An efficient regularization method for a large scale ill-posed geothermal problem. (August 2017)

• Record Type: Journal Article
• Authors: Berntsson, Fredrik; Lin, Chen; Xu, Tao; Wokiyi, Dennis
• Is Part Of: Computers & geosciences. Volume 105(2017)
• Page Start: 1
• Page End: 9
• Publication Date: 2017-08
• Subjects: Environmental policy -- Periodicals; 550.5
• DOI: 10.1016/j.cageo.2017.04.010
• Languages: English
• ISSNs: 0098-3004

Abstract

Abstract: The inverse geothermal problem consists of estimating the temperature distribution below the earth's surface using measurements on the surface. The problem is important since temperature governs a variety of geologic processes, including the generation of magmas and the deformation style of rocks. Since the thermal properties of rocks depend strongly on temperature the problem is non-linear. The problem is formulated as an ill-posed operator equation, where the righthand side is the heat-flux at the surface level. Since the problem is ill-posed regularization is needed. In this study we demonstrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a well-posed problem related to the above mentioned operator. The algorithm is designed in such a way that it can deal with both 2 D and 3 D calculations. Numerical results, for 2 D domains, show that the algorithm works well and the inverse problem can be solved accurately with a realistic noise level in the surface data.