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Although mantle rheology is one of the most important properties of the Earth, how a radial mantle viscosity structure affects lithosphere dynamics is still poorly known, particularly the role of the lithosphere, asthenosphere, transition zone, and D '' layer viscosities. Using constraints from the geoid, plate motions, and strain rates within plate boundary zones, we provide important new refinements to the radial viscosity profile within the key layers of the lithosphere, asthenosphere, transition zone, and D '' layer. We follow the approach of the joint modeling of lithosphere and mantle dynamics (Ghosh and Holt, 2012; Ghosh et al., 2013b, 2019; Wang et al., 2015) to show how the viscosities within these key layers influence lithosphere dynamics. We use the viscosity structure SH08 (Steinberger and Holme, 2008) as a starting model. The density variations within the mantle are derived from the tomography models which, based on prior modeling, had provided a best fit to the surface observables (Wang et al., 2015). Our results show that narrow viscosity ranges of moderately strong lithosphere (2.6-5.6 x 10(22) Pa-s) and moderately weak transition zone (5-9.3 x 10(20) Pa-s), as well as slightly large ranges of moderately weak asthenosphere (5-34 x 10(19) Pa-s) and D '' layer (4.8-18 x 10(20) Pa-s), are necessary to match all the surface observables. We also find that a very strong lithosphere (> 8.6 x 10(22) Pa-s) along with a weak asthenosphere (< 5.4 x 10(19) Pa-s) fits well with the surface observables. Our results show that the geoid is very sensitive to the viscosities of both the transition zone and D '' layer, while plate motions are slightly sensitive to them, but the orientations of stresses are insensitive to them.