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Here we quantify the potential contribution of grain\u2010scale and rock\u2010scale compositional anisotropy to the observations by (i) combining effective medium theories with realistic estimates of mineral isotropic elastic properties and (ii) measuring velocities of synthetic seismic waves propagating through modeled strain\u2010induced microstructures. It is shown that for typical mantle and oceanic crust subsolidus compositions, rock\u2010scale compositional layering does not generate any substantial extrinsic anisotropy (&lt;1%) because of the limited contrast in isotropic elastic moduli among different rocks. Quasi\u2010laminated structures observed in subducting slabs using <jats:italic>P<\/jats:italic> and <jats:italic>S<\/jats:italic> wave scattering are often invoked as a source of extrinsic anisotropy, but our calculations show that they only generate minor seismic anisotropy (&lt;0.1\u20130.2% of Vp and Vs radial anisotropy). More generally, rock\u2010scale compositional layering, when present, cannot be detected with seismic anisotropy studies but mainly with wave scattering. In contrast, when grain\u2010scale layering is present, significant extrinsic anisotropy could exist in vertically limited levels of the mantle such as in a mid\u2010ocean ridge basalt\u2010rich lower transition zone or in the uppermost lower mantle where foliated basalts and pyrolites display up to 2\u20133% Vp and 3\u20136% Vs radial anisotropy. Thus, seismic anisotropy observed around the 660\u2010km discontinuity could be possibly related to grain\u2010scale shape\u2010preferred orientation. Extrinsic anisotropy can form also in a compositionally homogeneous mantle, where velocity variations associated with major phase transitions can generate up to 1% of positive radial anisotropy.<\/jats:p>","DOI":"10.1029\/2018jb016482","type":"journal-article","created":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T12:11:53Z","timestamp":1547640713000},"page":"1671-1687","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Extrinsic Elastic Anisotropy in a Compositionally Heterogeneous Earth's Mantle"],"prefix":"10.1029","volume":"124","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7717-5931","authenticated-orcid":false,"given":"Manuele","family":"Faccenda","sequence":"first","affiliation":[{"name":"Dipartimento di Geoscienze Universit\u00e0 di Padova  Padua Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9492-6415","authenticated-orcid":false,"given":"Ana M. 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