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In this thesis I tried to develop new automatic imaging methods, aiming at improving the interpretation of potential field anomalies related to mining and environmental studies. The major improvements, which I obtained, are the stability, which is normally low for methods such as the local wavenumber, and the full automaticity in retrieving the source parameters (depth and structural index). Starting from the theory of the Depth from Extreme Points (DEXP) method, I first applied it to the self-potential data related to mineralization and to groundwater flow. DEXP is a fast imaging method transforming the field data, or its derivatives, into a quantity proportional to the source distribution. The method is particularly suited to handle at high-resolution noisy data, as it is stable even using high-order derivatives. DEXP imaging depends on the knowledge of the structural index of the source. While this parameter may be a priori determined by the method itself, i.e., by a preliminary application of related multiscale methods based on the study of the scaling function, it may also assumed a priori, as done for other imaging methods such as migration, correlation or the sandwich model. I showed the usefulness of DEXP method to self-potential datasets, regarding mineral exploration at Malachite mine, Colorado, (USA), Sariyer area (Turkey) and Bender area (India) and water-table depth estimation in a pumping well and in sinkholes at the area of San Vittorino Plain (Rieti, central Italy). The estimated depths well agree with the known information about the sources. As any imaging method (DEXP, correlation, migration and others) needs to assume, inherently or explicitly, a value for the structural index and that it is valid throughout the whole explored source volume, I tried to develop new imaging methods to estimate the depth to the sources of potential fields independent from value of the structural index. The first of them consists of applying the DEXP transformation to the ratio ( ) between two different-order partial derivatives of the field. While the scaling function used in the DEXP transformation depends on the structural index, I showed that the scaling function of merely depends on the difference between the two used orders of differentiation. This allows three main features to be established for the DEXP transformation of : a) it is independent from the structural index; b) the estimation of the source depths is fully automatic, simply consisting in the search of position of the extreme points of the DEXP image; c) the structural index of each source is finally determined from the scaling function or the extreme points using the estimated depth. Besides the well known characteristics of the DEXP transformation, such as high-resolution and stability, the DEXP transformation of enjoys one more relevant feature: it can be applied to multi-source cases, yielding simultaneously correct estimations of structural index and depth for each source in the same image. However, while the DEXP transformation is a linear transformation of the field, the DEXP transformation of is nonlinear, and a procedure is described to circumvent the nonlinear effects. The method is tested with synthetic examples and applied to real magnetic data for mineral exploration from the Pima copper mine, Arizona, USA, Hamrawien area, Egypt and Cataldere, Bala district of Turkey. The results are consistent with the known information about the causative sources. I developed also a method for source parameter estimation, based on the local wavenumber function. Even in this case I made use of the stable properties of the DEXP method, so to deal with local wavenumber of high-order, as DEXP is able to overcome its known instability caused by the use of high-order derivatives. Also in this case, i.e., the DEXP transformation of the local wavenumber, the scaling-law is independent of the structural index, is fully automatic and may be implemented as a very fast imaging method, mapping different-kind sources at their own correct depth. The method was demonstrated to synthetic cases and applied to real-data examples from Bulgaria and from a test site for buried drums in Italy. I also developed a new method to analyze the local wavenumber, based on the fractional-order differentiation of potential fields, to the end of applying it in a more stable way. Such kind of differentiation allows a fractional-order local wavenumber to be defined, whose usefulness is two-fold: a) the positions of the peaks of the two different-order local wavenumber are essentially the same; b) the well known instability of the method, due to the noise-enhancement related to the field standard differentiation, may be kept to a minimum, if a fractional-order field differentiation is used. The method is applied to synthetic and real examples for mineralization and archaeological exploration and it provided a good estimation of both depth to sources and structural index.

In this paper we present an improvement to the local wavenumber method able to overcome its instability caused by the use of high-order derivatives. We make use of the stable properties of the Depth from EXtreme Points (DEXP) method, in which the depth to the source is determined at the extreme points of the field scaled with a power law of altitude. As DEXP transformation is applied to the local wavenumber function, we show that the scaling law is independent on the structural index. This allows the technique to be fully automatic, so that it may be implemented as a very fast imaging method, mapping every source, of different homogeneity degree, at the correct depth.

We illustrate a new imaging method to estimate the depth to the sources of potential fields and the structural index. The method consists of applying the Depth from EXtreme Point (DEXP) transformation to the ratio (R) between two different-order partial derivatives of the field. While the scaling function of the potential field depends on the structural index, we show that the scaling function of R merely depends on the difference between the two used orders of differentiation. This allows three main features to be established for the DEXP transformation of R: (1) it is independent from the structural index; (2) the estimation of the source depths is fully automatic, simply consisting in the search of position of the extreme points of the DEXP image and (3) the structural index of each source is finally determined from the scaling function or the extreme points using the estimated depth. Besides the well-known characteristics of the DEXP transformation, such as high-resolution and stability, the DEXP transformation of R enjoys one more relevant feature: it can be applied to multisource cases, yielding simultaneously correct estimations of structural index and depth for each source in the same image. However, while the DEXP transformation is a linear transformation of the field, the DEXP transformation of R is non-linear, and a procedure is described to circumvent the non-linear effects. The method is tested with synthetic examples and the estimated source parameters show a good agreement with the true values. The method was applied also to real magnetic data from the Pima copper mine, Arizona, USA, Hamrawien area, Egypt and Cataldere, Bala district of Turkey. The results are consistent with the known information about the causative sources.