We have developed a new method to locate geologic bodies using the gravity gradient tensor. The eigenvectors of the symmetric gravity gradient tensor can be used to estimate the position of the source body as well as its strike direction. For a given measurement point, the eigenvector corresponding to the maximum eigenvalue points approximately toward the center of mass of the causative body. For a collection of measurement points, a robust least-squares procedure is used to estimate the source point as the point that has the smallest sum of square distances to the lines defined by the eigenvectors and the measurement positions. It’s assumed that the maximum of the first vertical derivative of the vertical component of gravity vector [Formula: see text] is approximately located above the center of mass. Observation points enclosed in a square window centered at the maximum of [Formula: see text] are used to estimate the source location. By increasing the size of the window, the number of eigenvectors used in the robust least squares and subsequently the number of solutions increase. As a criterion for selecting the best solution from a set of previously computed solutions, we chose that solution having the minimum relative error (less than a given threshold) of its depth estimate. The strike direction of the source can be estimated from the direction of the eigenvectors corresponding to the smallest eigenvalue for quasi 2D structures. To study the effect of additive random noise and interfering sources, the method was tested on synthetic data sets, and it appears that our method is robust to random noise in the different measurement channels. The method was also tested on gravity gradient tensor data from the Vredefort impact structure, South Africa. The results show a very good agreement with the available geologic information.

The analytic signal concept can be applied to gravity gradient tensor data in three dimensions. Within the gravity gradient tensor, the horizontal and vertical derivatives of gravity vector components are Hilbert transform pairs. Three analytic signal functions then are introduced along [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-directions. The amplitude of the first vertical derivative of the analytic signals in [Formula: see text]- and [Formula: see text]-directions enhances the edges of causative bodies. The directional analytic signals are homogenous and satisfy Euler’s homogeneity equation. The application of directional analytic signals to Euler deconvolution on generic models demonstrates their ability to locate causative bodies. One of the advantages of this method is that it allows the automatic identification of the structural index from solving three Euler equations derived from the gravity gradient tensor for a collection of data points in a window. The other advantage is a reduction of interference effects from neighboring sources by differentiation of the directional analytic signals in [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-directions. Application of the method is demonstrated on gravity gradient tensor data in the Vredefort impact structure, South Africa.

For a number of widely used models, normalized source strength (NSS) can be derived from eigenvalues of the magnetic gradient tensor. The NSS is proportional to a constant q normalized by the nth power of the distance between observation and integration points where q is a shape factor depending upon geometry of the model and n is the structural index. The NSS is independent of magnetization direction, and its amplitude is only affected by the magnitude of magnetization. The NSS is also a homogenous function and satisfies Euler's homogeneity equation. Therefore, Euler deconvolution of the NSS can be used to estimate source location. In our algorithm, we use data points enclosed by a square window centered at maxima of the NSS for simultaneously estimating the source location and structural index. The window size is increased until it exceeds a predefined limit. Then the most reliable solution is chosen based on some statistical analysis (minimum uncertainty). One of the advantages of the presented method is that it allows automatic identification of the structural index as the constant background field is eliminated. Another advantage is reduction of interference effects from neighboring sources by differentiation of the NSS. We have compared our method with the analytic signal amplitude and when the magnetic source contains remanent magnetization with a different direction to the inducing field, the NSS provides more reliable information about source geometry. Application of the method has been demonstrated on an aeromagnetic data set from the Tuckers Igneous Complex, Queensland, Australia. The NSS has improved interpretation of magnetic anomalies for this igneous complex, for which available geologic information shows relatively strong remanent magnetization.

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We have developed an approach for the interpretation of magnetic field data that can be used when measured anomalies are affected by significant remanent magnetization components. The method deals with remanent effects by using the normalized source strength (NSS), a quantity calculated from the eigenvectors of the magnetic gradient tensor. The NSS is minimally affected by the direction of remanent magnetization present and compares well with other transformations of the magnetic field that are used for the same purpose. It therefore offers a way of inverting magnetic data containing the effects of remanent magnetizations, particularly when these are unknown and are possibly varying within a given data set. We use a standard 3D inversion algorithm to invert NSS data from an area where varying remanence directions are apparent, resulting in a more reliable image of the subsurface magnetization distribution than possible using the observed magnetic field data directly.