsci.2021.104318","article-title":"Effects of mantle dynamics on estimating effective elastic thickness of the lithosphere","volume":"183","author":"Gedamu","year":"2021","journal-title":"J. African Earth Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1029\/2001GC000252","article-title":"An updated digital model of plate boundaries","volume":"4","author":"Bird","year":"2003","journal-title":"Geochem. Geophys. Geosystems"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Varet, J. (2017). Geology of Afar (East Africa), Springer.","DOI":"10.1007\/978-3-319-60865-5"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hayes, G.P., Jones, E.S., Stadler, T.J., Barnhart, W.D., McNamara, D.E., Benz, H.M., Furlong, K.P., and Villase\u00f1or, A. (2014). Seismicity of the Earth 1900-2013 East African Rift.","DOI":"10.3133\/ofr20101083P"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1007\/s00024-018-2018-3","article-title":"Elastic Thickness Determination from on-orbit GOCE Data and CRUST1.0","volume":"176","author":"Eshagh","year":"2019","journal-title":"Pure Appl. Geophys."},{"key":"ref_30","unstructured":"Laske, G., Masters, G., Ma, Z., and Pasyanos, M. (2013). Update on CRUST1.0-A 1-degree Global Model of Earth\u2019s Crust. EGU General Assembly Conference Abstracts, Available online: https:\/\/ui.adsabs.harvard.edu\/abs\/2013EGUGA..15.2658L."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"103741","DOI":"10.1016\/j.jafrearsci.2019.103741","article-title":"Moho determination from GOCE gradiometry data over Ethiopia","volume":"163","author":"Gedamu","year":"2020","journal-title":"J. African Earth Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s10712-020-09626-0","article-title":"An Improved Model of the Earth\u2019s Static Gravity Field Solely Derived from Reprocessed GOCE Data","volume":"42","author":"Brockmann","year":"2021","journal-title":"Surv. Geophys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1038\/ngeo2063","article-title":"Mapping the mass distribution of Earth\u2019s mantle using satellite-derived gravity gradients","volume":"7","author":"Panet","year":"2014","journal-title":"Nat. Geosci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4389","DOI":"10.1029\/JZ069i020p04389","article-title":"Satellite Gravity Measurements and a Laminar Viscous Flow Model of the Earth\u2019s Mantle","volume":"69","author":"Runcorn","year":"1964","journal-title":"J. Geophys. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.epsl.2010.01.033","article-title":"Mantle dynamics, geoid, inertia and TPW since 120Myr","volume":"292","author":"Rouby","year":"2010","journal-title":"Earth Planet. Sci. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Conrad, C.P., and Lithgow-Bertelloni, C. (2006). Influence of continental roots and asthenosphere on plate-mantle coupling. Geophys. Res. Lett., 33.","DOI":"10.1029\/2005GL025621"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Farr, T.G., Rosen, P.A., Caro, E., Crippen, R., Duren, R., Hensley, S., Kobrick, M., Paller, M., Rodriguez, E., and Roth, L. (2007). The Shuttle Radar Topography Mission. Rev. Geophys., 45.","DOI":"10.1029\/2005RG000183"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Schubert, G., Turcotte, D.L., and Olson, P. (2001). Mantle Convection in the Earth and Planets, Cambridge University Press.","DOI":"10.1017\/CBO9780511612879"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1029\/RG018i001p00027","article-title":"Gravity fields of the terrestrial planets: Long-wavelength anomalies and tectonics","volume":"18","author":"Phillips","year":"1980","journal-title":"Rev. Geophys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.epsl.2015.05.049","article-title":"Martian sub-crustal stress from gravity and topographic models","volume":"425","author":"Tenzer","year":"2015","journal-title":"Earth Planet. Sci. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3297","DOI":"10.1007\/s12517-013-0979-1","article-title":"The Arabian Plate: Unique fit of the earth\u2019s surface jig saw puzzle","volume":"7","year":"2014","journal-title":"Arab. J. Geosci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.tecto.2009.05.009","article-title":"African stress pattern from formal inversion of focal mechanism data","volume":"482","author":"Delvaux","year":"2010","journal-title":"Tectonophysics"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/2\/462\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:04:22Z","timestamp":1760119462000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/2\/462"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,12]]},"references-count":42,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["rs15020462"],"URL":"https:\/\/doi.org\/10.3390\/rs15020462","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,12]]}}}