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本文通过自然正交分解方法,对含有12个地震区的云南地震强度场的21年(1958—78)样本资料 _nM_k(n=21,k=12)进行了统计处理,得到自然正交函数展开式 _nM_k=_nZ_pφ_k,即将_nM_k 分解成依赖于空间坐标的场强波动面矩阵_pφ_k 与依赖于时间的波动面振幅矩阵_nZ_p 之积。同时重点解释了前几个主要特征值λ_p 所对应的特征向量(?)p 的物理意义,从地震活动特点及能量释放水平的角度,大致划分出最近21年来控制云南地震时空变化的几个强震活动带,这对进一步探讨现今云南的地震成因是有一定裨益的。另外,为建立预报式并留几年检验之,文中又特别截取了前18年(1958—75年)的资料样本,再次进行了自然正交分解,而且仅用相对较大的5个特征值λ_p(P=1,2,……,5)所对应的特征向量 (?)_p(P=1,2,……,5)的组合就可以84%的精度模写出这期间场量_nM_k(n=18,k=12)的分布。这一自然正交函数展开式当然也是个预测系统,只要将有关时间信息输入进右端矩阵_nZ_p,公式左端就可输出下一时刻的多维场强,所留3年(1976—78)的内验结果及1979年的预报结果表明这一统计模型是有一定应用价值的。
In this paper, the 21-year (1958-78) sample data of nM_k (n = 21, k = 12) from 12 earthquakes in Yunnan earthquake intensity field are statistically processed by natural orthonormal decomposition method to obtain natural orthogonal function Expansion_nM_k = _nZ_pφ_k, that is, decomposing _nM_k into the product of the field-dependent fluctuating surface matrix _pφ_k and the time-dependent fluctuating surface amplitude matrix _nZ_p. At the same time, the physical meaning of the eigenvectors (?) P corresponding to the first few main eigenvalues λ_p is explained emphatically. From the perspectives of seismicity and energy release, some strong points controlling the spatial and temporal variations of Yunnan earthquakes in recent 21 years Earthquake belt, which is to further explore the cause of the earthquake in Yunnan today is of some benefit. In addition, in order to establish a predictive model and stay a few years of testing, the paper intercepts the data samples of the first 18 years (1958-75), re-conducts natural orthogonality decomposition again, and only uses relatively large five eigenvalues The combination of the eigenvectors (p) _p (P = 1,2, ..., 5) corresponding to λ_p (P = 1,2, ..., 5) can be modeled with a precision of 84% (n = 18, k = 12). Naturally, this natural orthogonal function expansion is also a prediction system. As long as the relevant time information is input into the right-end matrix _nZ_p, the left end of the formula can output the multi-dimensional field strength of the next time, which is within 3 years (1976-78) The test results and the 1979 forecast show that this statistical model has some application value.