Leveling method for airborne electromagnetic data based on the curvelet transform and adaptive group-sparse variational model

Abstract In airborne electromagnetic data processing, correcting leveling errors is critical for ensuring data accuracy. Traditional leveling methods predominantly rely on time-domain and frequency-domain analysis to characterize leveling errors. However, a significant challenge remains in balancing the effective elimination of leveling errors, the preservation of data details, and the achievement of real-time performance. To address this issue, this paper introduces an adaptive group-sparse variational model grounded in the curvelet transform. The multi-scale and multi-directional properties of the curvelet transform, together with the directional and structural characteristics of leveling errors, facilitate the development of a group-sparse variational model for curvelet sub-band coefficients. To address the challenge of assigning uniform weights to the variational model in the curvelet domain representation of leveling errors, this study adaptively adjusts the weights of different components, effectively isolating the leveling errors from the surveyed data. Experimental validation using both simulated and measured data demonstrates that the proposed method effectively extracts leveling errors while preserving geological information with greater accuracy, thereby significantly enhancing the reliability of airborne electromagnetic data. Graphical Abstract