Forward Method for Gravity, Gravity Gradient and Magnetic Anomalies of Complex Body
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摘要: 在改进均匀多面体重力场正演公式基础上, 利用二阶张量的坐标变换实现对多面体重力场梯度的求解, 推导了新的多面体重力梯度和磁场的正演公式, 给出了新的统一的均匀多面体重力场、梯度及磁场正演表达式形式, 并用理论模型进行了检验.同时, 应用新的多面体重力场梯度正演公式推导出新的长方体重力场垂直梯度理论表达式.本文给出的均匀多面体重力场、梯度及磁场正演表达式形式统一, 重磁场联合正演中可相互利用其计算过程中的结果, 避免重复计算以提高正演计算效率.Abstract: Based on the improved analytical expression for computing the gravity anomalies due to a homogeneous polyhedral body composed of polygonal facets, and by applying the forward theory with the coordinate transformation of vector and tensor, we deduced the analytical expressions for both gravity gradient tensor and magnetic anomalies due to a polygon, and obtained new analytical expressions for computing vertical gradient of gravity anomalies and vertical component of magnetic anomalies due to a polyhedral body. And we also explicitly developed the complete and unified expressions for calculating gravity anomalies, gravity gradient and magnetic anomalies due to the homogeneous polyhedra. Furthermore, we deduced new analytical expressions for computing the vertical gradient of gravity anomalies due to a finite rectangular prism by applying the new obtained expressions for gravity gradient tensor due to a polyhedral target body. Comparison with forward calculation of models testified the correctness of these new expressions. It will reduce forward time of gravimagnetic anomaly and improve computational efficiency by applying our unified expressions for joint forward of gravimagnetic anomalies due to homogeneous polyhedral bodies.
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图 4 多面体重力场UZ (a) 及其梯度UZZ (b) 和ΔT场(c) 等值线图
图中实线为正值, 虚线为负值; 模型计算参数I=60°, A=30°, 网格间距5 m×5 m, 等值线单位分别10-6m·s-2, 10-6s-2, nT.
Fig. 4. The gravity UZ (a), gravity gradient UZZ (b) and ΔT (c) contour map
表 1 组合四面体模型顶点坐标
Table 1. Vertices of homogeneous polyhedral bodies
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