Bounds on properties of continental crustal heat production

Abstract

Linear programming is applied to the inverse problem of placing bounds on various properties of the continental crustal heat-source function for a given heat flow province, specifically the maximum value and the total crustal power. Data to be satisfied are the measured surface heat-flow values, and an approximate linear relation throughout the province between heat flow and surface heat production. For the latter, the approximation imposed is a linear relation between the smoothest components of the two functions, thereby allowing the observed short-wavelength scatter about the conventional linear regression. Its incorporation into the linear programming problem is done by equating a chosen set of lowest degree Fourier components. Because heat flow measurements tend to be very uncertain, a large dataset can be replaced by a relatively small number of the most reliable independent linear combinations of data, thereby reducing the size of the linear programming problem significantly. These combinations are constructed using a generalization of the standard spectral expansion method, for problems cast in normed vector spaces which are not inner product spaces. Application to the New England dataset demonstrates a significant effect on computed bounds, even when only a few of the smoothest Fourier components are matched.