位场垂向高阶导数的Tikhonov正则化迭代法

Tikhonov Regularization Iteration Method for High-Order Vertical Derivatives of Potential Field

在位场数据处理中,垂向导数具有重要的物理意义。其在一定程度上可以划分不同深度和大小异常源产生的叠加异常,且导数的阶次越高,这种分辨能力就越强,但通常认为高阶导数的换算是不稳定的。本文在Tikhonov正则化求位场垂向高阶导数的基础上,结合迭代法进行逐次逼近,提出了位场高阶导数的Tikhonov正则化迭代法,并且得到Tikhonov正则化迭代法的递推公式。通过对该方法的滤波特性分析可以看出,该方法计算的位场垂向高阶导数具有一定的稳定性及保幅性。模型试验和实际数据的处理表明,该方法计算结果较常规FFT求导法有更高的稳定性和实用价值。

In potential field data processing,high-order vertical derivative has important physical significance.It can divide superimposed anomalies generated by sources with different depth and size.With the order increase of the derivative,the resolution becomes higher,however the calculation of the higher order derivative is unstable.In this study we proposed the Tikhonov regularization iteration method for high-order vertical derivatives based on the combination of Tikhonov regularization method and iteration method,and obtained the recursive formula of Tikhonov regularization iterative method.Through analyzing the filter characteristics of the method,we can see that the method has certain stability and amplitude preservation in the calculation of high-order vertical derivative.The results of the model test and the real data show that the stability and practical value of the method are higher than that of the routine FFT method.