Thermal structure of old continental lithosphere from the inversion of surface-wave dispersion with thermodynamic a priori constraints.

We present a reformulation of the seismic surface wave inverse problem by replacing the ad-hoc seismic parameterization with physical parameters that describe the thermal state and evolution of the upper mantle. We apply the method to estimate the thermal structure of old continental lithosphere that can be described with a steady-state temperature model. The inverse problem is recast in terms of three thermal parameters: temperature in the uppermost mantle directly beneath the Moho, the mantle temperature gradient (or mantle heat flux), and the potential temperature of the sublithospheric convecting mantle. In addition to the steady-state constraint, prior physical information on the 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. The combination of seismic and thermal data is based on the interconversion between temperature and seismic velocity. The inversion is formulated as a Monte-Carlo sampling of model space which results in an ensemble of models that fit the data, providing estimates of uncertainties in model parameters. We apply this Monte Carlo inversion of surface wave data with the "thermal parameterization" subject to the physical constraints in order to determine the upper mantle shear velocity and temperature structure of the Canadian Shield.