Euler deconvolution is widely used to estimate the three-dimensional locations of geological sources from magnetic anomaly data. However, traditional Euler deconvolution is commonly performed on planar gridded data, whereas magnetic surveys in mountainous and hilly areas are often acquired over undulating terrain. Reducing such data to a horizontal plane before derivative calculation can introduce transformation errors, and derivative calculation by the conventional FFT-based (wavenumber-domain) method becomes less suitable under variable topographic conditions. To address these limitations, this study proposes an equivalent source method based on correlation imaging for calculating the spatial derivatives required by Euler deconvolution directly from magnetic anomaly data acquired over undulating terrain. An improved Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is further introduced to suppress spurious Euler solutions and retain valid source location estimates. Synthetic model experiments show that the proposed equivalent source method yields more accurate derivatives than the conventional FFT-based method under undulating terrain conditions. The improved DBSCAN algorithm effectively removes spurious solutions while preserving clustered solutions associated with geological sources. The proposed workflow was further applied to magnetic data from a coal fire zone in Shenmu, Shaanxi Province, China, to estimate the 3D locations of underground magnetic sources related to underground coal fires. The interpreted source locations are consistent with surface validation evidence, demonstrating the applicability of the proposed method for magnetic anomaly interpretation in complex topographic settings.
Jin et al. (Mon,) studied this question.