This paper is based on data sets acquired by a fast and efficient ground-based measurement system, which is based on superconducting quantum interference device technology and ensures geo-magnetic mapping of large areas. The local variations (gradients) of the Earth's magnetic field are represented in so-called magnetograms, which typically include a large number of magnetic anomalies with different appearance and shape. Here, elongated anomalies are investigated, which are explainable by a polyhedral source body. These underground structures can be represented by a cross section that is approximately uniform along the main strike extent of the source. After introducing the measurement system, a source description model is developed theoretically and in the following adapted to practical problems. In order to illustrate the utility of this kind of minimization-based inversion and to validate the produced results, an example of archaeological measurements in Mongolia is shown. Results of the field measurements are used for inversion toward a description of possible subsoil situation. Finally, an excavation shows the accuracy of the results.