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在地质统计学中,采用变异函数来描述区域化变量的变化特征。但变异函数的实验曲线很不稳定,特别是在抽样观测数据比较少和抽样点比较分散时,很难得到比较理想的实验曲线。克里金法在建立数学模型的时候,往往要用手工法来拟合数学模型。在“杨赤中滤波与推估”法中,采用一种广义滤波法,即采用逐步增大游动区间半径取二项式系数加权游动平均的方法来建立随机特征函数的实验曲线。这种实验曲线是自然的光滑曲线,能够灵敏地反映变量的变化特征,并且采用一种特殊形式的与实验曲线有很好的吻合性的负幂指数函数来拟合它。用它来作数学模型,既能反映变量的宏观变化特征,又能反映局部变化特征,建立数学模型的全过程,可以通过一个计算程序来实现。不需要很多的已知点,也不要求点位很规则,只要把已知值输入计算机(点位不规则时,还要同时输入点的坐标),就可以很快打印输出数学模型的函数式。各向异性的数学模型也不需要用手工来套合。这样就完全实现了建立数学模型的自动化。上述自动建立数学模型的方法,不论用于金属或非金属矿,都取得了完满成功。建立矿体数学模型的完全自动化,是数学地质领域的一个重要创造。
In geostatistics, the variogram is used to describe the changing characteristics of regionalized variables. However, the experimental curve of the variation function is very unstable, especially when there is less sampling observation data and sampling points are scattered, it is difficult to obtain the ideal experimental curve. Kriging method in the establishment of mathematical models, often using manual methods to fit the mathematical model. In “Yang Chizhong filtering and estimating” method, a generalized filtering method is adopted, that is, the experimental curve of stochastic eigenfunction is established by taking the binomial coefficient weighted moving average step by step. This experimental curve is a naturally smooth curve that responds sensitively to the variability of the variables and fits it with a special form of exponential function that is well-matched to the experimental curve. Using it as a mathematical model can not only reflect the macroscopic change characteristics of variables, but also reflect the characteristics of local changes and establish the whole process of mathematical models, which can be realized through a calculation program. Do not need a lot of known points, nor point is very rules, as long as the known value into the computer (irregular points, but also enter the coordinates of the point), you can quickly print out the mathematical model of the function . Anisotropic mathematical models do not need to be set by hand. This fully achieved the establishment of mathematical models of automation. The above method of automatically building a mathematical model has achieved great success, both for metal and non-metal mines. The establishment of fully automated mathematical model of ore body is an important creation in the field of mathematical geology.