Abstract The general protocol for quantitative petrographic description of clastic sediments envisioned by J.C. Griffiths approximately 60 years ago is built on specification of the following five statistically independent fundamental properties of aggregates: modal composition, spatial arrangement, size distributions, shape distributions, and orientation distributions of the elements. Each element is represented by a grain falling into one of an exhaustive set of petrographic classes. We introduce the so-called Generalized Griffiths Descriptor (GGD) which extends this protocol to igneous and metamorphic rocks. Statistical independence of the fundamental properties permits rigorous testing of petrogenetic hypotheses as well as simulation of rocks based on any conceivable combination of them. The benefits of a unifying scheme for description of crystalline parent rocks and their weathering products are illustrated by exploratory analysis of a petrographic data set derived from five granodiorites from across North America, comprising the parent rocks and three size fractions (coarse, medium, and fine) of their detritus. Compositional data analysis is used to estimate sediment generation and evolution (SGE) trajectories for each of the plutons sampled. The bulk mineral composition and the mineral composition of the rock-fragment assemblage display a common trend of relative depletion of quartz and K-feldspar with decreasing grain size, compensated for by relative enrichment of biotite and accessory minerals. The evolution of crystal interface composition suggests that the balance between chemical and mechanical weathering may be reflected in relative stabilities of crystal interfaces. We propose a computationally efficient stereological inversion procedure for estimating the parameters of crystal-size probability distributions in rocks based on the assumption of lognormality. The lognormal distribution is an acceptable default model for crystal size in granitoids at the level of individual thin sections (about 87% passes the tests for lognormality), but less so at the level of entire plutons (only 62% success ratio). The current implementation of the GGD is not yet complete, because it deals explicitly with the first three fundamental properties only, as a consequence of adopting the simplifying assumption that all elements which make up a rock are spherical. Shape and orientation distributions may be included in future implementations of the GGD. Dedicated data sets comprising sediments generated from a single parent rock under different conditions will be needed to advance SGE studies by shedding more light on the balance between chemical and mechanical weathering.

中文翻译：

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薄片中岩石质地和成分的联合变异性定量分析：广义格里菲斯描述符及其在花岗岩沉积物中的应用

摘要 JC Griffiths 大约 60 年前设想的碎屑沉积物定量岩相学描述的一般协议建立在以下五个统计上独立的聚集体基本属性的规范之上：模态组成、空间排列、尺寸分布、形状分布和方向分布要素。每个元素都由落入一组详尽的岩相类中的一个的颗粒表示。我们引入了所谓的广义格里菲斯描述符 (GGD)，它将该协议扩展到火成岩和变质岩。基本属性的统计独立性允许严格测试岩石成因假设以及基于它们的任何可能组合的岩石模拟。通过对来自北美各地的五个花岗闪长岩的岩相数据集的探索性分析，说明了描述结晶母岩及其风化产物的统一方案的好处，该数据集包括母岩和三个粒度部分（粗、中和细） ）他们的碎屑。成分数据分析用于估计每个采样的岩体的沉积物生成和演化 (SGE) 轨迹。块体矿物组成和岩屑组合矿物组成显示出石英和钾长石相对贫化的共同趋势，随着晶粒尺寸的减小，黑云母和副矿物的相对富集弥补了这一趋势。晶体界面组成的演变表明化学和机械风化之间的平衡可能反映在晶体界面的相对稳定性上。我们提出了一种计算有效的立体反演程序，用于基于对数正态性假设估计岩石中晶体尺寸概率分布的参数。对数正态分布是单个薄片水平的花岗岩晶体尺寸的可接受默认模型（约 87% 通过对数正态性检验），但在整个岩体水平上则较少（只有 62% 的成功率）。GGD 的当前实现尚未完成，因为它仅明确处理前三个基本属性，由于采用了构成岩石的所有元素都是球形的简化假设。形状和方向分布可能包含在 GGD 的未来实现中。需要包含在不同条件下从单一母岩产生的沉积物的专用数据集，通过更多地了解化学风化和机械风化之间的平衡来推进 SGE 研究。