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Euler deconvolution has been widely used in automatic aeromagnetic interpretations because it requires no knowledge of the source magnetization direction and assumes no particular interpretation model. This rapid inversion method produces stable estimates for the horizontal and vertical positions and respectively) of point sources. Another main advantage of this method is that it does not demand a detailed geologic knowledge of the area. However the two crucial weakenesses of this method are: i) the need of knowing the nature of the magnetic point or line source, that is, the knowledge of the structural index and ii) the presence of an undesirable “spray” of solutions which is obtained when the method is applied in a redundant way by moving the discrete inverse operator around the anomalous area. We present two new criteria for solving these difficulties. The first criterion is aimed at determining It is based on the correlation between the total-field anomaly and the estimates of a baselevel (b) computed at the same locations of the observations and using different This correlation attains a minimum when the correct is assumed. The second criterion selects, from the “spray” of solutions, only the best solutions. We propose that, besides selecting the solutions producing a standard deviation for smaller than a threshold value, only those solutions producing the “best fit” to the known quantities be selected. This additional criterion substantially reduces the “spray” of solutions.

We present a gravity interpretation method for estimating the relief of an arbitrary interface separating two homogeneous media. The upper medium is discretized into rectangular, juxtaposed prisms whose thicknesses represent the depths to the interface and are the parameters to be estimated from the gravity anomaly. To stabilize the inversion, we introduce two kinds of constraints on the depths. The first one requires proximity between the observed and computed depths at isolated points such as those obtained from boreholes (absolute equality constraint). The second one requires that groups of depths approximately follow an established linear relationship among them (relative equality constraint). Both kinds of constraints are imposed in the least-squares sense. This stabilization procedure does not bias the solution either toward an initial approximation, or toward the null solution. The method is applied to synthetic data, producing a good reconstruction of a complex basement consisting of several structural high and lows. It is also applied to real data of Reconcavo Basin, Brazil, leading to a sharper definition of the basement structures as compared with previous gravity interpretations of the area.

We present theoretical uniqueness, stability, and parameter bias analyses for the simultaneous estimation of: the structural index the horizontal and vertical positions and respectively) of a point magnetic source, and a baselevel b, using Euler’s differential equation. We found that and are independent of the other parameters and can be estimated from the knowledge of the total-field anomaly and its gradients only. On the other hand, and cannot be simultaneously estimated because they are linearly dependent. As a result, to estimate must be either known a priori or independently determined (and vice versa). For a known estimates of and are unique and stable regardless of the value of However, if the vertical (or horizontal) gradient of the observed total field assumes negligible values, the estimation of (or becomes unstable. In contrast, as far as is not too close to zero, estimates of are stable. For equal to zero, estimates of are undetermined.