Heat flows inferred from a Parker's-like formula for stable or quasi-stable continents

TL;DR

This paper introduces a novel method to infer three-dimensional surface heat flow in stable continental regions using a Parker-like formula, enabling accurate estimations where direct measurements are scarce.

Contribution

The authors develop a new approach transforming the nonlinear heat conduction equation into a Poisson's equation, linking surface heat flow to interface geometry via a Parker-like formula.

Findings

Estimated heat flows in the Ordos region with less than 20% error.

Method effectively infers heat flow where measurements are limited.

Provides a new tool for geothermal studies in stable continents.

Abstract

Surface heat flow is a key parameter for the geothermal structure, rheology, and hence the dynamics of continents. However, the coverage of heat flow measurements is still poor in many continental areas. By transforming the stable nonlinear heat conduction equation into a Poisson's one, we develop a method to infer surface heat flow for a stable or quasi-stable continent from a Parker's-like formula. This formula provides the relationship between the Fourier transform of surface heat flow and the sum of the Fourier transform of the powers of geometry for the heat production (HP) interface in the continental lithosphere. Once the interface geometry is known, one to three dimensional distribution of the surface heat flow can be calculated accurately by this formula. As a case study, we estimate the three-dimensional surface heat flows for the Ordos geological block and its adjacent areas in China on a $1^\circ \times 1^\circ$ grid based on a simple layered constant HP model. Comparing to the measurements, most relative errors of the heat flows inferred are less than 20\%, showing this method is a favorable way to estimate surface heat flow for stable or quasi-stable continental regions where measurements are rare or absent.