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Abstract

Seismic tomography maps seismic-velocity distributions within the Earth. Lateral variations of seismic velocities in the mantle depend primarily on variations in temperature. Thus, tomography gives us a proxy for the thermal heterogeneity in the Earth, of great interest because it determines the thickness and mechanical strength of the lithosphere and the density variations and convection patterns in the sub-lithospheric mantle. Obtaining accurate, quantitative mapping of temperature, however, is not straightforward. Tomographic models are non-unique solutions of inverse problems, regularized to yield solutions with properties such as smoothness or small model norm, not physical plausibility. For example, lithospheric geotherms computed from tomographic models typically display unrealistic temperature oscillations, with implausible temperature decreases with depth. If a tomographic model is all we have, a reasonable approach is to look for a physically plausible geotherm that fits seismic velocities in the entire lithospheric depth range best, in some sense. A generally more accurate approach is to invert seismic data, from the start, directly for what we want to know. Using computational petrology and thermodynamic databases, we can invert seismic-surface-wave and other data for temperature and composition at depth, equilibrium lithospheric geotherms and the lithospheric thickness. We must use accurate surface-wave measurements and fit them closely; impose constraints on the models from other available data and physical relationships; and tune the inversions so as to resolve essential parameter trade-offs. With these developments, thermodynamic inversions yield increasingly accurate models of the lithosphere's temperature, thickness and internal structure, with important inferences on its dynamics and evolution.