测井曲线的自相似性研究
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摘要
陆敬安李舟波：测井曲线的自相似性研究，测井技术，１９９６（６）２０，４２２～４２７。沉积地层的旋回构造使得反映地层物理响应的测井曲线局部和整体之间呈现不同程度的自相似性。因此，可以利用分形理论来分析和研究测井曲线的几何结构。本文简要介绍了两种常见的分维数的求法并从应用的角度详细分析了分形插值原理，利用其对稀疏采样后的声波和密度测井曲线作了插值处理。试验表明插值结果与原始曲线之间具有较好的相似度，并且各曲线对自身模拟后的垂直比例因子非常接近，从而为根据一条测井曲线来修复另一条曲线提供了理论依据，最终为解决实际测井过程中产生的曲线断缺问题开辟了新的途径。
The tectonic cycle of sedimentary formation makes part of a well logging curve similar to the whole in shape to a certain extent. So fractal theory can be used to analyse and study the geometrical structure of logging curves. This paper briefly introduces the solutions of two kinds of fractal dimensions and details the principle of fractal interpolation, by which interpolation is made for acoustic and density logs with large sampling interval. The result demonstrates that the interpolated curves are much similar to the original ones, and that the vertical proportional fractors obtained from self simulation are almost the same. Thus, it provides theoretical basis for patching one curve according to another, providing a new method to solve practical logging problems such as uncontinuity or lack of well logging curves.
The tectonic cycle of sedimentary formation makes part of a well logging curve similar to the whole in shape to a certain extent. So fractal theory can be used to analyse and study the geometrical structure of logging curves. This paper briefly introduces the solutions of two kinds of fractal dimensions and details the principle of fractal interpolation, by which interpolation is made for acoustic and density logs with large sampling interval. The result demonstrates that the interpolated curves are much similar to the original ones, and that the vertical proportional fractors obtained from self simulation are almost the same. Thus, it provides theoretical basis for patching one curve according to another, providing a new method to solve practical logging problems such as uncontinuity or lack of well logging curves.
引文
1，曾文曲等编著：分形理论与分形的计算机模拟，东北大学出版社，1993。2，陈禺页译：分形和分维在地质学和地球物理学中的应用，地震出版社，1992。3，IteratedFunctionSystemsandtheGlobalConstructionofFractals．Proc．R．Soc．Lord．A399，1985：243～275．4，杨新社：地球物理学中的分形几何特征，地球物理学进展，1991（3）6：78～87。5，潘葆芝等：分数维及其在测井地质解释中的应用，测井技术，1992（3）16：214～221。
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