Objective The inversion of controlled-source audio-frequency magnetotelluric (CSAMT) data remains challenging due to two key issues: computational efficiency and resolution. To tackle these two issues, especially the over-smoothing effect caused by traditional regularization methods in estimating complex geological structures, this study proposed an improved regularization inversion method to reflect the spatial distribution characteristics of subsurface physical property parameters more accurately.

Methods The proposed method was developed using the method for establishing the stochastic partial differential equation (SPDE) based on the Matérn covariance function. By introducing vector fields and the shape parameters of a range ellipse, this method fully considered both variations in the inclination of strata and the non-stationary nature of physical property distribution. Accordingly, this study developed a model covariance matrix meeting the non-stationary assumption. Then, inversion was conducted using the model covariance matrix as the regularization constraint. From the perspective of inversion results, residuals, relative residuals of apparent resistivity, and uncertainty, this study compared the proposed method with traditional maximum smoothness-constrained inversion and covariance-constrained inversion based on the stationary assumption. In addition, the proposed method was applied to measured data from the exploration of the Ye’erkeman-Jinba gold deposit in Habahe County, Xinjiang to validate its practical application effects.

Results The results from the theoretical model indicate that the four experiments with the non-stationary constraint yielded residuals ranging from 20.47% to 21.29%, which were lower than those of experiments with the stationary constraint (21.25% and 22.83%) and those of experiments using traditional maximum smoothness-constrained inversion (32.46%). Furthermore, the proposed method could characterize geological structures more accurately and delineate geological boundaries more distinctly. The results from measured data show that the covariance-constrained CSAMT inversion based on the non-stationary assumption delivered significantly higher imaging performance than the conventional Occam-type (smoothness constrained) inversion, achieving a 51.47% reduction in data fitting residuals. The proposed method exhibited a remarkably enhanced capacity to identify complex geological structures and reduced the uncertainty in the inversion results of deep areas, thereby effectively improving the overall reliability of inversion results.

Conclusions The non-stationary assumption-based inversion method with the Matérn covariance function as the regularization constraint provides a novel technical solution for addressing the issues of the insufficient computational efficiency and resolution of CSAMT inversion. This method holds great significance for advancing geophysical inversion technology.