On the basis of the results of improved analytical expression of computation of gravity anomalies due to a homogeneous polyhedral body composed of polygonal facets, and applying the forward theory with the coordinate ...On the basis of the results of improved analytical expression of computation of gravity anomalies due to a homogeneous polyhedral body composed of polygonal facets, and applying the forward theory with the coordinate transformation of vectors and tensors, we deduced both the analytical expressions for gravity gradient tensors and for magnetic anomalies of a polygon, and obtained new analytical expressions for computing vertical gradients of gravity anomalies and vertical component of magnetic anomalies caused by a polyhedral body. And also we developed explicitly the complete unified expressions for the calculation of gravity anomalies, gravity gradient, and magnetic anomalies due to the homogeneous polyhedron. Furthermore, we deduced new analytical expressions for computing vertical gradients of gravity anomalies due to a finite rectangular prism by applying the newly obtained expressions for gravity gradient tensors due to a polyhedral target body. Comparison with forward calculation of models shows the correctness of these new expressions. It will reduce forward calculation time of gravity-magnetic anomalies and improve computational efficiency by applying our unified expressions for joint forward modeling of gravity-magnetic anomalies due to homogeneous polyhedral bodies.展开更多
The forward and direct inversion of complex gravity and magnetic field of regular 2Dbodies under the condition of undulate topography" consists of four successive papers. The forward problem of complex gravity ...The forward and direct inversion of complex gravity and magnetic field of regular 2Dbodies under the condition of undulate topography" consists of four successive papers. The forward problem of complex gravity and magnetic fields is expounded in the first and the second paper. Mainly using Russian scholars’ method, the author deduced strictly and simply the complex gravity and magnetic field expressions of regular 2Dbodies and their combination bodies in complex field. Compared with the gravity and magnetic field expressions of these bodies in rectangular coordinates system, these expressions of complex fields have very simple forms. In the third and the fourth paper, the direct inversion problem of complex gravity and magnetic fields is expounded, which makes up the core of the serial papers. In these two papers, according to the complex gravity and magnetic field expressions of regular 2Dbodies and their combination bodies, the author first established linear simultaneous equations for solving middle variables in the complex coordinates system by use of his creative method of linearization, then established the highorder complex equation by use of middle variables to be solved out. As for the linear simultaneous equations and the high-order complex equation, the author solved successfully the direct inversion problem of complex gravity and magnetic fields of almost all regular 2Dbodies under the condition of undulate topography (or under the condition that the observation line lies in the arbitrary direction of 2Danomaly sources or is even closed).展开更多
基金This paper is supported by the National Natural Science Foundation of China (No.40374039)Program for New Century Excellent Talents in University (No. NCET-04-0726)the Focused Subject Program of Beijing (No. XK104910598).
文摘On the basis of the results of improved analytical expression of computation of gravity anomalies due to a homogeneous polyhedral body composed of polygonal facets, and applying the forward theory with the coordinate transformation of vectors and tensors, we deduced both the analytical expressions for gravity gradient tensors and for magnetic anomalies of a polygon, and obtained new analytical expressions for computing vertical gradients of gravity anomalies and vertical component of magnetic anomalies caused by a polyhedral body. And also we developed explicitly the complete unified expressions for the calculation of gravity anomalies, gravity gradient, and magnetic anomalies due to the homogeneous polyhedron. Furthermore, we deduced new analytical expressions for computing vertical gradients of gravity anomalies due to a finite rectangular prism by applying the newly obtained expressions for gravity gradient tensors due to a polyhedral target body. Comparison with forward calculation of models shows the correctness of these new expressions. It will reduce forward calculation time of gravity-magnetic anomalies and improve computational efficiency by applying our unified expressions for joint forward modeling of gravity-magnetic anomalies due to homogeneous polyhedral bodies.
文摘The forward and direct inversion of complex gravity and magnetic field of regular 2Dbodies under the condition of undulate topography" consists of four successive papers. The forward problem of complex gravity and magnetic fields is expounded in the first and the second paper. Mainly using Russian scholars’ method, the author deduced strictly and simply the complex gravity and magnetic field expressions of regular 2Dbodies and their combination bodies in complex field. Compared with the gravity and magnetic field expressions of these bodies in rectangular coordinates system, these expressions of complex fields have very simple forms. In the third and the fourth paper, the direct inversion problem of complex gravity and magnetic fields is expounded, which makes up the core of the serial papers. In these two papers, according to the complex gravity and magnetic field expressions of regular 2Dbodies and their combination bodies, the author first established linear simultaneous equations for solving middle variables in the complex coordinates system by use of his creative method of linearization, then established the highorder complex equation by use of middle variables to be solved out. As for the linear simultaneous equations and the high-order complex equation, the author solved successfully the direct inversion problem of complex gravity and magnetic fields of almost all regular 2Dbodies under the condition of undulate topography (or under the condition that the observation line lies in the arbitrary direction of 2Danomaly sources or is even closed).
