基于二维地震时间序列的PPAR模型在天山地区的应用研究
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摘要
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,在固定研究区内,同时实现地震震级和时间的2要素预测,进而建立二维地震时间序列的投影寻踪自回归模型(PPAR模型)。研究中选取新疆天山地区不同空间尺度的14个实验区进行验算,首先选取范围较大地区作为实验区,然后,逐渐缩小研究区范围,建立相应的PPAR模型。针对每个区域分别尝试以未删除余震的序列、删除余震序列及同时删除余震和前震的序列建立模型,一般来说,以同时删除余震和前震的序列建立的模型具有普适性。研究结果表明:范围较大和地震发生频度高、强度大的研究区建立二维地震时间序列的PPAR模型,其内符、外符检验的合格率均较高,故所建的模型是可行的、有实际意义的。而对于范围相对较小、地震发生频度相对较低的研究区建立二维地震时间序列的PPAR模型,由于受样本量的制约,其信度降低,但其对震级和时间2要素的预测在现实的地震预报实践中仍具有一定实效和指示意义。
By combining PP technique with auto-regression model (AR), this paper proposes optimum projection pursuit auto-regression model(PPAR), and realize two-factor prediction of occurring magnitude and time in selected regions, i.e. building up PPAR model of two-dimensional time sequence. This study chooses 14 research regions with different spatial range from Xinjiang Tianshan Mountain region Larger regions are forit chosen, then smaller regions for building corresponding PPAR models. For every research region, building PPAR model respectively with such sequences as undeleting aftershocks, deleting aftershocks and deleting both aftershocks and foreshocks are deleted. In general, PPAR model built by sequences with deleting both aftershocks and foreshocks is reasonable. Comparing PPAR moedls of all regions with different magnitude thresholds, it is shown that prediction efficiency of both magnitude and time sequence with magnitude thresholds M0 = 4. 5 are reasonable, and the qualified rate of 3 of 5 regions (smaller range, weaker seismicity)are above 75 per cent. The efficiency larger range, stronger seismicity) with magnitude thresholds M0 = 5. 0 are high with qualified rate of 5 of 6 regions above 62. 5 per cent. The efficiency (larger range, stronger seismicity) with magnitude thresholds M0 = 5. 5 are very high with qualified rate of 1 of 2 regions above 80. 0 per cent. Results from different research regions show that qualified rates of checking from PPAR models of larger regions with high frequency and strength of earthquake occurrence are high, therefore PPAR models are applicable and efficient. The confidence of the model for smaller regions with low frequency decreases due to limitedsamples, but prediction for magnitude and time sequence is still of practical value.
By combining PP technique with auto-regression model (AR), this paper proposes optimum projection pursuit auto-regression model(PPAR), and realize two-factor prediction of occurring magnitude and time in selected regions, i.e. building up PPAR model of two-dimensional time sequence. This study chooses 14 research regions with different spatial range from Xinjiang Tianshan Mountain region Larger regions are forit chosen, then smaller regions for building corresponding PPAR models. For every research region, building PPAR model respectively with such sequences as undeleting aftershocks, deleting aftershocks and deleting both aftershocks and foreshocks are deleted. In general, PPAR model built by sequences with deleting both aftershocks and foreshocks is reasonable. Comparing PPAR moedls of all regions with different magnitude thresholds, it is shown that prediction efficiency of both magnitude and time sequence with magnitude thresholds M0 = 4. 5 are reasonable, and the qualified rate of 3 of 5 regions (smaller range, weaker seismicity)are above 75 per cent. The efficiency larger range, stronger seismicity) with magnitude thresholds M0 = 5. 0 are high with qualified rate of 5 of 6 regions above 62. 5 per cent. The efficiency (larger range, stronger seismicity) with magnitude thresholds M0 = 5. 5 are very high with qualified rate of 1 of 2 regions above 80. 0 per cent. Results from different research regions show that qualified rates of checking from PPAR models of larger regions with high frequency and strength of earthquake occurrence are high, therefore PPAR models are applicable and efficient. The confidence of the model for smaller regions with low frequency decreases due to limitedsamples, but prediction for magnitude and time sequence is still of practical value.
引文
[1] 郑祖国.投影寻踪自回归模型及其在新疆春早期降水量长期预测中应用[J].八一农学院学报,1993,(2) :1-7．
[2] 朱令人,周仕勇,邓传玲.地震综合预报的新方法--投影寻踪回归[J].地震学报,1994,16(增刊):1-9．
[3] 周仕勇,朱令人,杜宇梅,等.PP聚类在震群分析中的应用研究[J].地震学报,1995,17(3) :312-321．
[4] 赵翠萍,周仕勇,朱令人.新疆主要地震区PP回归综合预报模型研究[J].西北地震学报,1999,21(1) :37-43．
[5] 李柞泳,邓新民.大气污染物的投影寻踪自回归预测[J].上海环境科学,1997,16(7) :17-19．
[6] 王琼,朱令人.时间序列的投影寻踪自回归在新疆地震预报中的应用[J].内陆地震,2002,16(2) :118-125．
[7] 王琼,王海涛,李莹甄.基于PPAR模型二维地震时间序列预测的初步研究[J].地震,2003,23(3) :10-18．
[8] 安鸿志,顾岚.统计模型与预报方法[M].北京:气象出版社,1986．
[9] A. Le M haut,C. Rabut, L. L. Schumaker (eds.).Approximating By Ridge Function [M]. Vanderbilt university Press, Nashville, TN, 1197． 1-14．
[10] 邓传玲.SMART多重平滑回归技术的原理及计算软件[J].八一农学院学报,1988,(4) :47-55．
[11] 陆远忠,李胜乐,邓志辉,等.基于GIS的地震分析预报系统[M].四川:成都地图出版社,2002． 120．
[12] 陆远忠,陈章立,王碧泉,等.地震预报的地震学方法[M].北京:地震出版社,1985． 125-141．
[2] 朱令人,周仕勇,邓传玲.地震综合预报的新方法--投影寻踪回归[J].地震学报,1994,16(增刊):1-9．
[3] 周仕勇,朱令人,杜宇梅,等.PP聚类在震群分析中的应用研究[J].地震学报,1995,17(3) :312-321．
[4] 赵翠萍,周仕勇,朱令人.新疆主要地震区PP回归综合预报模型研究[J].西北地震学报,1999,21(1) :37-43．
[5] 李柞泳,邓新民.大气污染物的投影寻踪自回归预测[J].上海环境科学,1997,16(7) :17-19．
[6] 王琼,朱令人.时间序列的投影寻踪自回归在新疆地震预报中的应用[J].内陆地震,2002,16(2) :118-125．
[7] 王琼,王海涛,李莹甄.基于PPAR模型二维地震时间序列预测的初步研究[J].地震,2003,23(3) :10-18．
[8] 安鸿志,顾岚.统计模型与预报方法[M].北京:气象出版社,1986．
[9] A. Le M haut,C. Rabut, L. L. Schumaker (eds.).Approximating By Ridge Function [M]. Vanderbilt university Press, Nashville, TN, 1197． 1-14．
[10] 邓传玲.SMART多重平滑回归技术的原理及计算软件[J].八一农学院学报,1988,(4) :47-55．
[11] 陆远忠,李胜乐,邓志辉,等.基于GIS的地震分析预报系统[M].四川:成都地图出版社,2002． 120．
[12] 陆远忠,陈章立,王碧泉,等.地震预报的地震学方法[M].北京:地震出版社,1985． 125-141．
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