【摘要】 随着地球物理勘探从传统的二维模型向三维模型发展，由此产生的海量数据给反演带来巨大挑战，尤其在重构大规模三维构造时。对于有限差分离散化边值问题引起的病态线性方程组，直接求解器比迭代求解器需要更多的内存和时间。为了解决这一难题，应用一种高效的三维有限差分迭代求解器，实现三维重力位正演计算。首先，利用长方体网格的中心有限差分方法对三维重力位的边值问题进行离散，并将广义最小残差算法(GMRES)迭代求解器与不完全LU因子分解相结合，以求解大型非对称稀疏线性方程组；其次，为了获得高精度的重力场，采用高阶拉格朗日插值格式求解重力位的一阶偏导数；最后，应用三个密度模型测试三维有限差分算法的准确性、可靠性和灵活性。数值模拟结果表明，格点型有限差分法能够提供重力场的精确近似，并为实测数据的定性解释提供指导。更多还原

【Abstract】 With the evolution of geophysical surveys from traditional two-dimensional(2D) to three-dimensional(3D) models, the resulting large data volumes pose significant challenges to inversion, particularly when resolving large-scale 3D structures. A direct solver for solving an ill-conditioned linear system resulting from the finite-difference approximation of a boundary value problem requires more memory and time than iterative solvers. To overcome this limitation, an efficient iterative solver for 3D finite-difference approach is introduced to calculate the 3D gravitational potential and the associated gravitational field. Firstly, the boundary value problem associated with 3D gravitational potential is discretized using central finite-difference technique based on right rectangular prismatic grids. The resulting large unsymmetric sparse systems are then solved using the generalized minimal residual algorithm(GMRES) iterative solver in combination with incomplete LU factorization. Secondly, to obtain high-accuracy partial derivatives of gravitational potential, a high-degree Lagrange interpolation scheme is employed. Finally, three density models are applied to test the accuracy, reliability, and flexibility of our 3D finite-difference algorithm. All computational results demonstrate that our method provides an accurate approximation of the gravitational field and is applicable to 3D forward modeling.更多还原