Abstract Sediment-generation models need an accurate specification of the fundamental properties of parent rocks and their variability at the scale of first-order (mono-lithologic) drainage basins. Georeferenced point-count data of five extensively surveyed plutons were extracted from the literature to examine the spatial variability of modal composition in granitoids. Point-count data must be considered inherently noisy from the point of view of geospatial analysis because sampled areas (thin sections) are small compared to the average crystal size of granitoids. Geostatistical modelling of such data is further complicated by the fact that crucial information on short-range variability is unavailable because sampling was carried out according to more or less regular patterns to achieve an equal density of data coverage across plutons. Geostatistical modelling of compositional data was carried out by transforming the data to centred log-ratios and calculating their Principal Components (PCs). The PC scores were used as input for a geostatistical workflow based on Ordinary Kriging, coupled with cross-validation and stochastic simulation to assess the predictive capabilities of the models. Sets of omnidirectional exponential variogram models with fixed range and sill, and variable nugget were used for each pluton. The local neighbourhood (search radius) for geostatistical interpolation was set equal to the range. Variogram modelling was formulated as an optimisation problem aimed at estimating the nugget for which the mean squared cross-validation (prediction) error reaches its minimum. The best model of each pluton was selected from all possible combinations of models obtained from the PCs. Results of a permutation test indicate that the residuals of observed and predicted compositions do not exhibit significant cross-covariance within the search radius adopted and may be interpreted as stationary random errors, which suggests that little may be gained by application of co-kriging. Random sampling from the geostatistical models indicates that up to several hundreds of specimens must be analysed to successfully predict the area-weighted mean modal composition of plutons and its spatial covariance structure as depicted in single-component and QAPF (Streckeisen) maps. An illustration of the internal consistency of the log-ratio approach and petrogenetic models is provided by the analysis of the compositional pattern in one of the granite complexes, which can be explained by the combined effects of mixing and fractionation. The volumes sampled by bulk geochemical analysis are equivalent to the areas of thin sections, and geochemical data of coarse-crystalline rocks are thus subject to the same limitations as modal analyses. The combined data-reduction and geostatistical modelling strategy outlined in this study is expected to be particularly efficient for the modelling of such high-dimensional data. The advent of quick non-destructive measurement techniques such as XRF and NIR is expected to play a crucial role in future attempts at rigorous quantitative mapping of lithosomes. If sediment generation can be simulated, the uncertainties associated with the initial conditions (area-weighted means of parent-rock properties) can be propagated all the way through to uncertainties of predicted sediment properties.

中文翻译：

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花岗岩复合体成分变异性的地质统计学建模：其与沉积生成模型中的成岩解释和母岩特性规范的相关性

摘要 沉积物生成模型需要准确说明母岩的基本性质及其在一阶（单岩性）流域尺度上的可变性。从文献中提取了五个广泛调查的岩体的地理参考点计数数据，以检查花岗岩中模态成分的空间变异性。从地理空间分析的角度来看，点计数数据必须被视为固有的噪声，因为与花岗岩的平均晶体尺寸相比，采样区域（薄片）很小。由于采样是根据或多或少有规律的模式进行的，以便在整个岩体中实现相同密度的数据覆盖，因此无法获得关于短程变异的关键信息，因此对此类数据的地质统计建模更加复杂。通过将数据转换为中心对数比并计算它们的主成分 (PC) 来进行成分数据的地统计建模。PC 分数用作基于普通克里金法的地统计工作流程的输入，并结合交叉验证和随机模拟来评估模型的预测能力。每个岩体都使用了具有固定范围和基台的全向指数变异函数模型组以及可变块金模型。地统计插值的局部邻域（搜索半径）设置为等于范围。变差函数建模被表述为一个优化问题，旨在估计均方交叉验证（预测）误差达到其最小值的金块。每个岩体的最佳模型是从从 PC 获得的模型的所有可能组合中选出的。置换检验的结果表明，在所采用的搜索半径内，观察到的和预测的组成的残差没有表现出显着的交叉协方差，并且可能被解释为平稳随机误差，这表明应用协同克里金法可能获得的收益很小。地质统计模型的随机抽样表明，必须分析多达数百个样本才能成功预测岩体的面积加权平均模态组成及其空间协方差结构，如单分量和 QAPF (Streckeisen) 地图所示。对数比方法和成岩模型的内部一致性的说明是通过对其中一个花岗岩复合体的成分模式的分析提供的，这可以通过混合和分馏的组合效应来解释。大块地球化学分析采样的体积相当于薄片的面积，因此粗晶岩的地球化学数据受到与模态分析相同的限制。本研究中概述的组合数据缩减和地质统计建模策略预计对于此类高维数据的建模特别有效。XRF 和 NIR 等快速无损测量技术的出现有望在未来对岩体进行严格定量定位的尝试中发挥关键作用。