Abstract
This paper derives an inverse set of equations for equilibrium situations to discuss the resolution and sensitivity of models used to describe tectonic uplift and thermal heat flux. The sensitivity of results to variations in single parameters away from a described set of canonical values is given first. This sensitivity study is followed by a detailed treatment describing the probabilities of obtaining mantle thickness, surface heat flux, thermal expansion coefficient, base crustal heat flux, and Moho temperature at or above particular values as the water density, crustal density, asthenospheric density, uplift, crustal thickness, average lithospheric density, base lithospheric temperature, and water depth to the free asthenosphere marker are all allowed to vary simultaneously around their canonical values. In addition, a relative contribution plot for each of the five output variables identifies which of the eight input variables is causing the greatest contribution to the uncertainty. In this way one can identify which variables need to have their ranges of uncertainty narrowed in order to be more precise about the chances of obtaining particular values for the five outputs. A skewness estimate also is given that enables one to determine the most likely directions one should expect improvement to occur with a probability plot of obtaining particular values, or higher, for each of the output variables. Numerical illustrations show how one goes about performing the quantitative assessments and also show how the inverse procedure allows one to be more definitive concerning the five output values, and their ranges of uncertainty, because of uncertainties in the eight input parameter values.