基于PPAR模型视二维地震时间序列预测的初步研究

Preliminary forecast study of two-dimensional seismic time sequence based on pr ojection pursuit auto-regression model

PP投影寻踪是一种长于分析非正态、非线性的高维数据的新统计方法,它通过投影降维,客观地寻找反映高维数据结构特征的投影方向,从而解决"维数祸根"和高维数据间的非正态、非线性问题。将PP理论和时间序列分析中的自回归(AR(K))模型结合起来,建立投影寻踪自回归预测模型(PPAR),尝试实现地震震级和时间的视二维预测,即在固定研究区里,实现震级和时间二要素的预测,进而建立视二维地震时间序列的投影寻踪自回归模型。研究中首先选取北天山地区作为实验区,模型的回归拟合和外符检验效果较理想,可实现视二维预测目标。考虑到实际预测意义,即中强地震的预测,又以天山地区为研究区。令其震级序列的震级阈值分别为5.0和5.5,分别以未删除余震和删除余震的序列建立模型。对比分析表明,后者所建立的模型要优于前者的模型,特别是对时间间隔序列的预测。两者外符检验的合格率均较高,故认为对于震级和时间二要素的预测是有一定实效的。

Projection pursuit (PP) is a new statistic method, which is good at analyzing no n-normal and non-linear high-dimensional data. It searches for the project di rection reflecting on the structure characteristics of high-dimensional dada ob jectively by projecting and reducing dimensions, and solves 'dimension curse' and non-normality and non-linearity among high-dimensions data. The article c ombines the PP technique with auto-regression model of time sequence analysis, and builds up the prediction model of projection pursuit auto-regression (PPAR) . PPAR model tries to realize two-dimensional forecast of magnitude and time, i .e. forecasting the magnitude and time of an event in the fixed research region, and creates the projection pursuit auto-regression model of two-dimensional s eismic time sequence. In the study, we choose first the northern Tianshan area a s the test site, and the results of the regression fitting and pretest test are good, so we could realize tow-dimensional forecast. Considering the value of fo recast practice, i.e. moderately strong earthquake, we take the whole Tianshan m ountain area as our research area. Let the magnitude thresholds of time sequence are 5.0 and 5.5 respectively, and build up the models with data of undeleted-a ftershocks and deleted-aftershocks. Comparing the two models, the latter is bet ter than the former, particularly is to forecast time sequence. Their qualified ration of pretest tests are both high, so they are available for forecasting mag nitude and time of an event.