Potential fields generally require to be analyzed by different scales, owning to sources of different depth and extent. Fourier or wavelet filtering not always yield an optimal separation of those different source effects, often introducing some amount of distortion. We propose therefore a new method, the Multiscale Derivative Analysis (MDA), based on the Enhanced Horizontal Derivative (EHD) of the field, which does not imply any separation of the effects, but simply enhances those related to a given scale. Such process, based on a weighted sum of increasing order derivatives of the field, converges quickly toward the actual boundaries of the sources. MDA applied to gravity data of the of Thyrrenian Sea (Italia) yields 3 maps of structural lineaments, each one characterized by a different scale. Known, partially known or relatively new structures are described in the maps, allowing a rapid analysis of all the gravity-related structural lineaments of this region.