Horizontal heat transfer due to radioactivity contrasts: causes and consequences of the linear heat flow relation

Abstract

The effects of horizontal heat conduction due to radioactivity variations are investigated within the framework of the linear relation discovered by Birch and colleagues: Q,, = Q, + D . Ao! We study the relationship between the apparent depth-scale which is deduced from this relation and the true depth-scale for uniform and exponential vertical distributions of heat production.There are two different effects of horizontal heat transfer, both related to the smoothing of deep radioactivity variations. The first is the reduction of the apparent depth-scale, as reported by England, Oxburgh & Richardson. The second is the averaging of contributions from neighbouring formations. Because the exponential distribution extends to much greater depths than the uniform distribution for the same value of D , it enhances significantly the magnitude of these effects.We show that the two effects are very important for the large values usually found for D (around 10 km). This leads to two contradictions. First, surface heat flow integrates the heat production distribution over many different geological terrains and it is surprising to obtain a single and good linear correlation with local radioactivity over a whole province. Furthermore, the large thicknesses suggested imply a great sensitivity to formation shape and size which is not reflected in the data. Secondly, once a proper correction for horizontal conduction is made, the true values of D are unrealistically high and in disagreement with the crustal structure deduced from other geophysical studies in the State of New Hampshire and the Sierra Nevada (USA).This paradox can only be resolved if the true depth-scale of radioactive enrichment is smaller than what is indicated by the linear relation. This is probably due to the effects of alteration and weathering which deplete near-surface rocks in uranium and lead in compensation to an artificial increase of depth-scale. Even when these effects are corrected for, we find that the exponential distribution is too sensitive to size, shape and interunit distance to be realistic. The linear relation is made possible by two mechanisms. The first may 412 C Jaupart be the redistribution of radioelements by fluid circulation at the time of granite emplacement. The second is simply horizontal conduction which creates a rough alignment in a Qo versus A. plot whose slope is some complex average of the various thicknesses involved. Alteration then produces another apparent alignment with a larger slope which bears little resemblance to any physical dimension in the province. The linear relation remains a simple useful tool in the absence of more complete data coverage. Q, represents a large-scale average of heat flow which is free from the shallowest radioactivity contrasts and which allows the calculation of representative geotherms. It integrates the heat production distribution in the lower crust over a lateral distance as large as 350km. To compute the mantle heat flow beneath continents, it is therefore necessary to use a model of crus...

3-D numerical modelling of the conductive heat flow of SW England

“…The fact that the batholith tapers towards the surface, combined with the relatively high thermal conductivity of the granite, causes heat to be refracted in from the country rock, towards the outcrops (Richardson & Oxburgh 1979;England et al 1980). However, the effect of the higher heat production within the granite can be expected to set up gradients promoting heat flow out of the granite because, at equivalent depths, the granite is hotter than the country rock (Jaupart 1983). Thus there are two opposing effects in operation near the edges of the granite and the dominance of one over the other is dependent on all three parameters: the shape form, and the degree of contrast in conductivity and heat production.…”

Lithosphere Mantle Density of the North China Craton

“…For simplicity and given the uncertainty of thermal parameters, we define the thermal LAB by the 1300°C isotherm, which introduces only a minor difference to results based on a definition of the LAB by the intersection of geotherm with a 1300°C mantle adiabat. Our assumption on a 1-D steady-state heat transfer is justified by a relatively long-term stability of most of the region (which is therefore close to a steady-state regime) and the sparse distribution of borehole heat flow data (so that 3-D thermal effects cannot be taken into account; Jaupart, 1983;Petitjean et al, 2006;Stephenson et al, 2009). Note that the assumption of a steady-state heat transfer may not be entirely valid for the eastern part of the region affected by the Mesozoic subduction at 110-130 Ma.…”

Heat flow and deep temperatures in the Southeast Basin of France: Implications for local rheological contrasts

“…Nonetheless, even if mantle heat flow is reasonably determined, data on, or estimates regarding heat production rates and the thermal conductivities of crustal rocks are necessary to build a realistic thermal model of the crust. Moreover, the heterogeneous structure of the crust and associated variations in rock composition can result in significant contrasts in thermal properties [e.g., Jaupart, 1983]. As a result, the measured surface heat flow data and even the inferred shallow temperature gradients are not sufficient to provide reliable estimates of deep temperatures.…”