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Multifractal model of magnetic susceptibility distributions in some igneous rocks

机译：火成岩中磁化率分布的多重分形模型

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Measurements of in-situ magnetic susceptibility were compiled from mainly Precambrian crystalline basement rocks beneath the Colorado Plateau and ranges in Arizona, Colorado, and New Mexico. The susceptibility meter used measures about 30 cmsup3/sup of rock and measures variations in the modal distribution of magnetic minerals that form a minor component volumetrically in these coarsely crystalline granitic to granodioritic rocks. Recent measurements include 50–150 measurements on each outcrop, and show that the distribution of magnetic susceptibilities is highly variable, multimodal and strongly non-Gaussian. Although the distribution of magnetic susceptibility is well known to be multifractal, the small number of data points at an outcrop precludes calculation of the multifractal spectrum by conventional methods. Instead, a brute force approach was adopted using multiplicative cascade models to fit the outcrop scale variability of magnetic minerals. Model segment proportion and length parameters resulted in 26 676 models to span parameter space. Distributions at each outcrop were normalized to unity magnetic susceptibility and added to compare all data for a rock body accounting for variations in petrology and alteration. Once the best-fitting model was found, the equation relating the segment proportion and length parameters was solved numerically to yield the multifractal spectrum estimate. For the best fits, the relative density (the proportion divided by the segment length) of one segment tends to be dominant and the other two densities are smaller and nearly equal. No other consistent relationships between the best fit parameters were identified. The multifractal spectrum estimates appear to distinguish between metamorphic gneiss sites and sites on plutons, even if the plutons have been metamorphosed. In particular, rocks that have undergone multiple tectonic events tend to have a larger range of scaling exponents.
机译：现场磁化率的测量主要是从科罗拉多高原以下以及亚利桑那州，科罗拉多州和新墨西哥州范围内的前寒武纪晶体基底岩石中收集的。磁化率仪用于测量约30 cm 3 的岩石，并测量磁性矿物的模态分布的变化，这些矿物在体积上占这些粗晶花岗岩到花岗闪长岩的体积分数很小。最近的测量包括在每个露头上进行50-150次测量，结果表明磁化率的分布是高度可变的，多峰的和高度非高斯的。尽管众所周知，磁化率的分布是多重分形的，但露头处的数据点数量很少，因此无法通过常规方法计算多重分形谱。取而代之的是采用蛮力方法，使用乘法级联模型来拟合磁性矿物的露头尺度变化。模型段比例和长度参数导致26 676个模型跨越参数空间。将每个露头的分布归一化为统一的磁化率，并添加以比较岩体的所有数据，以解释岩石学和蚀变的变化。一旦找到最合适的模型，就可以对与段比例和长度参数有关的方程进行数值求解，以得到多重分形谱估计值。为了获得最佳拟合，一个片段的相对密度（比例除以片段长度）趋于占优势，而其他两个密度则较小且几乎相等。没有确定最佳拟合参数之间的其他一致关系。多重分形谱估计似乎可以区分变质片麻岩位点和云母上的位点，即使云母已变质。特别是，经历了多次构造事件的岩石往往具有更大的结垢指数范围。

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