Determining heat flows and radiogenic heat generation in the crust and lithosphere based on seismic data and surface heat flows

Abstract

The balance of the Earth’s energy involves the generation of radiogenic, gravitational, chemical, and other types of energy and the heat loss from the Earth’s surface. In the quasi-stationary formulation, heat losses through the surface are equal to the sum of energy generated by all sources in the Earth’s interiors. The flow from the continental surface is estimated at 47‐ 49 mW/m 2 [1]. Estimates (accomplished by various researchers) of the mantle component of the heat flows range from 3 to 25 mW/m 2 [1]. Mantle flows are usually assayed on the basis of extensive geothermal measurements at numerous sites around the world. The heat flow through the Earth’s surface Q 0 can be expressed as the sum of the mantle flow Q M and the contribution of radiogenic energy released within the crust Q Cr . The value of Q Cr is determined based on geochemical models currently adopted for the distribution of radiogenic elements and the solution of stationary heat conduction [1, 2]. At the same time, the mantle flow Q M is, in fact, calculated as the difference between Q 0 and Q Cr . The distribution of K, U, and Th are still known relatively poorly, so that these estimates for both the crust and the mantle broadly differ, and this problem is actively debated in the literature [3, 4]. Thermal models for the mantle are the least definite, mostly because of the uncertainties in the crustal and lithospheric contributions to the overall heat generation [1‐4]. The solution to the problem of determining the temperature and/or the chemical composition of the mantle from the velocities of seismic waves was debated in [5‐9]. It is quite difficult to derive mantle geotherms from the results obtained by measuring the surface heat flow because of the lack of information on the mantle contribution. This publication proposes a method for assaying the conductive heat transfer of the lithosphere of both mantle and crustal heat flows on the basis of the data of seismic models and the heat flow through the Earth’s surface Q 0 . As an example of such a calculation, we used the profiles of velocities from the IASP91 [10] global reference model (for the “averaged” continental crust) and the BP11A regional model [11], which was developed for the mantle beneath the Kaapvaal craton in South Africa. The solution routine was provisionally subdivided into two stages. During the first of them, the temperature of the mantle ( T P and T S ) is determined from the velocities of seismic P and S waves. The procedure of the conversion of seismic profiles into thermal ones is conducted based on the equations of state for the material with regard for anharmonic and anelastic effects. The temperature profile T P , S was then made consistent with the conductive heat transfer model for the crust and mantle, and this enabled us to derive an analytical expression for temperature variations with depth, the values of crustal heat sources, and the components of heat flows in the crust and mantle. Determining temperature in the mantle from the velocities of seismic waves. Geochemical, seismic, and thermal models for the Earth’s upper mantle were made mutually consistent using the THERMOSEISM computer program complex and database, by methods of physicochemical simulations, which make it possible to convert compositional models into physical characteristics and velocity profiles into models for the temperature distribution [5, 9, 12, 13]. The temperature T P in the mantle is determined by solving the inverse problem for the velocities of primary (and/or secondary) seismic waves and the bulk composition of the rock at any point in a depth profile. The equilibrium mineral composition of the rock is determined from the bulk composition by minimizing the Gibbs free energy for the system Na 2 O–TiO 2 –eaO–FeO–MgO–Al 2 O 3 –SiO 2 with solid solutions of the following minerals: binary solutions of Fe‐Mg olivine, spinel, and ilmenite; garnet ( Gar of the pyrope‐almandine‐grossular series); orthopyroxene ( Opx — MgSiO 3 , FeSiO 3 , Ca 0.5 Mg 0.5 SiO 3 , Ca 0.5 Fe 0.5 SiO 3 , Al 2 O 3 ); and clinopyroxene ( Cpx —same components plus the jadeite end member) [12, 13]. The