3D inversion of gravity and magnetic data with depth resolution

Magnetization and density models with depth resolution are obtained by solving an inverse problem based on a 3-D set of potential field data. Such a data set is built from information on vertical and horizontal variations of the magnetic or gravity field. The a priori information consists of delimiting a source region and subdividing it in a set of blocks. In this case, the information related to a set of field data along the vertical direction is not generally redundant and is decisive in giving a depth resolution to the gravity and magnetic methods. Because of this depth resolution, which derives solely from the potential field data, an unconstrained and joint inversion of a multiobservation‐level data set is shown to provide surprising results for error‐free synthetic data. On the contrary, a single‐observation level data inversion produces an incorrect and too shallow model. Hence, a good depth resolution is likely to occur for the gravity and magnetic methods when based on the information along the vertical direction. This is also evidenced by an analysis of the kernel function versus the field altitude level and by a singular value analysis of the inversion operators for both the single and multilevel cases. Errors connected to numerical upward continuation do not affect the quality of the solution, provided that the data set extent is larger than that of the anomaly field. Application of the method to a 3-D magnetic data set relative to Vesuvius indicates that the method may significantly improve interpretation of potential fields.