Geotherms and Thermal Parameters from the Curie Depth Constrained Solutions of the One-Dimensional Steady-State Heat-Flow Equation: A New Method and Its Applicability

We have developed a new method of constraining geotherms deep in the crust. Steady-state geotherms are most commonly derived by solving the heat flow differential equation with surface boundary conditions, and do not explicitly involve temperature constraints at depth. In a new method, we incorporate the magnetic Curie depth, derived from the spectral analysis of magnetic anomaly data, as an a posteriori condition into the solution of 1-D heat-flow equation to anchor geotherms at the Curie depth. The Curie depth is derived carefully from the Defractal Spectral Method where the fractal parameter of the field is also derived. The Curie depth constraint allows determination of an additional parameter: the ratio of radiogenic heat production (A) to thermal conductivity (K). When K is observed or can be estimated from geologic knowledge, A can be calculated. Furthermore, it is possible to renormalize the derived A to the value where radiogenic elements exponentially decrease with depth (the value of A at the surface denoted as As). The renormalization permits comparison of surface observed and computed values of As which we use to validate the method. We crosschecked observed values of As and K against the ratio As/K derived from the method in New Hampshire and across the border of Wyoming and Colorado. Excluding high heat-flow locations in these regions as anomalous, the difference between the observed and computed As in all these cases is less than 6-7%. There are also regions where both the derived parameters (As and K) are not within the acceptable range for the given reduced heat flow; these are generally the regions of complex active tectonics or anomalously high or low heat-flow values where the steady-state assumption is not valid. In the mid-oceanic ridge scenario of the Red Sea, the Curie depth corresponds to the Moho and reasonable values of K yield low values of A consistent with the expectation from mafic oceanic crust. There are many areas of the world where high quality aeromagnetic data are available and, therefore, our new method will be useful in constraining lithospheric geotherms and thermal parameters where the steady-state assumption is valid in a regional sense. One could also use the method of constraining geotherms to deep crustal temperature proxies other than the Curie depth.