任何物体在地球表面或附近空间都受到地球重力的作用，地下物质分布不均匀将会引起重力场变化。随着矿产从地下采出，形成采空区，也会导致地面重力场发生变化。在开采沉陷区进行重力勘查时，随着煤炭资源不断从地下采出，将引起地表不断下沉，这种采空区随时间由下向地面不断发展的过程中，将导致地面重力值发生动态变化。因此，在煤矿区研究开采引起的重力异常变化规律，对采空区位置探测及矿区大地水准面精化研究等具有重要意义。 本文利用开采沉陷理论分析了采空区残余空洞大小及分布特征，针对煤矿开采沉陷的特点，以现有的重力异常理论模型为基础，利用高斯公式对其进行数学变换，将三重积分变换成二重积分，并采用有限元法实现数值计算。同时，利用Matlab2014a软件平台进行模拟计算，探讨了影响有限元数值计算精度的因素，发现其精度与单元大小、计算方法及计算点至单元体的距离等密切相关。为了更好地发现重力异常与地质异常体之间的关系，利用Matlab编写了重力异常正演GUI程序，能够准确地展现出地质异常体产生的重力异常。 煤矿开采引起的地面沉陷按照概率积分法计算模型求取，并利用上述重力异常正演程序计算出工作面开采前、后的地面沉陷及相应的重力异常变化，通过回归分析得出重力场与地面沉陷的关系模型。同时，计算出采空区残余空洞引起的重力异常附加值。依据重力场的可叠加性，得到工作面开采及地表沉陷所引起的重力异常变化。 本文的研究改进了重力异常计算模型的适用性，建立了煤矿开采沉陷与重力异常的关系模型，具有一定的理论和实用价值。

Any object on the earth's surface or near space will receive the gravity, and uneven distribution of subsurface material will cause a change in gravity. With minerals mining from the underground, forming a goaf cavity, it the ground will lead to change in the gravity field. When gravity exploration in the mining subsidence, with coal resources mined from the underground that will cause the ground to sink unceasingly,at the same time the coal mining area will develop form underground to the ground along with time, this will lead to the ground gravity value of dynamic change.The surface will sink continuously because of the underground mining,which will cause the earth gravity’s changes. Therefore,the study the change law of gravity anomaly that caused by the diggings exploitation,which will have the vital significance on detecting goaf position and refining mining area geoid. The paper study the residual law of goaf residual cavity on the basis of the theory of mining subsidence, according to the characteristics of the mining subsidence, use the existing gravity anomaly theoretical model as the foundation, and use Gauss to make mathematical transform that make triple integral transform into double integral, and use the finite element to realize the numerical calculation. Meanwhile, the study use Matlab2014a software platform to discuss the factors influencing accuracy of finite element numerical calculation and find that the accuracy is related to the unit size,calculation methods and the distance between calculation points and unit. In order to well find and summary the relationship between gravity anomaly and geological anomalous body, using Matlab to compile GUI program to show the gravity anomaly. This program has the advantages of calculation quickly and accurately. The ground subsidence caused by coal mining is calculated by the Probability-integral Method ,and the gravity value simulation is used by the gravity anomaly forward program,then we use regression analysis to establish the relational model between gravity field and ground subsidence.At the same time, the additional value of gravity anomaly caused by residual cavity is calculated. In the end, Based on the gravity field additivity, we can get the gravity anomalies caused by the working face mining and ground subsidence. In this paper, this study has improved the application of gravity anomaly calculation, and build the relational model between coal mining subsidence and gravity anomaly, which has important theoretical and practical significance.