Thermodynamic constraints on seismic inversions

We discuss two types of physical constraints derived from thermodynamics that can be applied during seismic inversions. The first constraint involves assimilating heat-flow measurements in seismic inversions. This can improve seismic models beneath continents, particularly beneath cratons and continental platforms where uncertainties in crustal radioactive heat production and the anelastic correction are smallest. The second thermodynamic constraint involves replacing ad-hoc seismic parametrizations with physical parameters that describe the thermal state and evolution of the oceanic upper mantle. The inverse problem is, therefore, recast as a hypothesis test to determine if the data are consistent with the thermodynamic model, which here consists of a shallow conductive layer underlain by a convective mantle. We argue that this constraint produces more plausible models of the oceanic lithosphere and asthenosphere and reduces the uncertainty of the seismic model while negligibly degrading the fit to the seismic data in most places.