Automatic inversion of magnetic anomalies from two height levels using finite-difference similarity transforms

Abstract

We solve the inverse magnetic problem for the depth and shape of simple sources in the presence of a regional field and truly random noise. We do not use noise-generating derivatives nor are we forced to solve complex systems of equations. Our inverse operator applies a new geometric type of field transform, the finite-difference similarity transform (FDST), that is based on a postulated degree of homogeneity in the potential field. Magnetic data from two height levels are required for the calculation of the FDSTs. The FDSTs are generated for an assumed central point of similarity (CPS) and a trial value (index) for the coefficient of similarity, and they are sensitive to the distance between the source and the CPS and to the agreement between the index and the degree of homogeneity in the data. When the CPS converges to a singular point in the potential field, say, the center or the topedge of the source, and when the trial index converges on the degree of homogeneity present in the data, the FDST drops in amplitude and its plot approaches a straight line, thereby signaling an interpretation for the source position and type. All inverse operations are fully automated and applicable to the interpretation of large data sets. The necessary data for the second level can be obtained by actual measurement or, alternatively, by deriving them from the data at the first level by an upward, analytical continuation. Upward continuation suppresses high-wavenumber random noise and thus contributes to a stable inversion. Model tests show that a suitable height for the second level is less than the expected depth of the source below the first level, while a suitable window length is about twice that depth. Examples show that the proposed inversion is effective on both model and field data. Note that this approach can be extended to the inversion of any component or derivative of the 2D or 3D magnetic or gravity fields from simple sources.