Effective viscosities calculated from the resistivity cross-section under different electrical conduction models. (a)–(c) The effective viscosities transformed from eq. (10) for |$V_\mathrm{Si}^{^{\prime\prime\prime \prime}}/\mathrm{ Fe}_\mathrm{m}^ \cdot $| (anhydrous) and |$( {3\mathrm{ H}} )_\mathrm{Si}^{\prime}$|/|${\mathrm{ H}^ \cdot }$| (hydrous) models and a combination of these two models at different depths. (d) and (e) are ‘soft’ and ‘hard’ lithosphere extracted from Deng et al. (2017). The five triangles in panels (a) and (d) mark the locations for comparison in Fig. 4.