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

本项目由数学地球科学合作计划（CMG）资助，研究人员：1)利用机载激光测绘（ALSM）数据和微分几何原理表征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折叠过程的动力学；3)利用断裂损伤力学研究km尺度褶皱与m尺度裂缝之间的物理相互作用。他们的基本假设是，褶皱地层的三维形状充分限制了内部变形，因此可以利用这些形状来预测m级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，利用ALSM数据和由美国国家科学基金会赞助的国家航空激光测绘中心（NCALM）获得的高分辨率数码照片，以分米精度描绘褶皱形状。该中心由佛罗里达大学和加利福尼亚大学联合运营。本研究选择的褶皱是怀俄明州的绵羊山背斜和犹他州的拉普利岭单斜。该团队解决了三个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；3)模拟具有广泛相互作用尺度的地球系统。主要研究团队包括一位具有构造地质学专长的地球科学家，一位具有微分几何专长的数学家，以及一位具有计算力学专长的土木工程师。这项研究的广泛影响源于褶皱是地下流体的常见圈闭，而油气藏和地下水含水层中的裂缝是流体流动的管道。在环境领域，褶皱被评价为储存过量二氧化碳的潜在储集层。此外，活动断层通常与褶皱有关，因此减轻地震危险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)微分几何在地质问题上的应用很少，但有很大的前景；2)计算力学的最新进展预示着在折叠过程中通过破裂进行应变局部化的新方法已经成熟；3)研究涉及新技术（ALSM）的创新应用，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.