We present an automatic procedure — Magnetic And Gravity SOUNDing Differential Similarity Transform (MaGSoundDST) — for inversion of regular or irregular magnetic- and gravity-grid data measured on even or uneven surfaces. It solves for horizontal position, depth, and structural index of simple sources and is independent of a linear background. In addition, it estimates the shape of sources consisting of several singular points and lines. The method uses the property of the differential similarity transform (DST) of a magnetic or a gravity anomaly to become zero or linear at all observation points when the central point of similarity of the transform, which we refer to as the probing point, coincides with a source's singular point. It uses a measured anomalous field and its calculated or measured (gradiometry) first-order derivatives. The method is independent of the magnetization-vector direction in the magnetic data case and does notrequire reduction-to-the-pole transformed data as input. With MaGSoundDST, we provide an important alternative interpretation technique to the Euler deconvolution procedures, combining a moving-window method, whereby the solutions are linked to singular points of causative bodies, with an approach in which the solutions are linked to the real sources. The procedure involves calculating a 3D function that evaluates the linearity of the DST for different integer or noninteger structural indices, using a moving window. We sound the subsurface along a vertical line under each window center. Then we combine the 3D results for different structural indices and present them in three easy-to-interpret maps, avoiding the need for clustering techniques. We deduce only one solution for location and type of simple sources, which is a major advantage over Euler deconvolution. Application to different cases of synthetic and real data shows the method's applicability to various types of magnetic and gravity field investigations.

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