A Python-Based Implementation of Modified Centroid and De-fractal Methods for Curie Depth Estimation

Curie Depth represents the depth within the Earth’s crust at which rocks lose their permanent magnetization upon reaching the Curie temperature. In most crustal environments, this transition is primarily governed by magnetite, one of the most abundant magnetic minerals whose Curie temperature is approximately 580°C. Determining the Curie depth is essential for interpreting the geothermal gradient, lithospheric thermal structure and tectonic processes associated with heat flow. Consequently, it serves as a valuable geophysical parameter not only for regional geothermal assessment, but also for broader geodynamic and tectonic investigations. Over the years, multiple spectral techniques have been developed and progressively refined to estimate Curie depth using the average Fourier spectrum of magnetic anomalies. This study focuses on the Modified Centroid and De-fractal methods. Both approaches incorporate a fractal parameter into their formulations to represent the statistical roughness of magnetic sources. This parameter is important because natural magnetization patterns are inherently irregular. Incorporating fractal behavior enhances the stability and reliability of the geological interpretation, yielding results that are more realistic and geologically meaningful. This thesis is organized into three main parts. The first part provides the theoretical foundations of the two methods, reviewing the physical principles of magnetism, the definition of Curie temperature and mathematical formulation underlying spectral techniques. It also examines the role of the fractal parameter in the interpretation of Fourier spectrum. The second part describes the implementation of Modified Centroid and De-fractal methods in a Python-based software developed during my internship at SLB. It outlines the workflow for loading and preprocessing magnetic data, followed by the computation of the Radially Averaged Amplitude Spectrum (RAAS), which prepares magnetic data for spectral analysis. Subsequently, a functional overview of the methodology is presented. This includes the incorporation of fractal parameter in the equations, depth estimations of magnetic source depths, forward and synthetic modeling and the derivation of the geothermal profile. The third part presents the validation of the developed tool and a real case study of the Red Sea. The first section compares the results obtained from this implementation with those published by Carrillo-de la Cruz et al. (2020). This comparison is used to assess the performance, reliability, and consistency of the new software, highlighting both its strengths and its limitations relative to existing approaches. The evaluation includes differences in spectral fitting behavior, depth estimations, and sensitivity, to the fractal parameter. The second section provides case study focused on the magnetic anomaly of the Red Sea from the World Digital Magnetic Anomaly Map. In this application, the new tool is used to generate a regional Curie depth map through domain decomposition, allowing the area to be divided into multiple analysis windows to capture spatial variations in magnetic source depths. This case study demonstrates the practical capabilities of the software in a real geological setting and illustrates how the combined use of spectral methods, fractal incorporation, and domain decomposition can support a detailed geothermal interpretation of a complex tectonic region.