# 로버스트추정에 의한 지구물리자료의 역산

• Kim, Hee Joon (Department of Applied Geology, National Fisheries University of Pusan)
• 김희준 (부산수산대학교 응용지질학과)
• Received : 1995.07.01
• Published : 1995.08.31

#### Abstract

The most popular minimization method is based on the least-squares criterion, which uses the $L_2$ norm to quantify the misfit between observed and synthetic data. The solution of the least-squares problem is the maximum likelihood point of a probability density containing data with Gaussian uncertainties. The distribution of errors in the geophysical data is, however, seldom Gaussian. Using the $L_2$ norm, large and sparsely distributed errors adversely affect the solution, and the estimated model parameters may even be completely unphysical. On the other hand, the least-absolute-deviation optimization, which is based on the $L_1$ norm, has much more robust statistical properties in the presence of noise. The solution of the $L_1$ problem is the maximum likelihood point of a probability density containing data with longer-tailed errors than the Gaussian distribution. Thus, the $L_1$ norm gives more reliable estimates when a small number of large errors contaminate the data. The effect of outliers is further reduced by M-fitting method with Cauchy error criterion, which can be performed by iteratively reweighted least-squares method.

#### Acknowledgement

Supported by : 한국과학재단