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We argue for and present a reformulation of the seismic surface-wave inverse problem in terms of a thermal model of the upper mantle and apply the method to estimate lithospheric structure across much of the Canadian Shield. The reformulation is based on a steady-state temperature model, which we show to be justified for the studied region. The inverse problem is cast in terms of three thermal parameters: temperature in the uppermost mantle directly beneath Moho, mantle temperature gradient, and the potential temperature of the sublithospheric convecting mantle. In addition to the steady-state constraint, prior physical information on these model parameters is based on surface heat flow and heat production measurements, the condition that melting temperatures were not reached in the crust in Proterozoic times and other theoretical considerations. We present the results of a Monte Carlo inversion of surface-wave data with this ‘thermal parameterization’ subject to the physical constraints for upper mantle shear velocity and temperature, from which we also estimate lithospheric thickness and mantle heat flux. The Monte Carlo inversion gives an ensemble of models that fit the data, providing estimates of uncertainties in model parameters. We also estimate the effect of uncertainties in the interconversion between temperature and seismic velocity. Variations in lithospheric temperature and shear velocity are not well correlated with geological province or surface tectonic history. Mantle heat flow and lithospheric thickness are anti-correlated and vary across the studied region, from 11 mW/m2 and nearly 400 km in the northwest to about 24 mW/m2 and less than 150km in the southeast. The relation between lithospheric thickness and mantle heat flow is consistent with a power law relation similar to that proposed by Jaupart et al. (1998), who argued that the lithosphere and asthenosphere beneath the Canadian Shield are in thermal equilibrium and heat flux into the deep lithosphere is governed by small-scale sublithospheric convection.

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