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对单一密度界面引起的重力进行非线性反演可通过幕级数展开式来实现。方法是以解非线性积分方程的Schmidt-Lichtenstein法为基础的。对重力效应非线性积分展开成算予幕级数之后,逆算子级数可通过形式上相当于标量幂级数的经典反演法的应用求得。然而,不同于正演幂级数展开式,逆级数的收剑只限于低频范围,因面具截止频率的特点,截止频率依赖于重力异常的幅度、密度差的大小和界面的平均深度。为了确保反演方法的稳定性,就要进行合适的低通滤波,由于反演法获得了好的迭代初值和应用了快速付氏变换,本方法有效地应用到剖面模型的正演和东斯洛伐克Outer Carpathians地区小型沉积盆地引起的三维野外重力异常处理实例(即Malcov重力异常)。
Nonlinear inversion of the gravitational force caused by a single density interface can be achieved by means of curtain series expansion. The method is based on the Schmidt-Lichtenstein method for solving nonlinear integral equations. After the non-linear integral of gravity effect has been calculated into the number of curtain series, the number of inverse operators can be obtained by applying the classical inversion method formally equivalent to the scalar power series. However, unlike the forward power series expansion, the inversion of the inverse series is limited to the low frequency range. Due to the cut-off frequency of the mask, the cut-off frequency depends on the magnitude of the gravity anomaly, the density difference, and the average depth of the interface. In order to ensure the stability of the inversion method, appropriate low-pass filtering is required. Because of the good iterative initial value obtained by the inversion method and the fast Fourier transform, the method is effectively applied to the forward and the east of the profile model An Example of Three-Dimensional Field Gravity Abnormalities Caused by Small Sedimentary Basins in the Outer Carpathians, Slovakia (ie, Malcov Gravity Anomalies).