Based on the governing equations of the electromagnetic radiation field and the theory of multi-layer media propagation, the governing equations for electromagnetic wave attenuation are derived. A stable solution to the resulting large-scale sparse linear system is obtained using Tikhonov regularization. A typical collapse column forward model is established using locally refined triangular mesh discretization. Forward and inverse modeling are conducted at three transmission frequencies: 0.3 MHz, 0.5 MHz, and 1.5 MHz. The results indicate that the 1.5 MHz frequency yields the best vertical resolution, with inversion results most closely matching the modeled anomaly location. In the field application at working face number 3308 using 1.5 MHz, the local polynomial interpolation inversion delineates an anomalous vertical extent of approximately 70 m (75–145 m), whereas the Kriging interpolation method yields a vertical extent of about 140 m (20–160 m), representing a reduction of approximately 50% in the vertical extent of the delineated anomaly. Post-mining exposure reveals the X16 collapse column, with a major axis of 53 m and a minor axis of 34 m, which is generally consistent with the detection results. This study confirms that local polynomial interpolation combined with locally refined triangular meshing effectively enhances the vertical resolution of radio wave transillumination, providing reliable technical support for the accurate delineation of concealed collapse columns.