用有限元法计算变密度三维物体的重力异常

用有限元法计算变密度三维物体在其内外空间产生的重力异常,可以分为以下几个步骤:1.计算物体的总质量及其质心坐标;2.选择适当的封闭边界,使得边界上的点至物体质心的距离约为异常体线度的7～8倍;3.用位于质心质量等于异常体质量的质点在边界上产生的重力代替异常体在边界上产生的重力;4.用有限元法解泊松方程的边值问题,求出异常体在其内部和外部产生的重力异常.计算实例表明,若选择合适的边界和对空间的合理剖分,有限元法的计算精度可达1～2%。

Calculating the gravity anomaly of variable density 3-D geological body by using finite element method

Using the finite element method to calculate the gravity anomalies which are caused by a 3D varied-density geological body in its inside and outside spaces involves these steps:1.Calculate both the mass center coordinates and the total mass of the geological body.2.Choose such a closed boundary surface that the distance from each point on the surface to the mass center will be 7-8 times as long as linear dimension of the geological body.3.Replace the gravity values that the geological body causes on the surface by the gravity values that the mass point at mass center whose mass is equal to mass of the body creates on the surface. 4.Solve the boundary problem of Poisson equation with the use of finite element method so as to calculate the gravity anomalies the geological body causes in its inside and outside spaces.Application examples show that finite element method can bring the accuracy of 1-2% when proper boundary and reasonable calculation grid are taken.