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重力单一密度界面的非线性反演可以通过幂级数展开式实现。该方法以解非线性积分方程的施密特-利希滕斯坦方法为基础,把重力效应中的非线性积分算子展开成为一个算子幂级数,并通过应用一种形式上等价于标量幂级数的经典反演方法来获得一个反演算子级数。然而,和前向幂级数展开所不同的是反演级数的收敛性局限在以截止频率为标志的低频域,该截止频率取决于重力异常的幅值、密度差的大小以及密度界面的平均深度。为确保反演方法的稳定性,必须进行适当的低通滤波。靠反演方法本身的非叠代性和快速付里叶交换取得的优势,该方法应用于仿真剖面模型的转换和由外喀尔巴阡山东斯洛伐克一个小沉积盆地引起的三维场实例(莫尔科夫重力异常)中,效果良好。
Nonlinear inversion of gravity single density interface can be realized by power series expansion. Based on the Schmidt-Lichtenstein method for solving nonlinear integral equations, the method expands the nonlinear integral operator in the gravity effect into an order of power series. By applying a new method which is formally equivalent to Scalar power series classical inversion method to obtain an inversion operator series. However, unlike the forward power series expansion, the convergence of the inversion series is limited to the low-frequency domain marked by the cut-off frequency, which depends on the magnitude of the gravity anomaly, the magnitude of the density difference, Average depth. In order to ensure the stability of the inversion method, appropriate low-pass filtering must be carried out. This method is applied to the conversion of the simulation profile model and to the three-dimensional field case caused by a small sedimentary basin in Eastern Carpathians, Shandong Province, and beyond (Moore Cove gravity anomaly), the effect is good.