本文選題：地質(zhì)統(tǒng)計(jì) + 隨機(jī)模擬��； 參考：《南京大學(xué)》2017年碩士論文

【摘要】：研究地下水流相關(guān)問題時(shí),地下水模型構(gòu)建中的一個(gè)突出問題是勘探資料分布不均或缺乏,以及含水系統(tǒng)本身的非均質(zhì)性,造成了水文地質(zhì)參數(shù)的空間變異性。在通常的地下水?dāng)?shù)值模擬中只能用簡單的參數(shù)分區(qū)來描述參數(shù)的非均質(zhì)性,但由于分區(qū)過大而忽略分區(qū)內(nèi)部參數(shù)的差異性,往往導(dǎo)致模擬結(jié)果的不確定性。尋求一種盡可能利用有限的勘探資料,對(duì)未知區(qū)域內(nèi)的含水層參數(shù)進(jìn)行合理估值的方法,是目前大區(qū)域地下水流模擬中的關(guān)鍵問題。自然情況下,含水層參數(shù)不僅具有隨機(jī)性,也具有一定的結(jié)構(gòu)性。地質(zhì)統(tǒng)計(jì)學(xué)就是研究這種具有"二重性"的區(qū)域化變量的數(shù)學(xué)工具,其以變異函數(shù)為基本工具來研究分布于空間并呈現(xiàn)一定結(jié)構(gòu)性與隨機(jī)性的自然現(xiàn)象。作為地質(zhì)統(tǒng)計(jì)學(xué)的基本工具,變異函數(shù)不僅影響區(qū)域化變量的結(jié)構(gòu)分析,還將決定插值結(jié)果的精度。。為探究在空間變異分析過程中變異函數(shù)模型的選取問題,以及變異函數(shù)模型的不同對(duì)克里格插值或模擬的影響,本文分別基于球狀模型、指數(shù)模型和高斯模型,利用非條件模擬生成隨機(jī)場(chǎng),通過Monte Carlo法分別獲得樣本數(shù)為50、100、150和200的樣本,再利用球狀模型、指數(shù)模型和高斯模型估計(jì)不同樣本的變異函數(shù)模型參數(shù),最后基于這3種模型及對(duì)應(yīng)的參數(shù)估計(jì)值進(jìn)行條件模擬,將模擬結(jié)果與原始值對(duì)比以評(píng)價(jià)其模擬精度。同時(shí),本文以新疆焉耆盆地和靜縣內(nèi)一農(nóng)用水源地第三含水層滲透系數(shù)采樣數(shù)據(jù)為例,對(duì)比分析了高斯模型、球狀模型、指數(shù)模型在擬合實(shí)驗(yàn)變異函數(shù)時(shí)的差異,以及這種差異對(duì)克里格插值的影響。研究結(jié)果顯示:(1)采用非條件模擬生成隨機(jī)場(chǎng)的方法存在非遍歷性問題,即單次模擬實(shí)現(xiàn)的數(shù)據(jù)統(tǒng)計(jì)特征與期望值會(huì)有所偏差,但多次實(shí)現(xiàn)的平均值與期望值接近。(2)對(duì)于球狀模型和指數(shù)模型,非條件模擬實(shí)現(xiàn)的變異函數(shù)模型曲線絕大部分平均分布在標(biāo)準(zhǔn)模型曲線上下兩側(cè),且基臺(tái)值的平均值等于原始模型,但塊金常數(shù)和變程值要略大,高斯模型非條件模擬實(shí)現(xiàn)的變異函數(shù)模型曲線全部位于標(biāo)準(zhǔn)模型曲線左側(cè),變程值相較于原始模型總體明顯偏小,塊金常數(shù)略微偏大。(3)采用最小二乘法或者GS+軟件自動(dòng)擬合實(shí)驗(yàn)變異函數(shù)時(shí),得到的變程值指數(shù)模型球狀模型高斯模型,塊金常數(shù)高斯模型球狀模型指數(shù)模型,基臺(tái)值指數(shù)模型球狀模型=高斯模型。(4)采用與原始模型相同函數(shù)形式的模型進(jìn)行變異函數(shù)擬合,擬合得到的變異函數(shù)模型參數(shù)與初始場(chǎng)變異函數(shù)模型參數(shù)最為接近,球狀模型次之。(5)當(dāng)采樣點(diǎn)數(shù)較少時(shí),基于指數(shù)模型的條件模擬結(jié)果總是具有最高的精度、球狀模型其次、高斯模型最差;當(dāng)樣本點(diǎn)數(shù)較多時(shí),總體上,基于與原始模型相同函數(shù)形式的變異函數(shù)模型的條件模擬結(jié)果精度最高,基于球狀模型的條件模擬結(jié)果精度僅次于原始模型。(6)在選用多種模型擬合實(shí)驗(yàn)變異函數(shù)時(shí),變異函數(shù)模型的差異主要體現(xiàn)在變程值的不同:變程值通過影響實(shí)測(cè)點(diǎn)對(duì)待估點(diǎn)的作用大小從而影響克里格插值結(jié)果:變程值過小,用來進(jìn)行估值的實(shí)測(cè)點(diǎn)之間以及實(shí)測(cè)點(diǎn)與估值點(diǎn)之間相關(guān)性降低甚至消失,克里格法退化為簡單的算術(shù)平均;變程值過大,參與克里格計(jì)算的實(shí)測(cè)點(diǎn)多,插值結(jié)果趨近于平穩(wěn);當(dāng)變程值相對(duì)適中,克里格插值結(jié)果與實(shí)測(cè)值吻合較好,插值精度也達(dá)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.

【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：P641.7

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