地震烈度椭圆衰减的限定模型及其在华北地区的应用

采用在统计回归过程中加入限制条件的方法,建立一个地震烈度椭圆衰减的限定模型。该模型不但解决了地震烈度椭圆衰减的限头限尾问题,也考虑地震震级与有感半径的关系。利用华北地区48次地震、139条等震线资料,回归得到了华北地区的地震烈度衰减关系。最后将本模型得到的地震烈度衰减关系与华北地区其他烈度衰减关系进行了对比,认为本模型所得的烈度衰减关系在大震的远场更趋于合理。

A Constrained Model of Elliptical Attenuation of Earthquake Intensity and Its Application in North China

It is more reasonable to adopt elliptical model to describe the attenuation of seismic intensity, but respective statistical analyses along major axis and minor axis may lead to inconsistent intensities of the attenuation relationships along two directions from the epicenter. In order to make the two attenuation relationships consistent, it requires us to resolve the difficulty of "limited head". At the same time, it is necessary to constrain the regression of the attenuation relationship of minor axis and thus make the calculated intensity always smaller than that from the attenuation relationship of major axis from the epicenter to the farther distance. This is the difficulty of "limited tail". Based on the above reasons and by using the method of regression with constraints, a constrained model of elliptical attenuation of seismic intensity is presented in this paper. The difficulty of limited head and tail on the curve of the attenuation relationship is resolved and the relationships between the magnitude and the radius to felt-area in regression are also taken into account. Based on the latest intensity data of North China that include 48 earthquakes and 139 isoseismal lines, the attenuation relationship of seismic intensity is obtained. A comparison between this result and other attenuation relationships of North China is made. It proved that our result is more reasonable at the long distance for large earthquake.