Using inversion of magnetic data, geometrical parameters such as depth and horizontal positions and physical parameters like susceptibility of subsurface anomalies can be estimated. Magnetic data inversion has algebraic and theoretical ambiguities. In addition, the presence of noise on data propagate large perturbations on model parameters estimation procedure. A priori information and different constraints can be used to be solved these problems. Here, regularized minimum length solution including depth weighting and compactness constraints are utilized. The Algorithm was applied on synthetic data of a model of two dip dykes in order to investigate its efficiency. The result was enough promising and convince us to apply the algorithm on real data. We applied it on archeological data of old Pompeii city and reconstructed model of the data were in good agreement with real subsurface anomalies.