|本期目录/Table of Contents|

[1]王季雨,孙鸿博,梁霄,等.有限均质椭球体模型重力及梯度异常正演计算方法研究[J].地震研究,2025,(04):602-611.[doi:10.20015/j.cnki.ISSN1000-0666.2025.0061 ]
　WANG Jiyu,SUN Hongbo,LIANG Xiao,et al.Research on Forward Calculation Method of Gravity and Gradient Anomalies of Finite Homogeneous Ellipsoid Model[J].Journal of Seismological Research,2025,(04):602-611.[doi:10.20015/j.cnki.ISSN1000-0666.2025.0061 ]
点击复制

有限均质椭球体模型重力及梯度异常正演计算方法研究(PDF/HTML)

《地震研究》[ISSN:1000-0666/CN:53-1062/P]

卷:
期数:
2025年04期
页码:
602-611
栏目:
重力场及其变化观测与地球科学应用专辑
出版日期:
2025-05-01

文章信息/Info

Title:
Research on Forward Calculation Method of Gravity and Gradient Anomalies of Finite Homogeneous Ellipsoid Model
作者:
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)
Author(s):
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)
关键词:
椭球体模型;  重力异常;  正演;  计算方法
Keywords:
ellipsoidal models;  gravity anomaly;  forward modeling;  calculation method
分类号:
P315.726
DOI:
10.20015/j.cnki.ISSN1000-0666.2025.0061
摘要:
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。
Abstract:
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.

参考文献/References:


边少锋,李兆权,翟国君,等.2024.全张量重力梯度正演计算及其可视化系统构建[J].武汉大学学报(信息科学版),49(11):1992-2002.
Bian S F,Li Z Q,Zhai G J,et al.2024.Construction of full tensor gravity gradient orthogonal computation and its visualization system[J].Geomatics and Information Science of Wuhan University,49(11):1992-2002.(in Chinese)
胡双贵,李广,汤井田,等.2024.利用重力梯度张量等位面曲率的地质体定位[J].地球物理学报,67(4):1641-1655.
Hu S G,Li G,Tang J T,et al.2024.Localization of geologic bodies using the curvature of the equipotential surface in gravity gradiometry[J].Chinese Journal of Geophysics,67(4):1641-1655.(in Chinese)
冷洁,邱峰.2022.有限圆柱体重力位三阶梯度张量正演计算公式[J].大地测量与地球动力学,42(1):96-99.(in Chinese)
Leng J,Qiu F.2022.Forward modeling formulae for third-order gradient tensor of gravitational potential caused by finite cylinder[J].Journal of Geodesy and Geodynamics,42(1):96-99.(in Chinese)
李静,万晓云,徐铭.2023.基于GRACE卫星数据和位错模型的2007年印尼明古鲁MW8.4地震同震重力梯度信号对比分析[J].地震研究,46(4):521-528.
Li J,Wan X Y,Xu M.2023.Comparative analysis of the coseismic gravity gradient signals of the 2007 Bengkulu,Indonesia MW8.4 earthquake based on GRACE Satellite data and the dislocation Model[J].Journal of Seismological Research,46(4):521-528.
刘繁明,刘惠敏,荆心.2016.基于旋转椭球体的等轴状场源体重力异常场模型构建方法[J].中国惯性技术学报,24(1):26-29.(in Chinese)
Liu F M,Liu H M,Jing X.2016.Modeling of isometric field-source in gravity anomaly field based on rotational ellipsoid[J].Journal of Chinese Inertial Technology,24(1):26-29.(in Chinese)
刘金钊,梁星辉,叶周润,等.2023.考虑地表起伏的不规则区域重力梯度场模型构建方法——以云南地区为例[J].地震地质,45(5):1129-1146.
Liu J Z,Liang X H,Ye Z R,et al.2023.Study on the regional gravity gradient field modeling in irregular area with consideration of surface fluctuation:A case study of Yunnan province[J].Seismology and Geology,45(5):1129-1146.(in Chinese)
骆遥.2008.两种新的长方体重力场正演表达式及其理论推导[J].工程地球物理学报,5(2):210-214.
Luo Y.2008.New expressions for gravitational attraction of a homogeneous rectangular prism and its deduction[J].Chinese Journal of Engineering Geophysics,5(2):210-214.(in Chinese)
乔中坤,张家俊,张宗宇,等.2023.重力梯度测量在城市空间探测中的应用[J].地质论评,69(S1):419-422.
Qiao Z K,Zhang J J,Zhang Z Y,et al.2023.Application of gravity gradient measurements in urban space exploration[J].Geological Review,69(S1):419-422.(in Chinese)
孙文珂.2017.重力勘查资料解释手册[M].北京:地质出版社.
Sun W K.2017.Manual for interpretation of gravity exploration data[M].Beijing:Geology Press.(in Chinese)
曾华霖.1999.重力梯度测量的现状及复兴[J].物探与化探,23(1):1-6.
Zeng H L.1999.Present state and revival of gravity gradiometry[J].Geophysical and Geochemical Exploration,23(1):1-6.(in Chinese)
曾华霖.2005.重力场与重力勘探[M].北京:地质出版社.
Zeng H L.2005.Gravity field and gravity exploration[M].Beijing:Geology Press.(in Chinese)
詹毅.2003.应用三角元法计算垂直圆柱体的重力异常[J].物探化探计算技术,25(4):5.
Zhan Y.2003.The numerical solution of gravity anomaly of a vertical cylinder by the trangle element method[J].Computing Techniques for Geophysical and Geochemical Exploration,25(4):5.(in Chinese)
张赤军,边少锋,周旭华,等.2007.重力垂直梯度的测定及其应用与潜力[J].地球物理学进展,22(6):1686-1691.(in Chinese)
Zhang C J,Bian S F,Zhou X H,et al.2007.Determination of gravity vertical gradient and its application and potential[J].Progress in Geophysics,22(6):1686-1691.
张剑,师学明,刘梦花,等.2007.基于Matlab开发环境的球体重力正演[J].工程地球物理学报,4(5):460-464.
Zhang J,Shi X M,Liu M H,et al.2007.The spherical gravitational forward modeling based on Matlab development environment[J].Chinese Journal of Engineering Geophysics,4(5):460-464.(in Chinese)
Goodacre A K.1973.Some comments on the calculation of the gravitational and magnetic attraction of a homogeneous rectangular prism[J].Geophysical Prospecting,21(1):66-69.
Li X,Chouteau M.1998.Three-dimensional gravity modeling in all space[J].Surveys in Geophysics,19(4):339-368.
Mehanee S A.2014. Accurate and efficient regularized inversion approach for the interpretation of isolated gravity anomalies[J].Pure and Applied Geophysics,171(8):1897-1937.
Nagy D,Papp G,Benedek J.2000.The gravitational potential and its derivatives for the prism[J].J Geod,74(7-8):552-560.
Nagy D. 1966.The gravitational attraction of a right rectangular prism[J]. Geophysics,31(2):362-37l.


备注/Memo

备注/Memo:
收稿日期:2024-10-25.
基金项目:安徽蒙城地球物理国家野外科学观测研究站联合开放基金项目(MENGO-202410); 安徽省科技创新攻坚计划项目(202423l10050030).
第一作者简介:王季雨(1994-),工程师,主要从事重力正反演方法研究.E-mail:503527782@qq.com.
通信作者简介:梁 霄(1991-),工程师,主要从事流动重力、流动地磁、跨断层水准观测与数据处理及分析工作.E-mail:lx1068@126.com.
更新日期/Last Update: 2025-05-01