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We have developed a new method for interpretation of gridded magnetic data which, based on derivatives of the tilt angle, provides a simple linear equation, similar to the 3D Euler equation. Our method estimates both the horizontal location and the depth of magnetic bodies, but without specifying prior information about the nature of the sources (structural index). Using source-position estimates, the nature of the source can then be inferred. Theoretical simulations over simple and complex magnetic sources that give rise to noise-corrupted and noise-free data, illustrate the ability of the method to provide source locations and index values characterizing the nature of the source bodies. Our method uses second derivatives of the magnetic anomaly, which are sensitive to noise (high-wavenumber spectral content) in the data. Thus, an upward continuation of the anomaly may lead to reduce the noise effect. We …