Mathematics as a Geoheat Engine to Determine the Lithospheric Thermal Properties from an Aeromagnetic Data Over Southeastern Taraba State

The study is based on mathematical-geophysical model that incorporates potential field theory, Fourier spectral analysis and lithospheric thermal modelling as a solid foundation for estimating Curie Point Depth (CPD), geothermal gradient, and surface heat flow from aeromagnetic anomalies of Taraba State for geothermal applications. Aeromagnetic measurements provide indirect constraints on the crustal thermal structure of the earth, but these measurements demand stringent mathematical transformation for meaningful interpretation. The spectral decomposition theory, radial power spectrum analysis and the exponential decay of magnetic energy with depth are the basis of the methodology. FFT-based spectral analysis is a mathematically robust geophysical tool, as it balances between electromagnetism, Thermodynamics, Signal processing and allows to estimate indirectly Curie depth and Geothermal gradient and Heat flow. This mathematical model shows that FFT converts aeromagnetic data into physically meaningful spectral energy, CPD range of 13.16-29.09km was accurately estimated using spectral slope analysis, Geothermal gradient of 19.94-44.080C/km and heat flow of 49.85-110.19mWm-2 are mathematical derivatives of CPD and the method is a powerful, non-invasive geothermal exploration tool. The bridge between magnetic signals and the thermal structure of the Earth is mathematics (FFT and spectral theory). Aeromagnetic data without mathematics are noise but with FFT they become a geothermal diagnostic tool.