Proposal
Rapid and regional-scale erosion remains one of the most pivotal yet debated arguments within Flood Geology (Oard and Klevberg, 2008; Whitmore, 2013). This is particularly true in the Flood/post-Flood boundary debate on the regional-scale erosion of hundreds to thousands of meters of stratigraphy across many anticlines and fold systems (Matthews and Oard, 2015; Isaacs, 2020). Even so, no previous studies of erosion of anticlines have developed a rigorous mathematical model for systematic and repeatable modeling of fold surfaces for erosion estimates in data scarce locations. This is in part because fold systems remain one of the most challenging features to mathematically model in structural geology, often requiring up to hundreds of GPS points as well as drill hole data in order to tightly define the shape of the fold (Bergbauer and Pollard, 2004; Carrera et al., 2009; Hou et al., 2023). However, this study proposes a boundary value problem approach for reconstructing symmetric and non-verging anticlines. Through this method, only a single point, the slope of that point (or bed dip), and its position between the adjoining fold maximum (anticline) and minimum (syncline) are needed, making it optimal for reconstructing symmetric and approximately non-verging folds in data scarce locations. Furthermore, the modeled fold system may then be compared to its mapped counterpart to yield margins of error, thereby providing a gauge in the quality of the estimate. In application to a fold in the Mount St. Helens region (Washington), the model described characteristics of the half-wavelength of the fold system within 15% of its mapped extent. The modeled surface resulted in a calculation of 6.16 km of vertical relief eroded from the current topography, a value that could be increased to 10.1 km when transferring the modeled surface to the outermost observed fold surface. In continued research, this approach can be applied to the Colorado Plateau. Such a reconstruction can be integrated with surface topographic data and published isostatic models to investigate the interplay of erosion and tectonics in producing the regional scale erosion of fold belts we observe today. As such, this technique represents a first step towards developing an easily deployable yet rigorous approach to model fold systems for repeatable and consistent erosion estimates.
Bergbauer, S. and Pollard, D.D., 2004, A new conceptual fold–fracture model including pre-folding joints, based on the Emigrant Gap anticline, Wyoming. Geological Society of America Bulletin 116: 294–307.
Carrera, N., J.A. Muñoz, and E. Roca. 2009. 3D reconstruction of geological surfaces by the equivalent dip-domain method: An example from field data of the Cerro Bayo Anticline (Cordillera Oriental, NW Argentine Andes). Journal of Structural Geology 31(12):1573-1585.
Hou, W., Y. Chen, H. Liu, F. Xiao, C. Liu, and D. Wang. 2023. Reconstructing Three-dimensional geological structures by the Multiple-point statistics method coupled with a deep neural network: A case study of a metro station in Guangzhou, China. Tunnelling and Underground Space Technology 136:105089.
Isaacs, E.A. 2020. Tremendous Erosion of the Cascade Anticlinorium near Mount St. Helens: Part 1: Structure and Calculations. CRSQ 57(1):30-44.
Matthews, J. and M.J. Oard. 2015. Erosion of the Weald, Southeast England Part II: A flood explanation of the mystery and its implications. CRSQ 52(1):22–33.
Oard, M.J. and P. Klevberg. 2008. Green River Formation Very Likely Did Not Form in a Postdiluvial Lake. Answers Research Journal 1:99-108.
Whitmore, J.H. 2013. The potential for and implications of widespread post-Flood erosion and mass wasting processes; in: Horstemeyer, M. (editor), Proceedings of the Seventh International Conference on Creationism (technical symposium sessions), Creation Science Fellowship, Pittsburgh, PA.
Keywords
erosion, fold system reconstruction, structural geology, isostasy, Mount St. Helens
Submission Type
Oral Presentation
Copyright
© 2025 Edward A. Isaacs. All rights reserved.
A Differential Geometry Approach to Fold Belt Reconstruction for Rigorous Flood and post-Flood Erosion Estimates and Isostasy Modeling
Rapid and regional-scale erosion remains one of the most pivotal yet debated arguments within Flood Geology (Oard and Klevberg, 2008; Whitmore, 2013). This is particularly true in the Flood/post-Flood boundary debate on the regional-scale erosion of hundreds to thousands of meters of stratigraphy across many anticlines and fold systems (Matthews and Oard, 2015; Isaacs, 2020). Even so, no previous studies of erosion of anticlines have developed a rigorous mathematical model for systematic and repeatable modeling of fold surfaces for erosion estimates in data scarce locations. This is in part because fold systems remain one of the most challenging features to mathematically model in structural geology, often requiring up to hundreds of GPS points as well as drill hole data in order to tightly define the shape of the fold (Bergbauer and Pollard, 2004; Carrera et al., 2009; Hou et al., 2023). However, this study proposes a boundary value problem approach for reconstructing symmetric and non-verging anticlines. Through this method, only a single point, the slope of that point (or bed dip), and its position between the adjoining fold maximum (anticline) and minimum (syncline) are needed, making it optimal for reconstructing symmetric and approximately non-verging folds in data scarce locations. Furthermore, the modeled fold system may then be compared to its mapped counterpart to yield margins of error, thereby providing a gauge in the quality of the estimate. In application to a fold in the Mount St. Helens region (Washington), the model described characteristics of the half-wavelength of the fold system within 15% of its mapped extent. The modeled surface resulted in a calculation of 6.16 km of vertical relief eroded from the current topography, a value that could be increased to 10.1 km when transferring the modeled surface to the outermost observed fold surface. In continued research, this approach can be applied to the Colorado Plateau. Such a reconstruction can be integrated with surface topographic data and published isostatic models to investigate the interplay of erosion and tectonics in producing the regional scale erosion of fold belts we observe today. As such, this technique represents a first step towards developing an easily deployable yet rigorous approach to model fold systems for repeatable and consistent erosion estimates.
Bergbauer, S. and Pollard, D.D., 2004, A new conceptual fold–fracture model including pre-folding joints, based on the Emigrant Gap anticline, Wyoming. Geological Society of America Bulletin 116: 294–307.
Carrera, N., J.A. Muñoz, and E. Roca. 2009. 3D reconstruction of geological surfaces by the equivalent dip-domain method: An example from field data of the Cerro Bayo Anticline (Cordillera Oriental, NW Argentine Andes). Journal of Structural Geology 31(12):1573-1585.
Hou, W., Y. Chen, H. Liu, F. Xiao, C. Liu, and D. Wang. 2023. Reconstructing Three-dimensional geological structures by the Multiple-point statistics method coupled with a deep neural network: A case study of a metro station in Guangzhou, China. Tunnelling and Underground Space Technology 136:105089.
Isaacs, E.A. 2020. Tremendous Erosion of the Cascade Anticlinorium near Mount St. Helens: Part 1: Structure and Calculations. CRSQ 57(1):30-44.
Matthews, J. and M.J. Oard. 2015. Erosion of the Weald, Southeast England Part II: A flood explanation of the mystery and its implications. CRSQ 52(1):22–33.
Oard, M.J. and P. Klevberg. 2008. Green River Formation Very Likely Did Not Form in a Postdiluvial Lake. Answers Research Journal 1:99-108.
Whitmore, J.H. 2013. The potential for and implications of widespread post-Flood erosion and mass wasting processes; in: Horstemeyer, M. (editor), Proceedings of the Seventh International Conference on Creationism (technical symposium sessions), Creation Science Fellowship, Pittsburgh, PA.