A geophysical perspective on Earth's mantle water content: Inverting long-period electromagnetic sounding data using laboratory-based electrical conductivity profiles

We have applied electromagnetic sounding methods for Earth's mantle to constrain its thermal state, chemical composition, and "water" content. We consider long-period inductive response functionsin the form of C-responses from four stations distributed across the Earth (Europe, North America, Asia and Australia) covering a period range from 3.9 to 95.2 days and sensitivity to 1200 km depth. Rather than invert C-responses for conductivity profiles, we invert directly for chemical composition and thermal state using a self-consistent thermodynamic method to compute phase equilibria as functions of pressure, temperature, and composition (in the Na2O-CaO-FeO-MgO-Al2O3-SiO2 model system). Computed mineral modes are combined with recent laboratory-based electrical conductivity models from independent experimental research groups (Yoshino and coworkers and Karato and coworkers) to compute bulk conductivity structure beneath each of the four stations from which C-responses are estimated. This scheme is interfaced with a sampling-based algorithm to solve the resulting non-linear inverse problem. This approach has two advantages: (1) It anchors temperatures, composition, electrical conductivities, and discontinuities that are in laboratory-based forward models, and (2) At the same time it permits the use of geophysical inverse methods to optimize electrical profiles to match geophysical data. The results show variations in upper mantle temperatures beneath the four stations that appear to persist throughout the upper mantle and parts of the transition zone consistent with observations from seismic tomography images that show major lateral velocity variations in the upper mantle. Calculated mantle temperatures at 410 and 660 km depth lie in the range 1250-1650 deg C and 1500-1750 deg C, respectively, and generally agree with experimentally-determined temperatures at which the measured phase reactions olivine->beta-spinel and gamma-spinel->ferropericlase+perovskite occur. The retrieved conductivity structures beneath the various stations also tend to follow trends observed for temperature with the strongest lateral variations in the uppermost mantle, and for depths >300 km appear to depend less on the particular mineral electrical conductivity database. Electrical conductivities (log{sigma)) at 410 km depth have lateral variations that range from -3 to -1, while at 660 km depth log{sigma) varies from -2 to -0.5, in overall agreement with purely geophysically-derived global and semi-global one-dimensional conductivity models. Both electrical conductivity databases point to 0.001 wt% H2O in the upper mantle with values ranging from 0.0005-0.002 and 0.0007-0.0013 wt% H2O for the laboratory databases of Karato (2011) and Yoshino (2010), respectively. However, for transition zone minerals results from the different laboratory databases suggest that a much higher water content is required by the measurements of Yoshino (2010). Further, there is evidence of lateral heterogeneity: The sub-Australian mantle appears "drier" than that beneath southwestern North America, Europe, or Asia.