有限均质椭球体模型重力及梯度异常正演计算方法研究
王季雨1,2,3,孙鸿博1,2,3,梁霄1,2,3,倪红玉1,2,3,黄显良1,2,3,李文尧4,韩润生4

(1.安徽省地震局,安徽 合肥 230001; 2.安徽省郯庐—大别地球物理研究中心,安徽 合肥 230001; 3.安徽蒙城地球物理国家野外科学观测研究站,安徽 蒙城 233500; 4.昆明理工大学 有色金属矿产地质调查中心西南地质调查所,云南 昆明 650093)

椭球体模型; 重力异常; 正演; 计算方法

Research on Forward Calculation Method of Gravity and Gradient Anomalies of Finite Homogeneous Ellipsoid Model
WANG Jiyu1,2,3,SUN Hongbo1,2,3,LIANG Xiao1,2,3,NI Hongyu1,2,3,HUANG Xianliang1,2,3,LI Wenyao4,HAN Runsheng4

(1.Anhui Earthquake Agency,Hefei 230001,Anhui,China)(2.Anhui Key Laboratory of Subsurface Exploration and Earthquake Hazard Risk Prevention,Hefei 230001,Anhui,China)(3.Mengcheng National Geophysical Observatory,Mengcheng 233500,Anhui,China)(4.Southwest Geological Survey Institute,Nonferrous Metals Mineral Geological Survey Center,Kunming University of Science and Technology,Kunming 650093,Yunnan,China)

ellipsoidal models; gravity anomaly; forward modeling; calculation method

DOI: 10.20015/j.cnki.ISSN1000-0666.2025.0061

备注

在有限均质椭球体的特殊情况——球体、旋转椭球体模型的基础上,推出了更具普适性的三轴不等长椭球体模型的重力异常Vz及其重力梯度Vxz、Vyz、Vzz、Vzzz的积分计算公式,并用Matlab开发工具编制了计算程序,获得了相应的计算数据并绘出了各分量的重力异常剖面图与等值线图,通过与已公开的球体、旋转椭球体模型的典型算例进行比对,验证了公式的正确性。结果表明:三轴不等长椭球体与球体、旋转椭球体虽具有相似的重力异常变化规律,但数值特征受形态参数影响显著,验证了三轴不等长椭球体模型在表征复杂地质体时的合理性与优越性,其既继承了球状体的基本场特征,又能通过三轴差异精确刻画实际地质体体积、质量分布等关键参数引起的重力异常场细节变化。
Based on special cases of finite homogeneous ellipsoids—spherical and rotating ellipsoidal models,this paper derives more generally applicable formulas for calculating the gravity anomaly Vz and its gravity gradients Vxz,Vyz,Vzz,and Vzzz for a triaxial ellipsoid model with unequal axes.Using Matlab as a development tool,a computation program was developed to obtain the corresponding calculation data and plot profiles and contour maps of gravity anomalies for each component.By comparing the results with published typical examples of spherical and rotating ellipsoidal models,the correctness of the formulas was verified.The results demonstrate that although triaxial ellipsoids with three distinct axes share similar gravity anomaly variation patterns with spherical and rotational ellipsoidal models,their numerical characteristics exhibit significant dependence on morphological parameters. This investigation validates the rationality and superiority of the triaxial ellipsoid model in characterizing complex geological formations. The proposed model not only preserves the fundamental field characteristics inherent to spherical bodies,but also enables precise quantification of detailed gravity anomaly variations induced by critical parameters of practical geological structures. Particularly, the triaxial dimensional discrepancies facilitate accurate characterization of field perturbations caused by differential volume distributions and heterogeneous mass configurations within actual geological bodies.
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