变异函数模型的对比优选研究

发布时间：2018-04-24 14:03

本文选题：地质统计 + 随机模拟　；参考：《南京大学》2017年硕士论文

【摘要】：研究地下水流相关问题时,地下水模型构建中的一个突出问题是勘探资料分布不均或缺乏,以及含水系统本身的非均质性,造成了水文地质参数的空间变异性。在通常的地下水数值模拟中只能用简单的参数分区来描述参数的非均质性,但由于分区过大而忽略分区内部参数的差异性,往往导致模拟结果的不确定性。寻求一种尽可能利用有限的勘探资料,对未知区域内的含水层参数进行合理估值的方法,是目前大区域地下水流模拟中的关键问题。自然情况下,含水层参数不仅具有随机性,也具有一定的结构性。地质统计学就是研究这种具有"二重性"的区域化变量的数学工具,其以变异函数为基本工具来研究分布于空间并呈现一定结构性与随机性的自然现象。作为地质统计学的基本工具,变异函数不仅影响区域化变量的结构分析,还将决定插值结果的精度。。为探究在空间变异分析过程中变异函数模型的选取问题,以及变异函数模型的不同对克里格插值或模拟的影响,本文分别基于球状模型、指数模型和高斯模型,利用非条件模拟生成随机场,通过Monte Carlo法分别获得样本数为50、100、150和200的样本,再利用球状模型、指数模型和高斯模型估计不同样本的变异函数模型参数,最后基于这3种模型及对应的参数估计值进行条件模拟,将模拟结果与原始值对比以评价其模拟精度。同时,本文以新疆焉耆盆地和静县内一农用水源地第三含水层渗透系数采样数据为例,对比分析了高斯模型、球状模型、指数模型在拟合实验变异函数时的差异,以及这种差异对克里格插值的影响。研究结果显示:(1)采用非条件模拟生成随机场的方法存在非遍历性问题,即单次模拟实现的数据统计特征与期望值会有所偏差,但多次实现的平均值与期望值接近。(2)对于球状模型和指数模型,非条件模拟实现的变异函数模型曲线绝大部分平均分布在标准模型曲线上下两侧,且基台值的平均值等于原始模型,但块金常数和变程值要略大,高斯模型非条件模拟实现的变异函数模型曲线全部位于标准模型曲线左侧,变程值相较于原始模型总体明显偏小,块金常数略微偏大。(3)采用最小二乘法或者GS+软件自动拟合实验变异函数时,得到的变程值指数模型球状模型高斯模型,块金常数高斯模型球状模型指数模型,基台值指数模型球状模型=高斯模型。(4)采用与原始模型相同函数形式的模型进行变异函数拟合,拟合得到的变异函数模型参数与初始场变异函数模型参数最为接近,球状模型次之。(5)当采样点数较少时,基于指数模型的条件模拟结果总是具有最高的精度、球状模型其次、高斯模型最差;当样本点数较多时,总体上,基于与原始模型相同函数形式的变异函数模型的条件模拟结果精度最高,基于球状模型的条件模拟结果精度仅次于原始模型。(6)在选用多种模型拟合实验变异函数时,变异函数模型的差异主要体现在变程值的不同:变程值通过影响实测点对待估点的作用大小从而影响克里格插值结果:变程值过小,用来进行估值的实测点之间以及实测点与估值点之间相关性降低甚至消失,克里格法退化为简单的算术平均;变程值过大,参与克里格计算的实测点多,插值结果趋近于平稳;当变程值相对适中,克里格插值结果与实测值吻合较好,插值精度也达到最大。
[Abstract]:In the study of groundwater flow related problems, a prominent problem in the construction of groundwater model is the uneven distribution or lack of exploration data, as well as the heterogeneity of the water bearing system itself, resulting in the spatial variability of hydrogeological parameters. In the usual numerical simulation of groundwater, the heterogeneity of parameters can only be described by simple parameter zoning. However, owing to the oversize of the partition and ignoring the differences in the internal parameters of the partition, it often leads to the uncertainty of the simulation results. It is a key problem to find a method for the rational estimation of the aquifer parameters in the unknown region by using the limited exploration data as far as possible. In the natural case, the aquifer ginseng is the key problem. The number not only has random, but also has some structure. Geo statistics is a mathematical tool to study the "duality" regionalized variable. It uses the variation function as the basic tool to study the natural phenomena that are distributed in space and present a certain structure and randomness. As a basic tool of geostatistics, the variation function is not The structural analysis that affects only the regionalized variables will also determine the accuracy of the interpolation results, in order to explore the selection of the variation function model in the process of spatial variation analysis, and the influence of the variation of the variation function model on Kriging interpolation or simulation. This paper, based on the spherical model, the exponential model and the Gauss model, uses the non conditional simulation respectively. The sample number of 50100150 and 200 samples is obtained by Monte Carlo method, and then the parameter of the variant function model of different samples is estimated by the spherical model, the exponential model and the Gauss model. Finally, based on the 3 models and the corresponding parameter estimation, the simulated results are compared with the original values to evaluate the model. At the same time, taking the sampling data of the third aquifer permeability coefficient of a water source in the Yanqi basin of Xinjiang and Jing County as an example, the difference between the Gauss model, the spherical model and the exponential model in fitting the experimental variation function, and the influence of this difference on the Kerrey lattice interpolation are compared and analyzed. The results show that (1) the non condition is adopted. There is a non ergodicity problem in the simulation generation method of the random field. That is, the data statistical characteristics of the single simulation and the expected value will be deviated, but the average value of the multiple implementations is close to the expected value. (2) for the spherical model and the exponential model, most of the variation function model curves realized by the non conditional simulation are evenly distributed in the standard model curve. On both sides of the line, the average value of the base station value is equal to the original model, but the block gold constant and the variation value are slightly larger. The variation function model curve of the Gauss model is all located on the left of the standard model curve. The variation value is obviously smaller than the original model, and the block gold constant is slightly larger. (3) the least square method or GS is used. When the software automatically fits the experimental variation function, the variable range value index model Gauss model, the bulbous model index model of the block gold constant Gauss model, the ball model of the base value index model = the Gauss model. (4) the model of the same function as the original model is used to fit the variation function model, and the model of the variation function is fitted. The model parameters are the closest to the initial field variation function model parameters. (5) when the number of sampling points is less, the conditional simulation results based on the exponential model always have the highest accuracy, the spherical model is second, the Gauss model is the worst; when the number of sample points is more, the general body is based on the variation function of the same function as the original model. The precision of the conditional simulation results of the model is the highest, and the precision of the conditional simulation results based on the spherical model is second to the original model. (6) the difference of the variation function model is mainly reflected in the variation of the variation value when choosing a variety of models to fit the experimental variation functions: the variable range values affect the size of the estimation point by affecting the real point and thus influence Craig. Interpolation results: the variable range is too small, the correlation between the measured points used for valuation and the correlation between the measured points and the estimation points is reduced or even disappeared. The Craig method degenerates into a simple arithmetic mean; the variable range is too large, and the measured points in the Craig calculation are more stable; the interpolation results are relatively moderate, and the Craig interpolation results and the results are relatively moderate. The measured values are in good agreement, and the interpolation accuracy is also maximum.

【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P641.7

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