重力异常二维正演中的无网格方法

Meshfree method for 2-D forward modeling of gravity anomaly

无网格法是一类新型数值算法,具有精度高、高阶形函数构造与物性加载便利等特点,在计算力学领域应用广泛。将无网格方法(PIM、RPIM及EFGM)用于重力异常场二维正演计算:首先从重力异常二维变分问题出发,利用Galerkin法结合高斯积分公式推导了对应的无网格离散系统矩阵表达式;其次通过数值试验得出了RPIM-MQ、RPIM-exp及EFGM-exp形状参数的建议值,最后比较分析了最优形状参数下不同无网格法的计算效果。结果表明:无网格法适用于介质物性分布变化较大的重力异常二维正演,exp函数形状参数c?最优取值区间为[1.5,1.7],?建议值为0.6,MQ函数q取值区间为–4.1～1.9;EFGM较PIM及RPIM具有更高的计算精度。

Meshfree method as a kind of new numerical method has the advantages of high precision,high order function structure and convenient loading of physical properties,is widely applied in the field of computational mechanics.The meshfree method including PIM,RPIM and EFGM was used in the two-dimensional forward calculation of gravity anomaly field.Firstly,from the 2-D variational problem of gravity anomaly,the corresponding meshfree discrete system matrix expression was deduced by combining Galerkin method and Gauss integral formula.Then suggested values of the shape parameters of RPIM-MQ,RPIM-exp and EFGM-exp were obtained by numerical experiments,the calculation results of different meshfree methods under optimal shape parameters were compared and analyzed.The conclusions are verified as follow:Meshfree method is suitable for 2-D forward modeling of gravity anomaly with big variation of the distribution of medium physical properties,the optimal interval of exponential function shape parameterαc is in range of 1.5 to 1.7,the proposed value ofβis 0.6 and the proposed interval of q in MQ function is in range of– 4.1 to 1.9,EFGM has higher computational accuracy than PIM and RPIM.