The test of density constancy by gradient tensor for suitable usage of gradient space plot method

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.