CMG: Mathematical Modeling of the Dynamics of Multi-scale Phenomena During Folding and Fracturing of Sedimentary Rocks

在该项目中，在数学地球科学计划(CMG)的支持下，研究人员：1)利用机载激光条带测绘(ALSM)数据和微分几何原理表征Km尺度褶皱沉积地层的几何形状；2)利用连续介质力学和有限元方法(FEM)研究褶皱过程的动力学；3)利用断裂力学和损伤力学研究Km尺度褶皱与其中m尺度裂缝之间的物理相互作用。他们的基本假设是，褶皱地层的3D形状充分约束了内部变形，因此可以使用这些形状来预测m尺度裂缝的方向和空间密度。这项研究的动机是利用美国国家科学基金会赞助的国家机载激光测绘中心(NCALM)获得的ALSM数据和高分辨率数字照片以分米精度表征褶皱形状的前所未有的机会，该中心由佛罗里达大学和加州大学联合运营。该研究选择了怀俄明州的羊山背斜和犹他州的Raplee Ridge单斜褶皱。该团队致力于三个CMG主题领域：1)大型复杂地球系统的数学建模；2)分析大型地球科学数据集；以及3)具有广泛相互作用的尺度的地球系统建模。主要调查人员包括一名在构造地质学方面有专长的地球科学家，一名在微分几何方面有专长的数学家，以及一名在计算力学方面有专长的土木工程师。这项调查的更广泛影响源于这样一个事实，即褶皱是地下流体的常见圈闭，而碳氢化合物储层和地下水含水层中的裂缝被认为是流体流动的管道。在环境领域，褶皱被评估为可能储存过量二氧化碳的储集层。此外，活动断裂通常与褶皱有关，因此减轻地震灾害需要更好地了解褶皱过程。这项研究的学术价值包括：1)微分几何在地质问题中的应用很少，但前景广阔；2)折叠过程中通过破裂进行应变定位的新方法已经成熟，这是计算力学最新进展所预示的；3)这项研究涉及新技术(ALSM)的创新应用，有望获得前所未有的数据量和精度。

In this project, supported by the Collaborations in Mathematical Geosciences Program (CMG), the investigators are: 1) characterizing the geometric shapes of km-scale folded sedimentary strata using Airborne Laser Swath Mapping (ALSM) data and the principles of differential geometry; 2) investigating the dynamics of the folding process using continuum mechanics and Finite Element Methods (FEM); and 3) studying the physical interactions between km-scale folds and m-scale fractures within them using fracture and damage mechanics. Their underlying hypothesis is that the 3D shape of folded strata adequately constrains the internal deformation such that the orientation and spatial density of m-scale fractures can be predicted using these shapes. The study was motivated by the unprecedented opportunity to characterize fold shapes with decimeter precision using ALSM data and high resolution digital photography acquired by the NSF-sponsored National Center for Airborne Laser Mapping (NCALM), operated jointly by the University of Florida and the University of California. The folds selected for this study are Sheep Mountain Anticline, Wyoming, and Raplee Ridge Monocline, Utah.The team addresses three CMG theme areas: 1) mathematical modeling of large, complex geosystems; 2) analyzing large geoscience data sets; and 3) modeling geosystems with a broad range of interacting scales. The team of principal investigators includes a geoscientist with expertise in structural geology, a mathematician with expertise in differential geometry, and a civil engineer with expertise in computational mechanics. The broader impacts of this investigation stem from the fact that folds are common traps for subsurface fluids, and fractures in hydrocarbon reservoirs and groundwater aquifers are known to be conduits for fluid flow. In the environmental arena folds are being evaluated as potential reservoirs for excess CO2 storage. Furthermore, active faults commonly are associated with folds, so the mitigation of earthquake hazards requires a better understanding of the folding process. The intellectual merits of this investigation include the facts that: 1) applications of differential geometry to geological problems are rare, yet have great promise; 2) strain localization by fracturing during folding is ripe for a new approach heralded by recent advances in computational mechanics; 3) the research involves innovative applications of new technology (ALSM) that promise unprecedented data quantities and precision.