Application of the Euler deconvolution of directional analytic signal amplitudes in determination of location and type of gravity anomaly sources

The components of Gravity Gradient Tensor (GGT) is used for second-order derivatives of the gravitational potential field in the directions x, y and z in a Cartesian coordinate system. The third column of the gravity gradient tensor is Hilbert transform pairs of the first and the second columns. Many methods have been designed to estimate the depth, the horizontal position and the type of the sources from gravity gradient tensor components. Often, these methods are used derivatives of potential field data or their compounds in directions x, y, and z. Standard Euler deconvolution method is an approach in the interpretation of potential field data. It is able to locate the sources and to estimate the regional parameters with the assumption of the structural index. This approach is an automated method that has seen rapid development in recent years. The result of this method closely related to the precision of the assumed structural index parameter, and the accuracy is reduced in the presence of interference sources. Euler deconvolution of the directional analytic signal amplitudes is one of many methods to eliminate this problem. It is shown that the components of the gravity vector satisfy Euler's equation. Thus, it is proved that the amplitudes of directional analytic signal are homogenous and by putting in Euler's equation can estimate the location and the structural index of the gravity anomalies. In addition, two new equations were obtained from the combination of directional analytic signal amplitudes that is very effective in locating and estimating the structural index of gravity sources.
This paper was examined the application of Euler's equation of the directional analytic signal amplitudes to determine the location and the structural index of gravity anomaly sources. First, it is proved that each of directional analytic signal amplitudes in directions x, y, and z satisfy Euler's equation. Second, using the combination of directional analytic signal amplitudes derived two new equations that is more successful in determining the location (horizontal positions and depth) and source type (structural index) directly over the edges of gravity anomaly sources. The maxima of analytic signal amplitude in the z- direction place directly on the edge of the anomaly sources, but the maxima of analytic signal amplitude in the x- and y- directions deviate from the edges. That is why the simultaneous use of two or three-directional analytic signal amplitude can provide more accurate solutions.
The method described above was tested on the synthetic model in the presence of relatively high level Gaussian noise and interference sources. Finally, the method was applied to the Safoo manganese ore and obtained horizontal position, depth (~6 m) and structural index. MATLAB software was used to apply the above-mentioned methods.