Eigenvector analysis of gravity gradient tensor to locate geologic bodies

Abstract

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.

Determination of the Strike and the Dip of a Line Source Using Gravity Gradient Tensor

“…반면 중력 변화율 텐서의 측정은 여러 개의 가속도계를 복합적으로 이용하는 중력 변화율 측정 시스템이 개발되어 활발히 이용되 고 있다 (Dransfield, 2010;Lee, 2001). 중력 변화율 텐서는 기본적으로 서로 독립인 5개의 성분이 존재 하므로 중력이나 벡터 중력에 비해 정보의 양이 비 약적으로 증가하므로 이를 응용하려는 다양한 연구들 이 수행되고 있다 (Zhdanov et al, 2004;Beike, 2010;Beike and Pedersen, 2010;Rim and Li, 2012;Martinez et al, 2013;Braga et al, 2014).…”

New techniques for estimation of source parameters: Applications to airborne gravity and pseudo-gravity gradient tensors

“…In reality, many of 2D geological structures can be approximated by infinite dike and geological contact models which make them more practical than the infinite horizontal cylinder model for interpretation of magnetic and gravity field data (e.g., Nabighian, 1972 and1974;Hsu et al, 1998;Bastani and Pedersen, 2001;Beiki and Pedersen, 2010). Telford et al (1990) and Stanley and Green (1976) have shown expressions for the gravity gradients g xz and g zz caused by infinite dike and geological contact models, respectively.…”

“…In recent years, several new techniques for interpretation of GGT data have been introduced in the literature (e.g. Pedersen and Rasmussen, 1990;Vasco and Taylor, 1991;Edwards et al, 1997;Routh et al, 2001;Zhdanov et al, 2004;Droujinine et al, 2007;While et al, 2006;Mikhailov et al, 2007;Pajot et al, 2008;While et al, 2009;Beiki and Pedersen, 2010;Beiki, 2010). However, both processing and interpretation of GGT data are still challenging and requires further development.…”

Full-tensor gravity gradient eigenvector analysis for locating complex geological source positions

“…Although the practical geological structure is much complicated than a mass point, it can be considered 15 as a combination of many point mass cells, and the eigenvector of these sets of cells contains the boundary information of the total anomalous source. Beiki (2010) suggested that the eigenvalue decomposition could be considered as an equivalent point source method for a causative gravimetric body. Li (2015) presented theoretical and practical aspects related to the eigenvectors and rotations of the gravity gradient tensor.…”

“…Pedersen and Rasmussen (1990) introduced eigenvector analysis on the gradient tensor of potential field data and derived the relationship between the eigenvalues and eigenvectors of the potential field source parameters. Beiki and Pedersen (2010) combined Euler deconvolution and the eigenvector analysis to estimate 10 the depth of the geological body. Sertcelik and Kafadar (2012) suggested that the eigenvalues of CGGT (curvature gravity gradient tensor) could be used to detect the edges and corners of a subsurface source, while Oruc et al, (2013) applied the CGGT eigenvalue analysis on a complex field data interpretation application.…”