Effect of Radioactivity Decay and Erosion on Surface Heat Flow- Heat Production Time Plots

Using average heat flow-average heat production data for different cratons over the world we obtained the relationship Q = 10A+32, (Q surface heat flow mWm^-2, A is the radioactivity in μWm^-3 ). The linear relationship between surface heat flow and heat production , Q = Q_o+ A D is explained using models in which radioactivity decreases in some fashion with depth; for example as a step function, a linear function or exponential function. Conceptually, the slope of the line on the Q-A plot is affected by erosion of the radioactive layer but not by erosion of sediments or volcanics overlying the basement radioactive layer. The slope is variable, depends on the differential erosion and various correlation scales. We introduce time, the third dimension to the Q-A plots, and illustrate the effect of decay of radioactivity on the plots, referred to as Q-A-t plots. We show the effect of erosion and decay of radioactivity on the movements of points on the Q-A plot for step, linear and exponential depth functions. Decay of radioactivity in the upper crust independent of erosion brings the points closer to the intercept Q_o (reduced heat flow) ~32 mWm^-2 without changing the slope. Using various end member models of radioactivity with depth, we are able to constrain mantle heat flow Q_m using Q_o. Using terrain averaged Q-A relation in stable continents (> 250 Ma) we have robust constrains on mantle heat flow, which falls in the range of 20-30 mWm^-2 over the Pre-Mesozoic terrains. The second conclusion from terrain averaged Q-A plot is that the surface heat flow is not age dependent over age of 250 Ma but is a direct function of enrichment of heat producing element in the crust. Stabilization occurs when this condition is met, unless a tectonic event overprints the existing lithosphere.