Adaptive Inversion of the Curie Isothermal Surface in the Ordos Basin and Surrounding Regions Based on Multiple Constraints and Bayesian Optimization

The Curie isothermal surface (CIS), the depth at which crustal rocks reach the Curie temperature of magnetite, provides important information on the thermal state of the crust and, through it, of the lithosphere. Conventional magnetic anomaly spectral methods for CIS inversion commonly rely on manually selected spectral parameters, leading to considerable subjectivity and uncertainty. This study proposes an adaptive CIS inversion method based on multiple geophysical constraints and Bayesian optimization. The method integrates de-fractal spectral analysis with a Tree-structured Parzen Estimator (TPE) to jointly optimize the fractal index, moving-window size, and spectral fitting ranges for estimating the top and centroid depths of the magnetic layer. Multiple constraints, including heat flow, spatial distribution consistency and effective data coverage, are incorporated into the objective function. Synthetic experiments show that the proposed method improves inversion accuracy, reducing RMSE and MAE by 24.3% and 33.8%, respectively, compared with the conventional fixed-parameter method. Application to the Ordos Basin and surrounding regions reveals CIS depths of 20–40 km, with deeper values in the western and northern parts of the basin interior, and shallower values in the eastern and southern parts of the basin interior and in surrounding tectonic zones. The spatial distribution of the CIS in the study area, together with the crustal structures and the seismicity, helps to clarify the regional thermal state and tectonic evolution.