Delineation of overlapping magnetic field source boundaries with a 3-D multi-layer convolution model

One of the obstacles in magnetic field boundary detection is the interference from overlapping anomalous sources at different depths. In this paper, we propose a new method to delineate overlapping sources by eliminating these interferences in the data. A new 3-D multi-layer convolution model is innovatively derived based on the classical 3-D magnetic field forward model. With this multi-layer convolution model, interferences from the overlapping sources are considered as systematic errors and generally expressed through the Impulse Response Function (IRF). A TV (Total Variation) regularization deconvolution algorithm is suggested to delineate the clear horizontal boundaries of magnetic anomalous sources by filtering the convolution IRF. We conduct the experiments on synthetic and field data sets to confirm the validity of the proposed multi-layer convolution model and deconvolution boundary delineation algorithm. This study suggests that magnetic field interpretation through the deconvolution method with the multi-layer convolution method is theoretically feasible, and it delineates clearly boundaries of overlapping sources.