Analysis of the Euler Method and Its Applicability in Environmental Magnetic Investigations

The analysis of the Euler method from the perspective of three-dimensional semi-compact magnetic sources shows that for arbitrarily shaped sources, the anomaly attenuation rate varies with increasing source-to-observation distance. For such sources, the value of n (commonly known as the structural index) is a function of the size of the window and the distance to the window. The variation of the n in the case of arbitrarily shaped sources is an inherent source of scatter in the derived solutions because no single n is correct at all source-to-observation distances. Because the Euler method is able to place the horizontal positions of the sources more precisely, much of the error due to an incorrect choice of n is mapped into the depth error. The percent depth error resulting from an incorrect choice of n is scale-independent, resulting in smaller physical errors in an application involving small distances and larger physical errors in an application involving large distances. It is shown with heuristic and actual examples from steel drums that the physical location errors resulting from the application of the Euler method can be within an acceptable range for environmental applications.