extended euler deconvolution

In this paper, the extended Euler deconvolution method is studied for interpreting magnetic and gravity anomalies. This method, overcoming some limitations of the conventional Euler deconvolution method, is utilized for simultaneous and automatic estimate of the depth, structural index and horizontal location of potential field sources. The main limitation of the conventional Euler deconvolution method is non-linear dependency of structural index and background field; hence a simultaneous estimation of these parameter is not possible. For overcoming this problem, a value of structural index is presumed and the obtained results are evaluated according to various criteria. A wrong structural index affects the final results. In the extended Euler deconvolution, the Euler differential equation is solved for Hilbert transform of the field and its derivatives. Since the Hilbert transform of a constant value is zero, the linear dependency of structural index and background filed will be removed, and therefore the automatic calculation of structural index will be possible and the presumption of structural index is not required anymore. Moreover, since Hilbert transform has two components of x and y, the number of equations to be solved at each point is increased, and consequently the solutions are more reliable. In this paper, firstly, a background theory of the extended Euler deconvolution is discussed in detail. Then the method is applied to a magnetic anomaly produced over eighteen magnetic sphere (dipole) having different magnetic properties. Finally, the method is used for interpreting a Bouguer gravity anomaly of Noranda in Quebec province of Canada and also a magnetic anomaly of an area located near Anar city of Kerman province of Iran.