关键词: 地震, 活动性参数, 似然比检验

Abstract: The estimation of the parameters of seismic activity is very critical for earthquake prediction, engineering seismic hazard analysis and earthquake damage evaluation. However, different researchers may get different results in this estimation, even though for the same seismic data in the same region by using the same analyzing method. Obviously, the different results of estimation will affect seriously the results of earthquake prediction, engineering seismic hazard analysis and earthquake damage evaluation. A question arises: how to evaluate properly these different estimation results? In this paper, an evaluating method, the likelihood ratio testing is introduced. The basic theoretical features of likelihood ratio testing are discussed statistically, and especially the evaluating and processing methods of likelihood ratio testing for two data sets are demonstrated in detail. For an example, the method is practically used to evaluate seismic activity parameters in North China. The concrete procedures are as follows: Assuming that there are three different division schemes for the seismic activity in North China. The first scheme is adopted from the study by Gao Weiming (1990), in which the seismic activity of North China is divided into 4 active periods since the existence of historic record of earthquake. The seismic data from 15th century till now are relatively complete, so that two seismically active periods can be identified for this period of time. In this scheme, the seismically active period is subdivided into quiet and active sub periods. Assuming that the second scheme is similar to the first scheme in the division of the third and fourth seismically active periods, but does not subdivide these periods into sub periods. Assuming that the third scheme considers the third and fourth periods as a single period and no subdivision is made. Then the three different schemes will get different estimation results of seismic activity parameters for this region, and these different estimations will lead to different results in seismic hazard analysis and seismic prediction by using inhomogeneous compound Poisson probabilistic model for earthquake occurrences. The rationality of these different estimation results can be evaluated by using the Likelihood ratio testing method, and then a final sorting of the results can be made. The following conclusions can be drawn from this study: (1) For different sets of estimated parameters involving different time periods, the strength function values of Poisson process are different. Therefore, special attention should be paid to the probability at the dividing point of different time periods; (2) When different results of estimation arise due to the different recognition of different researchers for the same seismic data using the same mathematical processing method, then the likelihood ratio testing method can be used to evaluate and to sort these different results.

Key words: Earthquake, Activity parameter, Likelihood ratio testing