Weighted two-step regression method of attenuation relationship considering sample uneven distribution

Weight is introduced into two-step method by grading distances and magnitude. In the first step, the recordings are divided into several intervals by range of distances. Every recording gets one weight w'_ij=1/(n_jn_i) (n_j is the number of earthquakes in the interval in which the recording is located, n_i is the number of recordings of the earthquake in this interval). Not only does the way of getting weight keep equal weight for every interval, but also promises the same weight for earthquakes in any interval. In the second step, the earthquakes are divided into several intervals by range of magnitudes. Every earthquake get one weight v'_k=1/n_k (n_k is the number of earthquakes in the interval in which the earthquake is located). Taking the recordings used by Joyner and Boore (1981) as instance, comparing results from weighted two-step method with that from traditional one, the results show that values of peak ground acceleration (PGA) in near sites fitted by traditional method are higher than that fitted by weighted method for small events and lower for large events, attenuating rates are much rapider in far sites; weighted two-step method is better to simulate spatial distribution laws of ground motions than traditional method.