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ABSTRACT Downward continuation is a useful transformation, mainly used to enhance measured gravity or magnetic field anomalies. It is known to be an unstable transformation that should be strictly used only in the harmonic region, apparently preventing any meaningful application to continuations inside the source volume. Despite these well-known theoretical and practical limitations it has been used to recover source parameters by different methods, here referred to as normalized full gradient methods. Such methods show that downward continuation may be extended to the source volume, which is assumed to contain one-point, isolated singularities, which is a quasi-harmonic region. We modify the normalized full gradient method focusing our attention to the way the downward continuation is normalized. Differently from normalized full gradient methods, we study the effect of the normalization not only on the analytical signal modulus of the downward continued field but also on the downward continuation of the gravity or magnetic fields themselves. With our method, called normalized downward continuation, several statistically meaningful normalizations are considered, some of them yielding improved, more resolved depth estimations for synthetic as well as measured total-field anomalies. From a statistical point of view, the downward continued field tends to have right-skewed histograms at shallow depths, while becoming symmetrically distributed at greater depths. This occurs because, as the depth of continuation increases, the intrinsic error propagation of the downward continuation allows the error to dominate with respect to the source-related signal. For non-isolated anomalies, consistent results are also obtained but the normalizing factors must be computed within windows centred to the studied anomaly. [ABSTRACT FROM AUTHOR]

A new method based on 3D multiridge analysis of potential fields assumes a 3D subset in the harmonic region and studies the behavior of potential field ridges, which are built by joining extreme points of the analyzed field computed at different altitudes. Three types of ridges are formed by searching for the zeros of the first horizontal and first vertical derivatives of the potential field (types I and II, respectively) and the zeros of the potential field itself (type III). This method uses a redundant set of ridges, called a multiridge set, to determine source type and location. For homogeneous potential fields generated by simple sources, all of the ridges are straight lines converging to the source position. This method analyzes the multiridges by using a geometric criterion to find the source position at the intersection of the multiridge set and by solving the three reduced Euler equations associated with ridge types I, II, and III. The reduced Euler type I and II equations are used to obtain the structural index and the vertical and horizontal source positions; equation type III estimates the horizontal and vertical source positions. Tests on synthetic as well as the Bishop model field yield good results even with noise-corrupted data. Results obtained using magnetic data collected over the wreck of a military ship in the Tyrrhenian Sea successfully determine its vertical and horizontal positions and the structural index. [ABSTRACT FROM AUTHOR]

ABSTRACT The problem of removing directional trends frequently occurs in the processing of magnetic data and also in the subsequent steps of data interpretation. The so-called corrugations are typical directional trends occurring in levelled data, which may be removed in several ways. Classical techniques are based on high-pass filtering of the data and successively filtering these transformed data with directional cosine filters. Other linear features are due to real sources, such as pipelines in shallow surveys or dike swarms in regional surveys. They should, nevertheless, be considered as noise, due to the fact that their effect is strong and tends to hide the field features related to structures of more interest. We deal with both kinds of problem, presenting the results of a study in an archaeological area of southern Italy. Decorrugation of magnetic field anomalies is performed using a method based on the excellent space–frequency localization properties of wavelet bases, allowing a very sharp filtering of the field along a selected direction. We compare this technique with the classical one in a synthetic case and find that the wavelet decorrugation is simpler and produces low distortion maps. Besides the field decorrugation, the wavelet approach was also shown to be useful in the subsequent enhancement of the measured field. In fact, we show that the wavelet analysis offers a unique framework where various filtering problems (directional, isotropic, global or local as well) may be easily solved. As regards the archaeological case, strong noisy effects from elongated sources (pipelines) were successfully removed in a sharp and local way. [ABSTRACT FROM AUTHOR]

In potential field inversion problems we usually solve underdetermined systems and realistic solutions may be obtained by introducing a depth-weighting function in the objective function. The choice of the exponent of such power-law is crucial. It was suggested to determine it from the field-decay due to a single source-block; alternatively it has been defined as the structural index of the investigated source distribution. In both cases, when k -order derivatives of the potential field are considered, the depth-weighting exponent has to be increased by k with respect that of the potential field itself, in order to obtain consistent source model distributions. We show instead that invariant and realistic source-distribution models are obtained using the same depth-weighting exponent for the magnetic field and for its k -order derivatives. A similar behavior also occurs in the gravity case. In practice we found that the depth weighting-exponent is invariant for a given source-model and equal to that of the corresponding magnetic field, in the magnetic case, and of the 1st derivative of the gravity field, in the gravity case. In the case of the regularized inverse problem, with depth-weighting and general constraints, the mathematical demonstration of such invariance is difficult, because of its non-linearity, and of its variable form, due to the different constraints used. However, tests performed on a variety of synthetic cases seem to confirm the invariance of the depth-weighting exponent. A final consideration regards the role of the regularization parameter; we show that the regularization can severely affect the depth to the source because the estimated depth tends to increase proportionally with the size of the regularization parameter. Hence, some care is needed in handling the combined effect of the regularization parameter and depth weighting. [ABSTRACT FROM AUTHOR]