A Study of Improved Inversion Algorithms for Surface–Borehole Transient Electromagnetic Data Based on BFGS Method

The surface–borehole transient electromagnetic method (TEM) employs surface-based transmission and downhole reception to collect electromagnetic data. This configuration offers distinct advantages over traditional TEM approaches by effectively attenuating surface electromagnetic noise and cultural interference, leading to enhanced signal strength and vertical resolution. As a result, it has emerged as a key technique for the exploration of deep mineral resources. Although a relatively comprehensive three-dimensional (3D) theoretical system for surface–borehole TEM has been established, most existing studies remain focused on forward modelling, with inversion interpretation receiving comparatively limited attention. In this study, a one-dimensional (1D) inversion algorithm for surface–borehole TEM data is developed. The approach begins with forward modelling based on numerical simulation, followed by the integration of a prior model to formulate an objective function. Optimization is carried out using the Broyden–Fletcher–Goldfarb–Shanno (quasi-Newton) method. A parameter transformation approach was further applied to convert the constrained inversion into an unconstrained optimization problem. The effectiveness of the proposed algorithm is validated through inversions performed on synthetic data derived from theoretical models. This method offers a reliable interpretation tool for practical surface–borehole TEM applications and provides a theoretical basis for the design and optimization of related instrumentation.