Euler deconvolution using differential similarity transformations of gravity or magnetic anomalies 1 Petar Y. Stavrev 2 Abstract Euler deconvolution of gravity and magnetic anomalies can be used to estimate the coordinates of a simple point source and the level of a constant background in the deconvolved field by testing a series of structural indices. By using differential similarity transformations (DSTs), joint estimations of the source coordinates, the structural index and the coefficients of a linearbackground trend become possible. DSTs, calculated from the derivatives of the interpreted field, depend on the position of a chosen central point of similarity with respect to the source position. On this basis, techniques for Euler deconvolution of anomalous fields are presented. The theoretical formulations of DST and the deduced sets of equations for Euler deconvolution are tested and verified on model and field examplesof magnetic anomalies caused by one-point and two-point sources such as thin and thick dikes, semi-infinite and finite sills, contacts, steps,faulted beds, etc.The possibility of an optimum estimation of the structural index can be used to define a second acceptance criterion along with the criterion of relative standard deviations. The joint application of these two criteria ensures the selection of reliable results. The suggested DST techniques are suitable for initial rapid estimations of the source type, depth and plane location.They may be applied to either profile or gridded data acquired from one- componentmeasurements, as wellas from gradient or three-component measure- ments.Additionaldata on the density ormagnetization of the sourcesare not necessary. Introduction Euler deconvolutionof magneticand gravity anomaliesis based on Euler’s homogeneity of the anomalousfields.The degreesof homogeneity n were first determined for the field strengths of some elementary source models such as a point pole, dipole, sphere, infinite line of poles or dipoles, semi-infinite thin dike, sill, contact, pipe,etc.(Solovev 1960; Hood 1965;Slack,Lynch and Langan 1967; Reid etal. 1990). The degree n with an opposite sign N ¼ ¹n, which is called the structural index Geophysical Prospecting, 1997, 45, 207–246