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

本项目在数学地球科学合作项目（CMG）的支持下，主要研究内容如下：1）利用机载激光测绘（ALSM）数据和微分几何原理，描述千米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，研究褶皱过程的动力学;（3）利用断裂和损伤力学研究千米级褶皱和其中的m级断裂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，使得可以使用这些形状预测m尺度裂缝的方向和空间密度。这项研究的动机是前所未有的机会，以分米精度使用ALSM数据和高分辨率数码摄影获得的国家科学基金会赞助的国家中心机载激光测绘（NCALM），由佛罗里达大学和加州大学联合经营的褶皱形状。本研究选择的褶皱是怀俄明州的羊山背斜和犹他州的Raplee Ridge Monocline。该团队致力于CMG的三个主题领域：1）大型复杂地质系统的数学建模; 2）分析大型地球科学数据集; 3）建模具有广泛相互作用尺度的地质系统。主要研究人员团队包括一名具有结构地质学专业知识的地球科学家，一名具有微分几何专业知识的数学家和一名具有计算力学专业知识的土木工程师。这项调查的更广泛的影响源于这样一个事实，即褶皱是地下流体的常见陷阱，而油气藏和地下含水层中的裂缝是流体流动的管道。在环境竞技场中，褶皱被评价为潜在的储存过量CO2的储层。此外，活动断层通常与褶皱有关，因此减轻地震灾害需要更好地了解褶皱过程。这项研究的智力价值包括以下事实：1）微分几何应用于地质问题是罕见的，但有很大的希望; 2）在褶皱过程中通过断裂应变局部化是成熟的一种新方法，预示着在计算力学的最新进展; 3）研究涉及新技术的创新应用（ALSM），承诺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.