b值的稳健估计及其在地震预报中的应用

ROBUST ESTIMATION OF b VALUE AND ITS APPLICATION TO EARTHQUAKE PREDICTION

利用 Ｍ 估计的稳健回归方法，选取 ψ函数为正态密度型函数，计算震级频度关系中的 ｂ值，并讨论了稳健估计方法与最小二乘估计所得结果的差异。认为由稳健估计得到的 ｂ 值更加符合震级频度关系中的大小比例，可作为可靠的背景值使用。作为应用实例对新疆地区ｂ 值进行空间及时间扫描，并定义最小二乘估计ｂ 值与稳健估计ｂ 值的偏差，以此为中强震的前兆判定指标，对喀什－ 巴楚地区 ８０ 年代以来 ６ 级以上地震前的异常进行讨论，认为该指标间接地反映了地震前的降维过程，且具有一定的实用性。

b value in the relation between magnitude and frequency is calculated by using robust regression of M estimation and choosing function ψ as normal density type function. The difference between the results obtained by the methods of robust estimation and least square estimation is also discussed in the paper. It is considered that the b value obtained by robust estimation is more suitable for the dimension proportion in the relation between magnitude and frequency, and it can be used as a reliable background value. As an application example, the b value of Xinjiang region has been scanned spatially and temporally, and the difference between b value of least square estimation and robust estimation is defined and used as a discriminant index for precursors of moderate and strong earthquakes. Through discussion on anomalies appeared before earthquakes with M ≥6 which have occurred in Karshi Barchu area since 1980, we think that the index indirectly reflects the dimension declining process and has certain practical meaning.