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In this thesis we have implemented and studied on detail three different potential field inversion algorithms proposed by Li and Oldenburg (2003), Portniaguine and Zhdanov (2002) and Pilkington (2009). We focused our attention on the dependency of the solution with respect to external constraints and particularly with respect to the depth weighting function. This function is necessary to counteract the natural decay of the data kernels with depth, so providing depth resolution to the inverse solution. We derived invariance rules for either the minimum-length solution and for the regularized inversion with depth weighting and positivity constraints. For a given source class, the invariance rule assures that the same solution is obtained inverting the magnetic (or gravity) field or any of its kth order vertical derivatives. A further invariance rule regards the inversion of homogeneous fields: the homogeneity degree of the magnetization distribution obtained inverting any of the k-order vertical derivatives of the magnetic field is the same as that of the magnetic field, and does not depend on k. Similarly, the homogeneity degree of the density distribution obtained inverting any of the k-order vertical derivatives of the gravity field is the same as that of the 1st order vertical derivative of the gravity field, and does not depend on k. This last invariance rule allowed us using the exponent β of the depth weighting function corresponding to the structural index of the magnetic case, no matter the order of differentiation of the magnetic field. We also illustrated how the combined effect of regularization and depth weighting could influence the estimated source model depth, in the regularized inversion with depth weighting and positivity constraints. We found that too high regularization parameter will deepen the inverted source-density distribution, so that a lower value for the exponent of the depth weighting function should be used, with respect to the structural