gradient tensor

Summary: Edge detection of subsurface structures is an important objective in interpretation of magnetic data. In this paper, curvature gradient tensor (CGT) of magnetic data has been used along with tilt angle method to detect edges of subsurface structures. Application of these methods on synthetic and real gravity data has shown that the CGT of magnetic data, compared to the tilt angle method, can determine the edges of subsurface structures better. Introduction: The main objective of the interpretation of magnetic data is to extract information about subsurface structures. Edge detection is an important means to image the edges of subsurface structures. Therefore, edge detection has traditionally been an important objective in the interpretation of magnetic data. There are various methods for edge detection. Tilt angle method is a traditional method that can detect edges of subsurface structures quantitatively. The value of Tilt angle is zero above the edges of subsurface bodies. The curvature gravity gradient tensor (CGGT) has also been used to interpret subsurface geological structures quantitatively. The eigenvalues of CGGT are zero above edges of subsurface bodies. In this paper, the CGT of magnetic data has been used for edge detection of subsurface magnetic bodies. The results of using the CGT of magnetic data have been compared with the results obtained from applying Tilt angle method on the data. Methodology and Approaches: In order to obtain the CGT of magnetic data, at first, the magnetic data are reduced to pole (RTP). Then, horizontal vector gradients of the gradient tensors are computed from the RTP data using a Fourier transform technique. Then, the eigenvalues of the CGT of magnetic data are obtained. The small eigenvalue can only be used to detect the edges of bodies with positive susceptibility contrast, and the large eigenvalue can only be used to determine the edges of bodies with negative susceptibility contrast. As an example, chromite ore has positive density contrast with the host rock and produce positive gravity anomaly. Finally, the tilt angle method is also applied to compare its results with those of the CGT of magnetic data. Results and Conclusions: The robustness of the method used for the enhancement of edge detection is tested with a magnetic anomaly map caused by two prisms of synthetic bodies with positive and negative susceptibility contrast. The results have shown that the zero contour of the small eigenvalue of the CGT of magnetic data compared to the zero contour of the tilt angle method can better detect the edges of synthetic bodies with positive susceptibility contrast. Moreover, the zero contour of the large eigenvalue of the CGT of magnetic data compared to the zero contour of the tilt angle method can better detect the edges of synthetic bodies with negative susceptibility contrast. The Tilt angle method is also more sensitive to noise than the CGT of magnetic data. The CGT method has been applied to real magnetic data from Qahan porphyry copper deposit in Markazi Province, Iran. The results have indicated that the large eigenvalue of the CGT can determine the edges of porphyry deposit and the small eigenvalue can outline positive magnetic anomalies caused by propylitic alteration. However, the tilt angle method has not been capable of finding the edges of the porphyry deposit.

Gradient Space Plot (GSP) is a structural method for gravity data interpretation, which is used for depth estimation of buried structures. In this structural interpretation, determination of depth, size, geometry and density contrast using a gravity gradient is proposed. In 1995, a general procedure for classifying and analyzing gravity gradient profile data over 2D structures was presented completely by Butler. In that research, it was shown that GSP, i.e. plots of horizontal gradient versus vertical gradient, present the complete magnitude and phase information on the gradient profiles simultaneously. To perform this method, necessary parameters like length and angle are initially extracted from the gradient space plot. Then, they are transmitted to a plot of vertical gradient versus profile, which leads to depth estimation. It is worth remarking that a comparison of measured or calculated gradient space plots to a model gradient space plot catalogue allows a rapid, qualitative determination of structure or geometry. Here, we suppose the anomaly is similar to one of the presented structures in the Butler Catalogue. We know that the Butler method requires no quantitative information or assumptions regarding the density contrasts. In these structures, for a correct interpretation, the density is assumed to be constant. To assess the density consistency, we model any arbitrary anomaly with a series of right rectangular prism pairs, overlaid with their sides and parallel to x-axis. In previous research a method was developed to determine the gradient tensor components, based on a model consisting of four right rectangular prisms of the same size. On the other hand, a change in the density value for any prism leads to different values of a GYX plot peaks. Hence, a GYX plot can be used as an attribute to show a change in density over the anomaly. In other words, it is employed as a tool to select interpretable data in the GSP method in which the density of the considered anomaly should be constant. A 3D plot of the GYX component for the gravity gradient tensor produces a pair of peaks which lie above and below the model surface. The number of the peaks is equal to the number of the prisms. The most important feature of this plot is the complete symmetry that exists in its peak values which can be obtained from the constant density in all prisms. In the case of four prisms, we have four peaks the amplitudes of which are proportional to density contrasts of any prism. It can be possible to avoid the perspective issues by 3D rotating in a cyclic way. The 2D plots contain more accurate information to the size of the peaks. Application of the gradient tensor test for real data showed that the density was constant in the area of the first part of the profile. In the first section of the profile, present interpretation compared favorably with the Euler method. The density constancy test for the second part of the profile was performed. The density in this part of the profile was not constant. Therefore, the reason for an ill-posed usage of GSP was shown. Space plots due to this section of profile were not similar to those of the Butler catalogue.