Louisiana State University LSU Digital Commons LSU Doctoral Dissertations Graduate School 2013 Characterization and uncertainty analysis of siliciclastic aquifer-fault system Ahmed Saad Elshall Louisiana State University and Agricultural and Mechanical College, [email protected] Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_dissertations Part of the Civil and Environmental Engineering Commons Recommended Citation Elshall, Ahmed Saad, "Characterization and uncertainty analysis of siliciclastic aquifer-fault system" (2013). LSU Doctoral Dissertations. 3008. https://digitalcommons.lsu.edu/gradschool_dissertations/3008 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Digital Commons. For more information, please [email protected]. CHARACTERIZATION AND UNCERTAINTY ANALYSIS OF SILICICLASTIC AQUIFER-FAULT SYSTEM A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Civil and Environmental Engineering by Ahmed Saad Elshall B.S. The American University in Cairo, 2003 M.S. University of Tübingen, 2009 December 2013 Acknowledgements Dr. Frank Tsai provided the generalized parameterization method (see Section 3.1) and the hierarchical BMA Bayesian model averaging method (see Section 3.3). In addition, Dr. Frank Tsai carried out all the geophysical data interpretation (see Section 4.1.1) and prepared the GIS maps (see Figure 1, Figure 3 and Figure 33). The PhD students at the Civil and Environment Engineering Department Mr. Nima Chitsazan, Mr. Ihsan Beigi, Mr. Hai Pham and Mr. Amir Mani assisted with the geophysical data processing. The PhD student Mr. Hai Pham developed the grid of the groundwater flow models (see Section 6.2.1,Figure 32). Dr. Le Yan from the High Performance Computing parallelized the model calibration algorithm (see Section 6.2.2). I acknowledge Dr. Frank Tsai, Dr. Jeffrey Hanor, Dr. Le Yan and Mr. Hai Pham for their contribution to and for being coauthors on the four peer-reviewed manuscripts and the 13 conference proceedings, which were carried out during the study period. Acknowledgment is due to the PhD committee members Dr. John Pardue, Dr. Jeffrey Hanor, Dr. Carol Wicks and Dr. Robert Reigh for their support. I am thankful to the staff members Mrs. Janet Labatut and Mrs. Julie Mueller for their administrative support and to Mr. Dave Robertson and Mr. Al Pawlowski for their technical support. I acknowledge LSU HPC and LONI for permitting the use of their HPC clusters. This work is funded by the National Science Foundation–Hydrologic Sciences, the U.S. Geological Survey–National Institute for Water Resources, the Louisiana Water Resources Research Institute and Louisiana State University–Graduate School Supplementary Award. I am very thankful to Dr. Frank Tsai for his meticulous supervision and generous assistance without which this work would not have been possible. Finally, I am indebted to my parents and family for their priceless guidance. Thank you very much. ii Table of Contents Acknowledgements ......................................................................................................................... ii Table of Contents ........................................................................................................................... iii Abstract .......................................................................................................................................... vi 1 Introduction .................................................................................................................................. 1 2 Literature review .......................................................................................................................... 8 2.1 Baton Rouge aquifer-fault system ......................................................................................... 8 2.2 Hydrofacies architecture modeling using indicator geostatistics .......................................... 9 2.3 Model calibration and uncertainty quantification using CMA-ES ...................................... 12 2.4 Constructive epistemic modeling using hierarchical Bayesian model averaging ............... 15 2.4.1 Hierarchical Bayesian model averaging ..................................................................... 15 2.4.2 Constructive epistemic modeling under Bayesian paradigm ..................................... 19 3 Methods...................................................................................................................................... 24 3.1 Indicator geostatistics .......................................................................................................... 24 3.2 CMA-ES .............................................................................................................................. 25 3.2.1 CMA-ES algorithm .................................................................................................... 25 3.2.2 Review of CMA-ES with respect to comparison algorithms ..................................... 30 3.3 Hierarchical Bayesian model averaging .............................................................................. 34 3.3.1 Terminology and notation .......................................................................................... 34 3.3.2 Posterior model probability and conditional posterior model probability ................. 36 3.3.3 Prediction means and prediction covariances ............................................................ 40 3.3.4 Computation of posterior model probability with variance window ......................... 42 3.3.5 Similarities and differences between collection BMA and hierarchical BMA .......... 47 4 Constructive epistemic modeling of hydrofacies architecture under Bayesian paradigm ......... 49 4.1 Case Study: Hydrofacies architecture model of the Baton Rouge aquifer-fault system ..... 49 4.1.1 Model data .................................................................................................................. 49 4.1.2 Model data and model structure uncertainty .............................................................. 52 4.1.3 Model parameters and calibration .............................................................................. 55 4.2 Results and Discussion ........................................................................................................ 57 4.2.1 Calibration and BIC ................................................................................................... 57 4.2.2 Model propositions evaluation using the BMA tree .................................................. 60 4.2.3 Uncertainty propagation and prioritization ................................................................ 63 4.3 Conclusions ......................................................................................................................... 69 5 Hydrogeological characterization of the Baton Rouge aquifer-fault system ............................. 72 5.1 Case Study: Hydrofacies architecture model of the Baton Rouge aquifer-fault system ..... 72 5.1.1 Hydrofacies architecture model ................................................................................. 72 5.1.2 Model parameters and calibration .............................................................................. 73 5.2 Results and discussion ......................................................................................................... 76 5.2.1 Calibration results ...................................................................................................... 76 iii 5.2.2 Leaky faults ................................................................................................................ 80 5.2.3 Quantification of structural geology parameters ........................................................ 82 5.2.4 Interconnections between aquifer units ...................................................................... 89 5.2.5 Baton Rouge aquifer-fault connections for saltwater intrusion ................................. 91 5.3 Conclusions ......................................................................................................................... 94 6 Groundwater flow model calibration and uncertainty quantification using CMA-ES .............. 97 6.1 Synthetic groundwater flow problem .................................................................................. 97 6.1.1 Design of the synthetic problem................................................................................. 97 6.1.2 Ill-posedness and search difficulties .......................................................................... 98 6.1.3 Model parameters and calibration ............................................................................ 100 6.1.4 Algorithms tuning .................................................................................................... 101 6.1.5 Performance comparison .......................................................................................... 104 6.1.6 Parallel versus sequential implementation ............................................................... 106 6.1.7 Covariance matrix for Monte Carlo sampling .........................................................