地震波的分形维研究与应用
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摘要
分形作为非线性学科的一个新兴研究方向,在地震研究领域也得到了广泛应用。地震波具有分形特性。然而在实际的工程设计中,设计人员在考虑地震作用时却忽略了它的影响和意义。地震波是分形时间序列,其分形维是表征地震波时间序列充实时间-幅值平面程度的量。文中从研究地震影响系数出发,指出同样应当把分维值作为地震波的特征参数之一。简要介绍了一种改进的计盒维数法,并应用此方法计算了几条著名地震波的分维值,进一步说明地震波的分形维可以作为地震波的一种新的特性加以应用。
As a new research direction of the nonlinear science,fractal theory is also widely applied in the seismological fields.The seismic waves have fractal characteristics,while we always neglect the influence and significance of the fractal when we calculate the earthquake action in practical engineering design.Seismic wave is fractal time series data,and fractal dimension is the magnitude which characterizes the degree of the data enriching the time amplitude plane.Through researching the earthquake affecting coefficient,this paper points out that the fractal dimension value also should be as one of the parameters of the seismic waves.Then it briefly introduces an improved box counting method to calculate the fractal dimension value of several famous seismic waves.At last,it further illustrates that we can use the fractal dimension more widely as a new characteristic of seismic wave.
As a new research direction of the nonlinear science,fractal theory is also widely applied in the seismological fields.The seismic waves have fractal characteristics,while we always neglect the influence and significance of the fractal when we calculate the earthquake action in practical engineering design.Seismic wave is fractal time series data,and fractal dimension is the magnitude which characterizes the degree of the data enriching the time amplitude plane.Through researching the earthquake affecting coefficient,this paper points out that the fractal dimension value also should be as one of the parameters of the seismic waves.Then it briefly introduces an improved box counting method to calculate the fractal dimension value of several famous seismic waves.At last,it further illustrates that we can use the fractal dimension more widely as a new characteristic of seismic wave.
引文
[1]张济忠.分形[M].北京:清华大学出版社,1995.
[2]辛厚文主编.分形理论及其应用[M].合肥:中国科学技术大学出版社,1993.
[3]李水根,吴纪桃.分形与小波[M].北京:科学出版社,2002.
[4]赵春燕,谷峻松.地震波的分形特性[J].辽宁工程技术大学学报,2001,20(4):423-425.
[5]中华人民共和国建设部.GB 50011—2001建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.
[6]郭继武.建筑抗震设计[M].北京:中国建筑工业出版社,2002.
[7]解文荣,张莉.地震波形的分形判别与特征提取[J].华北地震科学,2004,22(4):22-24.
[8]洪时中,洪时明.一种客观确定分析“无标度区”的方法——自相似比法[J].大自然探索,1993,13(2):53-57.
[9]陈清军,叶锋.剪切型结构地震破坏准则与抗震可靠度分析[J].结构工程师,2006,22(3):52-56.
[2]辛厚文主编.分形理论及其应用[M].合肥:中国科学技术大学出版社,1993.
[3]李水根,吴纪桃.分形与小波[M].北京:科学出版社,2002.
[4]赵春燕,谷峻松.地震波的分形特性[J].辽宁工程技术大学学报,2001,20(4):423-425.
[5]中华人民共和国建设部.GB 50011—2001建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.
[6]郭继武.建筑抗震设计[M].北京:中国建筑工业出版社,2002.
[7]解文荣,张莉.地震波形的分形判别与特征提取[J].华北地震科学,2004,22(4):22-24.
[8]洪时中,洪时明.一种客观确定分析“无标度区”的方法——自相似比法[J].大自然探索,1993,13(2):53-57.
[9]陈清军,叶锋.剪切型结构地震破坏准则与抗震可靠度分析[J].结构工程师,2006,22(3):52-56.
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