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Quantification of Aquifer Properties with Surface Nuclear Magnetic Resonance in the Platte River Valley, Central Nebraska, Using a Novel Inversion Method

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Quantification of Aquifer Properties with Surface Nuclear Magnetic Resonance in the Platte River Valley, Central Nebraska, Using a Novel Inversion Method Prepared in cooperation with the Central Platte Natural Resources District and the Nebraska Environmental Trust Quantification of Aquifer Properties with Surface Nuclear Magnetic Resonance in the Platte River Valley, Central Nebraska, Using a Novel Inversion Method Scientific Investigations Report 2012–5189 U.S. Department of the Interior U.S. Geological Survey COVER: Collage showing multiple photographic images of surface nuclear magnetic resonance and aquifer-test data collection. Center top, a broad view showing trailer-mounted hydraulic pump, used in constant-discharge aquifer test. Project staff shown for general scale. Lower left, hydraulic head recording instrumentation in the observation wells, with wire reels (also shown in large photograph) approximately 25 centimeters in diameter. Lower right, surface nuclear magnetic resonance instrument. Boxes contain electronic equipment and are about 60 centimeters by 60 centimeters in plan view. Top and lower left photographs taken in November 2008 by Gregory V. Steele, U.S. Geological Survey, licensed under Creative Commons. Lower right photograph was taken by David Walsh, Vista Clara Inc., Mukilteo, Wash., November 2008. Quantification of Aquifer Properties with Surface Nuclear Magnetic Resonance in the Platte River Valley, Central Nebraska, Using a Novel Inversion Method By Trevor P. Irons, Christopher M. Hobza, Gregory V. Steele, Jared D. Abraham, James C. Cannia, and Duane D. Woodward Prepared in cooperation with the Central Platte Natural Resources District and the Nebraska Environmental Trust Scientific Investigations Report 2012–5189 U.S. Department of the Interior U.S. Geological Survey U.S. Department of the Interior KEN SALAZAR, Secretary U.S. Geological Survey Marcia K. McNutt, Director U.S. Geological Survey, Reston, Virginia: 2012 For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS. For an overview of USGS information products, including maps, imagery, and publications, visit http://www.usgs.gov/pubprod To order this and other USGS information products, visit http://store.usgs.gov Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner. Suggested citation: Irons, T.P., Hobza, C.M., Steele, G.V., Abraham, J.D., Cannia, J.C., Woodward, D.D., 2012, Quantification of aqui- fer properties with surface nuclear magnetic resonance in the Platte River valley, central Nebraska, using a novel inversion method: U.S. Geological Survey Scientific Investigations Report 2012–5189, 50 p. iii Contents Abstract ...........................................................................................................................................................1 Introduction.....................................................................................................................................................1 Acknowledgments ................................................................................................................................3 Purpose and Scope ..............................................................................................................................3 Study Area Description ........................................................................................................................3 Hydrogeology................................................................................................................................3 Description of Hydrostratigraphic Units ..................................................................................5 Methods and Approach ................................................................................................................................6 Site Selection.........................................................................................................................................6 Surface Nuclear Magnetic Resonance ...........................................................................................6 Nuclear Magnetic Resonance Dynamics ................................................................................6 Calculation of the Co-rotating Field .................................................................................7 Tipping of the Bulk Magnetization Vector .......................................................................8 NMR Relaxation and Recovery .................................................................................................9 Relaxation during the Tipping Pulse ..............................................................................10 Surface Nuclear Magnetic Resonance Voltage Response ................................................10 Effects of Inhomogeneities in the Static Magnetic Field ....................................................11 Spin-echo Pulses ..............................................................................................................11 Static Dephasing Processes ...........................................................................................11 Diffusion..............................................................................................................................12 Implications of Magnetic Field Inhomogeneities for Surface Nuclear Magnetic Resonance .........................................................................................12 Surface Nuclear Magnetic Resonance T2 Measurements ........................................12 Surface Nuclear Magnetic Resonance T1 Measurements .......................................14 Processing of Surface Nuclear Magnetic Resonance Field Data ....................................14 Inversion of Surface Nuclear Magnetic Resonance Data .................................................14 Estimation of Hydraulic Properties using Surface Nuclear Magnetic Resonance ........15 Frequency Domain Formulation ..............................................................................................15 Equation of Motion ...........................................................................................................16 Incorporating Dephasing Effects ...................................................................................17 Linear 1-D Inversion Formulation ............................................................................................18 Linearization of the Problem ...........................................................................................18 Modulus Solution .....................................................................................................18 Model and Data Space ...........................................................................................18 Tikhonov 1-D Inverse Problem Solution ........................................................................19 Non-negativity Constraint ......................................................................................19 Discussion of Inversion Performance ...........................................................................20 Transient Electromagnetic Data Collection and Processing .......................................................20 Aquifer Tests ........................................................................................................................................20 Design of the Aquifer Tests and Methods of Analysis .........................................................20 Analysis of Aquifer Tests in the Alluvial Deposits .......................................................23 Analysis of Aquifer Tests in the Ogallala Deposits ......................................................23 Borehole Geophysical Data Collection ...........................................................................................24 iv Analysis from Sites 58A and 72A ...............................................................................................................24 Aquifer Tests ........................................................................................................................................25 Uncertainty Analysis of SNMR Data Collection and Inversion Results .....................................27 Sources of Error in the Data ....................................................................................................27 Inversion and Analysis Uncertainty and Error ......................................................................28 Aquifer Test Process Discussion .....................................................................................................29 Analysis of Electromagnetic Flowmeter Tests ...............................................................................30 Surface NMR Inversions and Determination of the Cp Calibration Factor ...............................34 Site 58A ................................................................................................................................................34 Site 72A .................................................................................................................................................34 Application of Cp Factor to Previous Aquifer Tests ...............................................................................34
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