We want to characterize and localize the depth of archaeological structures from the measurement of magnetic potential anomalies above ground to have a non-destructive test of an archaeological site and to suggest a strategy of excavation. A class of tomography methods used in potential field theory are based on cross-correlation technique (Patella), Euler method or generalized Hilbert transform (Nabighian). New class of tomography methods is based on real continuous wavelet transform for characterizing and localizing “homogeneous” buried sources (magnetic, electric and gravity). These last methods use the properties of the Poisson kernel (real by definition), and the wavelet theory. We relax here, the assumption on sources and introduce a method that we call “multi-scale tomography”. Our approach is based on the harmonic extension of observated magnetic field to produce a complex source by the use of a complex Poisson kernel solution of the Laplace equation for complex potential field. A phase and modulus are defined. We show that the phase provides additional information on the total magnetic inclination and the structure of sources, while the modulus allows us to characterize its spatial location, depth and “effective degree”. Results of excavation of Roman kilns of Fox Amphoux site (Var, France) are then compared to the estimates.