多维分形克里格方法

doi:10.11867/j.issn.1001-8166.2005.02.0248

时间序列与空间场信号往往是非规则分布的，经常需要将非规则分布的时空信号插值为规则分布的信号或估计某些未知点的值。如油气田、煤田以及金属矿山储量估算，工程地质参数估计，病虫害区域分布调查等都要求根据少量不规则数据点进行插值估算。估值方法中应用最为广泛的地质统计学方法（或(Krige)克里格方法）是一种低通滤波器，无法重建原始信号中的高频、局部与弱信号。开发的多维分形克里格方法可以将不规则分布的时间—空间（时空）信号插值为规则分布的信号；可以提取时空信号中高频、局部与弱信号，估计过程参数可以作为特征参数用于模式识别。利用褶积滤波理论定量导出了地质统计学的低通滤波特性，它在插值过程中丢失了高频、局部和弱信号。在定义了时空信号的度量尺度与测度后，实现了多维分形插值，多维分形插值保留了系统中更多的高频信息。将克里格方法与多维分形方法有机的结合起来产生了多维分形克里格方法，它具有克里格方法和多维分形插值的共同优点。用大洋钻探(ODP)184航次1143A孔的岩芯密度分析进行了插值试验，对比了插值结果及其功率谱。多维分形克里格插值比克里格插值、多维分形插值更为接近已知点值并保留更多的高频信息。还定量分析、对比了影响多维分形克里格插值的因素、厘清了估值问题中固有的测不准关系。另外，多维分形克里格插值过程得到的局部奇异性、相关性和回归方差能有效地刻划高频、局部与弱信号。这样，多维分形克里格插值过程可以用于提取（非规则或规则网格）时空信号中的局部、高频与弱信号，用于信息提取、模式识别、找矿预测与信号增强等领域。

关键词: 多维分形插值, 克里格插值, 信号增强, 空间分析, 储量估计, 油藏描述, GIS, 时空预测

The Multifractal-Krige method developed in this study can not only interpolate irregular distributed values into regular distributed grids, but also extract the high frequency, local and weak signals, which are useful in feature retrieval or pattern recognition, from temporal-spatial signals. The signal from observing science is often distributed irregularly and it is often critical to interpolate irregular distributed signal into regular grids or estimate values at some points. For examples, in reservoir, coal bed and mineral tonnage estimations or in engineering parametric estimations, regional harmonious insects inspections, the interpolation is necessary. The Krige method had been widely used even though it is a low-pass filter and can not construct the high frequency, local and weak signals which are often play more important role in related study. The low-pass filtering property of Krige method is studied from the filtering points of view in frequency domain and it was found that Krige method is a low pass filters. In contrary, Multifractal interpolation method can reconstruct part of these signals. To implement the fractal interpolation, which keeps more high frequency information, the measure and scale pairs are defined, formula and procedures are studied in this study. The integration of Krige and Multifractal method produced Multifractal-Krige method that keeps benefits of both Krige and Multifractal interpolations. The core density data from Hole 1143A of Ocean Drilling Program (ODP) 184th cruise is used to test the algorithm. The interpolated results and power spectra are compared to show the benefits of Multifractal interpolation and Krige-Multifractal method. The results proved that the Multifractal-Krige interpolation approximates known points better and had richer high frequency frequencies than other methods. Factors that affect the method, such as uncertainty in the value estimation problems, had also been studied quantitatively.Further more, the local singularities, regression index and standard errors got from the interpolation procedure are good approximation of the high frequency, local and weak signals. So, Krige-Multifractal interpolation method can also be used in other kinds of applications, such as information retrieval, enhancement and pattern recognition.

Key words: Multifractal interpolation, Krige interpolation, Signal enhancement, Spatial analysis, Tonnage estimation, Reservoir description, GIS, Temporal-spatial prediction

中图分类号:

P628

［1］Ji Fahua,Xiong Qihua,Zhang Yiwei.The Application of Geostatistics in Oil Reservoir Description[M]. Beijing: Oil Industry Press, 1997.[纪发华,熊琦华,张一伟. 地质统计学在油藏描述中的应用[M].北京:石油工业出版社,1997.] 
［2］Li Qingmou. Multiwell data processing and oil reservoir description[J]. Technology and Sciences in Jilin Oil, 1989,18(1): 15-23. [李庆谋.多井处理与油藏描述[J]. 吉林油田科技,1989,18(1): 15-23.]［3］Zhang Ruixin,Han Jinyan,Liu Guang.Coal Resource Evaluation of No. 1 Coal Bed in Shengli Coal Bed Field[EB/OL]. http://www.gzit.edu.cn/gut/magazine/xb982/xb982-1/98xb21-7.html.2003-5-10. [张瑞新,韩金岩,刘光.胜利煤田1号煤层资源评价[EB/OL].http://www.gzit.edu.cn/gut/magazine/xb982/xb982-1/98xb21-7.html,2003-5-10.]
［4］Hou Jingru,Yin Zhen,Li Weiming,et al.Practical Geoststistics[M]. Beijing: Geological Publication Press,2000.[侯景儒,尹镇,李维明,等.实用地质统计学 [M]. 北京:地质出版社,2000.]
［5］Zhang Runjie,Gu Dexiang,Tang Jianqiu, et al. The occurrence evaluation technology of harmonious insects based on geostatistics in GIS environment[EB/OL]. http://www.ipmchina.net/meeting97/zfh519.html,2004.[张润杰, 古德祥, 汤鉴球,等.应用地质统计学在GIS 环境下评价害虫[EB/OL].http://www.ipmchina.net/meeting97/zfh519.html,2004.]
［6］Krige. A Statistical Approach to some basic mine valuation problems on the Witwatersland [J]. Journal of the Chemical and Metallurgical Mining Society of South Africa, 1951, 52:119-139.
［7］Carr J R. A treatise on the use of geostatistics for the characterization of nonrenewable resources[J]. Nonrenewable Resources, 1992, 1(1): 61-73.
［8］Clark I.Practical Geostatistics[M]. Landon: Applied Sciences, 2000.
［9］Matheron G. Principles of Geostatistics[J]. Principles of Geostatistics. Economic Geology, 1963, 58:1 246-1 266.
［10］Xiao Bin,Zhao Pengda,Hou Jingru. The progress of geostatistics[J].Advances in Earth Science,2000,15(3):293-296.[肖斌, 赵鹏大, 侯景儒.地质统计学进展[J].地球科学进展,2000,15(3):293-296.]［11］Mandelbrot. The Fractal Geometry of Nature[M].New York: W. H. Freeman, 1983.460.
［12］Li Qingmou,Cheng Qiuming.Fractal correction of well logging curves[J]. Earth Science—Journal of China University of Geosciences,2001, 12(3): 63-66. [李庆谋, 成秋明.测井曲线分形校正 [J]. 地球科学——中国地质大学学报,2001, 12(3): 63-66.]
［13］Li Qingmou. Fractal interpolation and application[A]: In:Li Zhoubo ed. Oil Well Logging Technology[C]. Beijing: Oil Industry Press, 2003.[李庆谋.分形插值与应用[A]. 见:李舟波编著.石油测井技术 [C]. 北京:石油工业出版社,2003.]
［14］Liu Guangding,Li Qingmou,Liu Shaohua.The study of global change with well logging data[J]. Progress of Geophysics, 1999,14(4): 1-8.[刘光鼎, 李庆谋, 刘少华.全球变化的地球物理研究[J]. 地球物理学进展,1999,14(4):1-8.]
［15］Liu Guangding, Li Qingmou.ODP and geophysical well logging[J]. Progress of Geophysics, 1997,12(3):1-8. [刘光鼎,李庆谋.大洋钻探与测井地质研究 [J]. 地球物理学进展,1997,12(3):1-8.]
［16］Li Zhoubo. The Principle of Well Logging for Mining Field [M]. Beijing: Geological Publication Press,1992.[李舟波.矿场地球物理测井[M]. 北京:地质出版,社,1992.]. 
［17］Turcotte D L. Fractals and Chaos in Geology and Geophysics(2nd)[M]. London: Cambridge University Press, 1997.
［18］Guratscio M, David M, Huijbregts C J, eds. Advanced Geostatistics for the Mining Industry[M]. Dortrecht, Netherlands: Reidel,1976.
［19］Verly G, David M, Journel A, et al. eds. Geostatistics for Natural Resources Characterization[M]. Dordrecht, Netherlands: Reidel, 1984.
［20］Armstrong Margaret ed. “Geostatistics”, Proceedings of the 3rd International Geostatistics Congress, Avignon, France, September 5-9, 1988, Serie Quantitative Geology and Geostatistics, volume 4[M]. Dordrecht, Holland: Kluwer Academic Publishers, 1989.

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摘要

MULTIFRACTAL-KRIGE INTERPOLATION METHOD