A multilevel generalization of Euler Deconvolution and its comparison with the Continuous Wavelet Transform

Abstract

Recent implementations of Euler deconvolution allow to solve simultaneously for the source position and the structural index. This opens the way to a comparison between this technique and the Continuous Wavelet Transform (CWT) method, that allows the estimation of essentially the same parameters. Direct comparison of Euler deconvolution and CWT methods is possible only by applying the first method to a potential field upward continued to many altitudes. While the two methods give very similar results when the gravity or magnetic field of a one-point source is concerned, they behave different for those sources characterized by fractional structural index, as many real geologic structures are (for example a limited throw fault). In this paper, the variation of the Euler estimated parameters at many altitudes above a magnetized prism is described. Such a variation gives additional information on source geometric parameters and position, which may be recovered from plots of estimated depth and structural index vs. altitude: a) the extended or one-point nature of the source results clearly; b) it is possible to understand to which part of the source the depth estimate is related to; c) it is possible to get indications about the source thickness and lateral dimensions. On the other hand, for sources of finite extent, the CWT analysis may be made only for sets of levels and not at any level, differently from the above outlined Euler deconvolution approach. Nevertheless the results from these two methods are substantially consistent at high or low altitudes.