岩柱形态的多样性和岩石中非均质性的统计特征
Variety of stylolites morphologies and statistical characterization of the amount of heterogeneities in the rock
摘要：
采用高分辨率激光轮廓术测量了石灰岩中几种柱状样的表面粗糙度。对获得的1D信号进行统计分析，以确定标度行为并计算粗糙度指数，也称为赫斯特指数。基于单个Hurst指数表征的统计方法意味着对信号的数学特性的强烈假设：信号的导数（或局部增量）应该是平稳的，并且具有有限的方差。对测得的触针的分析表明，这些性质并不总是同时得到验证。缝合线剖面显示出持续性和跳跃性，有几个缝合线不规则，规则和不规则部分交替出现。本文提出了一种基于非平稳高斯模型的统计方法来估计剖面的粗糙度，并定量描述柱状样的非均匀性。这种统计方法基于两个参数：描述缝合线局部振幅的局部粗糙度（H），以及信号上的不规则性（μ），其可以与缝合线形成之前岩石中最初存在的不均匀性相关联。使用这种技术，在两个家庭中的styleries的分类建议：那些形态是均匀的地方和那些交替的规则和不规则的部分。
英文摘要：
The surface roughness of several stylolites in limestones was measured using high resolution laser profilometry. The 1D signals obtained were statistically analyzed to determine the scaling behavior and calculate a roughness exponent, also called Hurst exponent. Statistical methods based on the characterization of a single Hurst exponent imply strong assumptions on the mathematical characteristics of the signal: the derivative of the signal (or local increments) should be stationary and have finite variance. The analysis of the measured stylolites show that these properties are not always verified simultaneously. The stylolite profiles show persistence and jumps and several stylolites are not regular, with alternating regular and irregular portions. A new statistical method is proposed here, based on a non-stationary but Gaussian model, to estimate the roughness of the profiles and quantify the heterogeneity of stylolites. This statistical method is based on two parameters: the local roughness (H) which describes the local amplitude of the stylolite, and the amount of irregularities on the signal (μ), which can be linked to the heterogeneities initially present in the rock before the stylolite formed. Using this technique, a classification of the stylolites in two families is proposed: those for which the morphology is homogeneous everywhere and those with alternating regular and irregular portions.
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