Deconvolução de Euler: passado, presente e futuro - um tutorial

In this tutorial we present a historical overview of the evolution of Euler deconvolution method consisting of three sections. In the first section, we recall the Euler deconvolution 2D and 3D classic formulation as a method to automatically locate sources of potential fields anomalies and point out the difficulties of this formulation: the presence of an undesirable spray of solutions, the empiric criteria used to determine the structural index (a parameter related with the source nature), the feasibility of applying Euler deconvolution to small ground data survey, and the determination of the dip and susceptibility contrast of geological contact (or the product of the susceptibility contrast and the thickness when applied to thin dike). In the second section, we present recent improvements aiming at minimizing some of the difficulties presented in the first section. They include: i) selecting the solutions essentially associated with observations presenting the largest signal-to-noise ratios; ii) using the correlation between the estimated anomaly baselevel and the observed anomaly itself or combining Euler deconvolution with the analytic signal to determine the structural index; iii) combining the results from (i) and (ii) to allow estimating the structural index independently of the number of solutions so that a small number of observations (such as in a ground survey) may be used; and iv) introducing additional equations, which are independent from Euler's equation to estimate the dip and susceptibility of 2D sources. In the third section we provide a short- to medium-term outlook into future developments. The main prospects are: i) furthering the improvements on the problems singled out in the second section; ii) developing methods to take vertical and lateral interferences into accounts; and iii) incorporating Euler deconvolution to constrain the source location estimates and use them in inversion methods to obtain a source delineation in a user-friendly computer environment.