Spatially Smooth Magnetization Mapping

Apparent susceptibility and magnetization mappings are traditionally obtained with the ridge regression, or generalized inverse (GI) estimators. These estimators constrain the solutions to have minimum Euclidian norms, which is equivalent to require that all parameters composing the solutions be as close as possible to zero. As a result, the ridge and GI solutions are almost always in conflict with the actual geological information. We present a stable inversion method to estimate the spatial distribution of magnetization which does not bias the solution against the known geological information. In addition, at points where there is no geological information, the proposed method assumes continuity of the spatial variation of magnetization. The continuity constraint obeys a general linear relationship stablished by the interpreter; smoothness is an important particular case. The utility of the particular estimator imposing smoothness on the spatial variation of magnetization is illustrated and compared with the ridge and GI estimators in a simulated magnetization mapping of a complex geologic area. We found that this particular estimator is more versatile, effective, and operationally simpler than either the ridge or the GI estimator.