Majid Beiki

Eigenvector analysis of gravity gradient tensor to locate geologic bodies

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 gzz is approximately located above the center of mass. Observation points enclosed in a square window centered at the maximum of gzz 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...

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

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 compo ...

Interpretation of aeromagnetic data using eigenvector analysis of pseudogravity gradient tensor

This study has shown that the same properties of the gravity gradient tensor are valid for the pseudogravity gradient tensor derived from magnetic field data, assuming that the magnetization direct ...

Leveling HEM and aeromagnetic data using differential polynomial fitting

We introduce a new technique to level aerogeophysical data. Our approach is applicable to flight-line data without any need for tie-line measurements. The technique is based on polynomial fitting of data points in 1D and 2D sliding windows. A polynomial is fitted to data points in a 2D circular window that contains at least three flight lines. Then the same procedure is done inside a 1D window placed at the center of the 2D window. The leveling error is the difference between 1D and 2D polynomial fitted data at the center of the windows. To demonstrate the reliability of the method, it was tested on a synthetic aeromagnetic data set contaminated by some linear artifacts. Using the differential polynomial fitting method, we can remove the linear artifacts from the data. The method then was applied to two real airborne data sets collected in Iran. The leveling errors are removed effectively from the aeromagnetic data using the differential polynomial fitting. In the case of helicopter-towed electromagnetic (HEM) data, the polynomial fitting method is used to level the measured real (in-phase) and imaginary (quadrature) components, as well as the calculated apparent resistivity. The HEM data are sensitive to height variations, so we introduce an average-height scaling method to reduce the height effect before leveling in-phase and quadrature components. The method also is effective in recovering some of the attenuated anomalies. After scaling, the differential polynomial fitting method was applied to the data and effectively removed the remaining line-to-line artifacts.

Comment on “Depth Estimation of Simple Causative Sources from Gravity Gradient Tensor Invariants and Vertical Component” by B. Oruç in Pure Appl. Geophys. 167 (2010), 1259–1272

ORUC (2010) proposes a new method for interpretation of gravity gradient tensor (GGT) data. This method seems interesting in theoretical point of view, although, we have found some flaws in the equations he has derived. In this paper, we correct the introduced equations and describe some theoretical points, briefly.

New Techniques for Estimation of Source Parameters : Applications to Airborne Gravity and Pseudo-Gravity Gradient Tensors

Gravity gradient tensor (GGT) data contains the second derivatives of the Earth’s gravitational potential in three orthogonal directions. GGT data can be measured either using land, airborne, marin ...

Interpretation of gravity gradient tensor data using eigenvector analysis: An example from the Vredefort impact structure, South Africa

The eigenvectors of the symmetric gravity gradient tensor can be used to estimate the position of source bodies as well as their strike directions. For a given measurement point, the eigenvector corresponding to the maximum eigenvalue approximately points towards the center of mass of the causative body. It is assumed that the maximum of the first vertical derivative of the vertical component of gravity vector gzz is approximately located above the center of mass. For a collection of measurement points enclosed in a square window, centered at the maximum of gzz, a robust least squares procedure is used to estimate the source location. The strike direction of the source is estimated from the direction of the eigenvectors corresponding to the smallest eigenvalue for quasi 2D structures. The application of the method is demonstrated on gravity gradient tensor data from the Vredefort impact structure, South Africa.

Leveling of Aerogeophysical Data Using Differential Polynomial Fitting

A new technique to level the aerogeophysical data has been introduced. This approach is applicable to regular and irregular flight line patterns without using tie line measurements. The technique is based on polynomial fitting to data points in 1D and 2D sliding windows. A polynomial is fitted to data points once in a 2D window. Then the same procedure is done inside a 1D window placed in the middle of the 2D window. The difference between estimated values using polynomials in the center of the windows is taken as leveling error. In order to demonstrate the application of the method, it has been used to level aeromagnetic and helicopter-towed EM (HEM) data. Results show that linear artifacts are successfully removed from the data.