Application of Tikhonov Regularization for 1D Geothermal Heat Flux Ill-Posed Inverse Problem: A Case Study on Chad Sedimentary Basin

Abstract

Subsurface heat flux information is important in geothermal exploration. With the information, geophysicists can map exactly the thermal potential in a particular area. Based on the surface heat flux, inverse modeling produces the 1D subsurface heat flux distribution. However, inverse problems in the geothermal system are generally ill-posed. Small changes in the data can cause large changes in the solution and the solution may not be unique. To solve the mentioned non-linear and ill-posed equation above, Tikhonov regularization is a choice for stabilizing the inverse calculation. This paper demonstrates how Tikhonov regularization is useful to solve subsurface heat flux distribution both in the synthetic model and real model. Based on surface heat flux distribution from the direct problem, the preconditioned conjugate gradient algorithm calculates the subsurface heat flux. With the correct choice of the regularization parameter, the inverse model fits the initial model. For the testing purposes in real-world conditions, Chad sedimentary basin located in Chad and Nigeria is used as a model. A high geothermal gradient is found in this area. Therefore, geothermal explorations are on the rise recently. Its thermal conductivity, heat production, and stratigraphy data from previous researches provide information about the initial model. The heat flux curve generated from inversion matches the initial noisy model with the error of around 10−9 mW/m2. Therefore, to answer the increasing energy demand, this method can be highly applicable to future geothermal prospecting.