地球物理抗差估计和广义逆方法

为进行观测数据误差较大的地球物理资料的反演，引人抗差估计，称作地球物理抗差估计；为使病态方程组的反演解更可靠，又结合广义逆方法进行了算法改进．首先介绍抗差最小二乘（ＲＬＳ）的基本原理，然后推寻出适于广义逆反演方法的改进算式，最后举例加以讨论．分析表明，抗差估计可以有效地抑制地球物理观测异常的影响，得出正常模式下的较好估计值；而用改进后的算式和广义逆反演可以使反演解更加改善，不仅如此，改进后的方法还能直接给出解估计的可靠性评价．

ROBUST ESTIMATION PLUS PSEUDO-INVERSE METHOD IN GEOPHYSICAL INVERSION

In order to invert geophysical data with large outliner to obtain a good solution. Which is called Geophysical Robust Estimation. If a linear equation system is ill conditioned, the inversion solution is not reliable. Therefore, the algorithm is improved by means of incorporating pseudo-inverse method into geophysical robust estimation. In this paper, firstly the basic principle of least square method with robust estimation （RLS） is demonstrated in detail. And then an improved algorithm for pseudo-inverse method is derived. Finally, tWo examples are shown and the method proves to be effective through the illustration of them. The results indicate that robust estimation is able to reduce the effects of large observational errors on geophysical data to obtain a good solution of a normal model. And the improved method by combining pseudo-inverse method with robust estimation not only upgrades the precision of the inversion solution, but also can be used directly to assess the reliability of the inversion solution.