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单一密度界面的重力非线性反演可以通过一个幂级数展开进行。这种方法是根据Schmidt-Lichtenstein逼近法来解非线性积分方程的。把重力的影响作为一个算子幂级数,展开非线性积分算子后,逆算子级数可以通过一种方法求出,这种方法形式上相当于标量幂级数的经典求逆方法。然而,与正向幂级数展开不同的是,逆级数的收敛只限于一个有截止频率特征的低频域,这个截止频率依赖于重力异常的幅度、密度差的大小和界而的平均深度。为保证反演方法的稳定性,必须要进行适当的低通滤波。利用该反演方法无需迭代的优点和快速傅里叶变换,该方法被成功地用来反演似剖面的模拟模型以及由东斯洛伐克外喀尔巴阡山脉的一个小沉积盆地引起的一个三维场的实例(Malcov重力异常)。
The gravity nonlinear inversion of a single density interface can be performed by a power series expansion. This method is based on Schmidt-Lichtenstein approximation to solve the nonlinear integral equation. Taking the influence of gravity as an order of power, after expanding the nonlinear integral operator, the inverse operator series can be obtained by a method that is formally equivalent to classical inverse method of scalar power series. However, unlike the forward power series expansion, the convergence of the inverse series is limited to a low-frequency domain with a cut-off frequency characteristic that depends on the magnitude of the gravity anomaly, the density difference, and the average depth of the boundary. In order to ensure the stability of the inversion method, we must make appropriate low-pass filtering. Using this inversion method without iterative advantages and fast Fourier transforms, this method has been successfully used to invert a model-like simulation model and a three-dimensional field caused by a small sedimentary basin in the Outer Carpathian Mountains of Eastern Slovakia (Malcov gravity anomaly).