Robust Estimation and the Pseudo‐Inverse Method for Geophysical Inversion

Abstract

AbstractRobust estimation is introduced into geophysical inversion for data with large errors which are named outliers in order to obtain a good solution, which is called Geophysical Robust Estimation. But if a linear equation system is ill‐conditioned, the inversion solution is still not reliable. Therefore, the algorithm is improved by means of incorporating pseudoinverse method into geophysical robust estimations. In this paper, the basic principle of least square method with robust estimation or robust lest square method (RLS) is presented. Then the improved algorithm for pseudo‐inverse method is derived. Finally, two examples are given to prove that the method is effective. The results indicate that the robust estimation is able to reduce the disadvantageous effects from large observational errors on geophysical inversion and obtain a good solution for a normal model. And the improved method by combining the pseudo‐inverse method with robust estimation can not only upgrades the precision of inversion solutions and also assess directly their reliability.