Analytic signals of gravity gradient tensor and their application to estimate source location

Abstract

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.

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

“…I described that in 3D case, the components of the third column of the GGT are Hilbert transform pairs of the components of the first and second columns (Beiki, 2010). Then I defined an analytic signal for every single row called directional analytic signals in x, y and z directions.…”

“…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.…”

The unified theory of n-dimensional complex and hypercomplex analytic signals

“…Having in mind the relations between octonions and the 7-dimensional cross-product [23], we are looking for its resolution in the exceptional Lie group G 2 -a subgroup of rotations in seven dimensions SO(7) [24,25].…”