Sparse Regularization Inversion Method for Transient Electromagnetic Data and High-Resolution Prospection of Subsurface Targets

Transient Electromagnetic Method (TEM) is a geophysical technique with great potential for high-resolution subsurface imaging. However, conventional inversion algorithms for TEM typically employ the L2-norm regularization in the objective function, which assumes a smoothly varying resistivity distribution. This assumption limits the resolution of sharp electrical interfaces. To address this issue, this paper implements an inversion algorithm that incorporates an L1-norm regularization term, promoting sparsity in the spatial gradient of the resistivity model and thereby enabling more accurate reconstruction of abrupt electrical boundaries under sufficient iteration. To overcome the numerical difficulties caused by the non-differentiability of the L1 norm at zero points, we adopt the Iteratively Reweighted Least Squares (IRLS) method within a Gauss-Newton (GN) inversion framework. In this approach, the L1 regularization problem is transformed into a sequence of weighted L2 regularization subproblems, each of which is solved using the GN method. This strategy retains the sparsity-promoting property of the L1 norm while effectively circumventing its computational challenges. Inversion results from both 1D and 2D synthetic models demonstrate that the proposed algorithm significantly improves the resolution of sharp resistivity transitions compared to traditional L2-norm regularization approaches. Furthermore, the method has been successfully applied to field TEM data from a real survey site, where it effectively identified underground coal mine voids and fault structures.