عنوان مقاله [English]
نویسندگان [English]چکیده [English]
In view of the numerous publications, there is clear interest in the application of the Finite Element Method (FEM) to compute the regional gravity anomaly involving only 8 nodes on the periphery of a rectangular map. Geophysical data processing methods, such as trend analysis, analytical continuation and filtering can reveal the general structural properties of a region. Although, there were improvements in distinguishing the regional and residual gravity anomalies, no progress has been made in trend analysis, filtering or analytical continuation methods. With improvements in scientific computing, high degree trend analysis and filtering methods have been used more efficiently for 2-D data. On the other hand, computed regional anomalies still contain residual anomaly effects. For this reason, the finite element method (FEM) might be used to eliminate the residual anomaly effects on the regional anomalies. A brief description of the theory of FEM is presented for the sake of completeness.
The gravity map in real space is superimposed by a weighted sum of discrete gravity values at eight stations coinciding with the eight nodes of a second-order iso-parametric element to compute the regional anomalies on the finite elements in the FEM application. For each node coordinate and field variable, the element can be defined by the same shape functions. Due to this feature, it could be named an isoparametric element. The observed gravity values for each node are obtained from the map. The non-dimensional reference plane, which is related to the real plane, was described by using the shape function to perform an easy computation. Eight observed gravity values on quadratic isoparametric elements, which were superimposed onto the gravity map, are needed to compute regional anomolies. Other observed gravity data are unnecessary.
Gravity anomalies always include the total effects (combination of the structures which have different densities and depths) of the study area and beyond. Moreover, the well-known non-uniqueness of potential field modeling may lead to very different interpretation results. FEM is here applied in order to determine the regional anomalies. The method has advantages over the traditional methods. For instance, only a few observation points on a Bouguer gravity map are needed to compute the regional gravity anomaly. The FEM can be applied for any size of gravity map. In addition, it will be shown that the computed regional anomaly contains minimal residual anomaly effects.
The FEM, which has been used in potential field interpretation for decades, allows complex problems to be solved easily and accurately. The first step of FEM is to identify the elements and then to identify the boundary of the solution space. In this step, the solution space is divided into elements. After determination of the geometrical structure of the solution space, the most suitable elements should be selected for this geometrical structure. The agreement between the geometry and the elements is quite important for the convergence to the best possible solution. FEM has been successfully applied to different modeling problems in the scientific world including in geophysics for decades. In this study, it was used to distinguish the regional and residual anomalies by using the necessary shape functions. These shape functions play quite an important role in changing the reference plane. After the method was applied, it was seen that it produced better results than those produced by the existing traditional methods. In addition to that, fewer gravity values were needed. For instance, only eight nodes with the shape functions were used to compute the regional anomaly.