Finite-difference Euler Deconvolution Algorithm Applied to the Interpretation of Magnetic Data from Northern Bulgaria

Here, we propose a new, finite-difference algorithm for Euler deconvolution, based on the Euler’s homogeneity equation accounting for a constant background field which allows simultaneous depth and shape estimation. The algorithm uses as input data the measured anomalous field and its firstorder derivatives, in contrast to methods based on the input of higher order field derivatives. The test of the algorithm on a model of interfering fields of elementary sources with different field fall-off rates, resulting in background close to a linear one, shows that it can give a good estimation of both the depth to the sources singular points and their respective structural indices. A set of tests was carried out on column-like models with shapes ranging from the elementary model of a dipole to that of a point pole, and of models of arbitrary shape with two singular points in between. It showed that when the ratio of the distance between the observation plane and the source’s top and the length of the body allows classification of it as a dipole or a point pole, the value of the estimated structural index is close to the integer value, typical for the respective elementary source. In such cases the estimated depth value refers to that of the special internal point of the respective type of source. This can facilitate in certain situations the interpretation of noninteger structural indices and their associated depth estimates obtained with the new Euler deconvolution algorithm. Inversion of a set of magnetic data from northern Bulgaria, caused by basaltic bodies of different shape, with the proposed method confirmed that the most intense anomalies are caused by column-like bodies outcropping on the surface and with considerable depth extent