重力归一化总梯度的稳定解法

Stable solution of normalized total gravity gradient

重力归一化总梯度法是20世纪80年代兴起的一种求解重力反演的方法,其关键运算是向下延拓及求导。原有的向下延拓方法大多数是在波数域实现的,由于稳定性差,影响了归一化总梯度法的效果,从而难以推广应用。本文以原先的希尔伯特变换法求解重力归一化总梯度值为基础,采用了一种新的、稳定的向下延拓算法——迭代法,替代了原有波数域的向下延拓算子,提高了计算的精度和稳定性。模型实验和实测资料应用显示效果明显改善。

The normalized total gravity gradient approach is a gravity inversion approach that rose in 1980s, the key operation of which is downward continuation and derivation. A most of the available downward continuation approaches is fulfilled in wavenumber domain, which affects the effect of normalized total gradient approach because of poor stability and is difficult to be generalized. Based on original Hilbert transform solving normalized total gravity gradient, the paper uses a new and stable downward continuation algorithm----iteration to replace original downward continuation operator in wavenumber domain, which improve the precision and stability of computation. The model test and real data application showed significant improvement of effects.