وارون‌سازی محتوای آب سیگنال سونداژ تشدید مغناطیسی، مطالعه موردی نینه محلات، ایران مرکزی

نویسندگان

1 دانشجوی دکتری، گروه فیزیک زمین، موسسه ژئوفیزیک دانشگاه تهران، ایران

2 استاد، گروه فیزیک زمین، موسسه ژئوفیزیک دانشگاه تهران، ایران

3 استادیار، گروه فیزیک زمین، موسسه ژئوفیزیک دانشگاه تهران، ایران

چکیده

روش سونداژ تشدید مغناطیسی تنها روش ژئوفیزیکی است که به‌طور مستقیم به مولکول‌های آب زیرسطحی حساس می‌باشد. با استفاده از وارون‌سازی داده‌های سونداژ تشدید مغناطیسی می‌توان اطلاعات مهمی از قبیل ضخامت و عمق لایه آبخوان، محتوای آب و در شرایطی مناسب، میزان رسانندگی هیدرولیکی لایه آبدار را به‌دست آورد. این روش به‌شدت به اندازه و نوع نوفه حساس است؛ لذا تخمین پارامترهای سیگنال و نیز وارون‌سازی آن حساسیت بالایی دارد. وارون‌سازی داده‌های سونداژ تشدید مغناطیسی یک مسأله بدوضع می‌باشد و نمی‌توان با استفاده از روش‌های مستقیم آن را حل کرد. به‌همین دلیل استفاده از روش‌های منظم‌سازی در وارون­سازی سونداژ تشدید مغناطیسی امری اجتناب‌ناپذیر است. روش‌های متعددی جهت حل مسأله وارون سونداژ تشدید مغناطیسی پیشنهاد شده است. رهیافت هندسه ثابت و رهیافت هندسه متغیر، همراه با بهره‌گیری از روش‌های مختلف بهینه‌سازی تابع هدف از جمله این روش‌ها است. در این مقاله از رهیافت هندسه ثابت و اعمال منظم‌سازی تیخنوف همراه با قیدهای مناسب، جهت وارون‌سازی و مدل‌سازی پیشرو استفاده شده است. خروجی حاصل از داده‌های مصنوعی، و داده‌هایی از ایران و آلمان به‌عنوان داده‌های کم آب و پرآب، نتایج قابل قبولی از تغییرات محتوای آب نسبت به عمق و به‌کار‌گیری روش ارائه شده نشان می­دهد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Water content inversion of MRS data a case study of Nineh Mahallat, central Iran

نویسندگان [English]

  • Mahdi Fallah Safari 1
  • Mohammad Kazem Hafizi 2
  • Reza Ghanati 3
1 Ph.D. Student, Department of Earth Physics, Institute of Geophysics, University of Tehran, Iran
2 Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Iran
3 Assistant Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Iran
چکیده [English]

Magnetic resonance sounding (MRS) is a relatively new approach and is the only geophysical method which is directly sensitive to the underground water molecules. MRS is based on the principal of Nuclear Magnetic Resonance (NMR). A wire loop with different diameter depending on the depth of aquifers, is laid out on the ground. The wire loop is used for both transmission of the oscillating magnetic field and reception of the MRS signal. This method proved to be sufficiently accurate and to have a high resolving capability. In the geophysical application of Magnetic Resonance, the groundwater is the target of investigation. Inverting MRS data provides significant information regarding depth and thickness of the aquifer, distribution of water content and, under favorable conditions, hydraulic conductivity. In this method water content is defined based on the portion of the total volume of subsurface occupied by the free water which is unattached to grain walls and can be extracted from the rock and signal of bounded water which is captured by grains is not included. That is to say that signals related to the bounded water which is absorbed by the grains of the medium is excluded from the calculation process. This method is sensitive to the noise level so estimation of signal parameters and inversion plays an important role. The inverse problem of MRS is ill-posed meaning that the solution is not unique. On the other hand, within a certain depth range, two layers with different thickness and water content but with the same product could return the same theoretical sounding curve. The inversion of this method is carried out according to the well-known Tikhonov method. Solution of MRS inversion like other inverse problems in geophysics is not a continuous function of the data in which there are a small perturbation of the input data that can cause a large perturbation of the model parameters. Consequently, regularization methods should be employed to tackle possible instabilities in solution process. Moreover defining the kind of regularization a proper choice of the regularization parameter is essential. There are various methods available. In this paper the L-Curve is used. From model space point of view,  there are various schemes for inverting MRS data including fixed geometry and variable geometry approaches in conjunction with using different methods of the objective function optimization. In fixed geometry approach, the model is assumed to have fixed layers with increasing layer thickness in depth, in fact the water content is allowed to vary; and in variable geometry approach it assumes a small number of layers, where both water content and layer thickness can vary. To numerically demonstrate the performance of the proposed inversion algorithm, we used a seven-layer model consisting of three horizontal, homogeneous, by 30% water content. In this paper, stable and unique solution is sought through the fixed geometry approach and imposing Tikonov regularization with constraints. After the test of inversion algorithm on synthetic data, Iran and Germany data were used to illustrate algorithm field use and to verify model results. Estimation of water content of synthetic data, Iran and Germany data shows a reasonable efficiency of the proposed strategy.

کلیدواژه‌ها [English]

  • Tikonov regularization
  • magnetic resonance sounding
  • Water content
  • inversion
فلاح صفری، م.، حفیظی، م. ک. و قناتی، ر.، 1395، وارون‌سازی خطی سونداژ تشدید مغناطیسی با استفاده از منظم‌سازی تیخونف، سی و پنجمین گردهمایی ملی علوم زمین، تهران، سازمان زمین‌شناسی و اکتشافات معدنی کشور.

وطن‌خواه، س.، 1393، استفاده از اطلاعات اولیه برای تخمین پارامتر منظم‌سازی تیخونف و کاربرد آن در وارون‌سازی خطی داده‌های گرانی، رساله دکتری، موسسه ژئوفیزیک دانشگاه تهران.

Ai-Hua, W., 2010, Occam’s inversion of magnetic resonance sounding on a layerd electrically conductive earth. Journal of applied geophysics, 70, 84-92.

Ai-Hua, W., Xue- Qiu, W., Guo- Xing, L., Xiu-Wen, M. and De- Li, W., 2007, Nonlinear inversion of surface nuclear magnetic resonance over electrically conductive medium, Chinese journal of geophysics, 50(3), 765-772.

Akca, I., Gunther, T., Muller-Petke, M., Basokur, A. and Yaramanci, U., 2013, Joint parameter estimation from magnetic resonance and vertical electric soundings using a multi-objective genetic algorithm, Geophysical Prospecting, DOI: 10.1111/1365-2478.12082.

Aster, R., Borchers, B. and Thurber, C., 2005, Parameter estimation and inverse problems, Elsevier Academic Press.

Behroozmand, A., Keating, K. and Auken, E., 2014, A review of the principles and application of the NMR technique for near-surface characterization, surv.Geophys, DOI 10.1007/s10712-014-9304-0.

Braun, M., 2007, Influence of the resistivity on magnetic resonance sounding: 1D inversion and 2D modelling, Ph.D. thesis, Fakultat VI Planen Bauen Umwelt, Technical University of Berlin.

Braun, M., Hertrich, M. and Yaramanci, U., 2005, Complex inversion of MRSdata, Near Surface Geophysics 3 (3) 155–163.

Braun, M. and Yaramanci, U., 2008, Inversion of resistivity in Magnetic Resonance Sounding, Journal of Applied Geophysics 66, 151–164.

Dalgaard, E., Auken, E. and Larsen, J. J., 2012, Adaptive noise cancelling of multichannel magnetic resonance sounding signals, Jeophysical Journal International, 119, DOI: 10.1111/j.1365-246X.2012.05618.x.

Gev, I., Goldman, M., Rabinovich, B. and Rabinovich, M., 1996, Detection of the water level in fractured phreatic aquifers using nuclear magnetic resonance (NMR) geophysical measurements,Journal of Applied Geophysics, 33, 277–282.

Ghanati, R., 2016, Improvement of processing and parameter estimation of magnetic resonance sounding signal.Geophysics, 81, no., Z27-Z27.

Ghanati, R. and Fallahsafari, 2015, Comment on: ‘Time-Based noise removal from magnetic resonance sounding signals’ By Shahi, M., Khaloozadeh, H., Hafizi, M. K., International Journal of Innovative Computing, Information and Control,11(1), 387-390.

Ghanati, R., Fallahsafari, M. and Hafizi, M., 2014, Joint application of a statistical optimization process and Empirical Mode Decomposition to Magnetic Resonance Sounding Noise Cancelation, J. Appl Geophys, 111, 110–120.

Ghanati, R., Hafizi, M. and Fallahsafari, M., 2015a, CEEMD-DFA and Variance Criterion Based De-noising Method Applied to Magnetic Resonance Sounding. 6th International workshop on magnetic resonance, Aarhus, Denmark.

Ghanati, R., Hafizi, M. and Fallahsafari, M., 2015b, Surface nuclear magnetic resonance signals recovery by integration of a non-linear decomposition method with statistical analysis. Geophysical Prospecting, DOI: 10.1111/1365-2478.12296.

Ghanati, R. and Hafizi, M. K., 2017, Statistical de-spiking and harmonic interference cancellation from surface-NMR signals via a state-conditioned filter and modified Nyman-Gaiser method. Bollettino Di Geofisica Teorica Ed Applicata, 58(3), 181-204.

Goldman, M., Rabinovich, B., Rabinovich, M., Gilad, D., Gev, I. and Schirov, M., 1994, Application of the integrated NMR-TDEM method in groundwater exploration in Israel, Journal of Applied Geophysics 31, 27–52.

Guillen, A. and Legchenko, A., 2002a, Application of linear programming techniques to the inversion of proton magnetic resonance measurements for water prospecting from the surface, Journal of Applied Geophysics 50 (1–2) 149–162, special issue.

Guillen, A. and Legchenko, A., 2002b, Inversion of surface nuclear magneticresonance data by an adapted Monte Carlo method applied to water resource characterization, Journal of Applied Geophysics, 50 (1–2), 193–205.

Hertrich, M., 2005, Magnetic resonance sounding with separated transmitter and receiver loops for the investigation of 2d water content distributions, Ph.D. thesis, School of Civil Engineering and Applied Geosciences, Technical University of Berlin.

Hertrich, M., 2008, Imaging of groundwater with nuclear magnetic resonance, Programing in nuclear magnetic resonance spectroscopy, 53, 227-248.

Hertrich, M., Braun, M., Gu¨nther, T., Green, A. G. and Yaramanci, U., 2007, Surface nuclear magnetic resonance tomography, Geoscience and Remote Sensing, IEEE Transactions on 45 (11) 3752–3759.

Hertrich, M., Braun, M. and Yaramanci, U., 2005, Magnetic resonance soundings with separated transmitter and receiver loops, Near Surface Geophysics 3 (3) 131–144.

Hertrich, M. and Yaramanci, U., 2002, Joint inversion of surface nuclear magnetic resonance and vertical electrical sounding, Journal of Applied Geophysics 50 (1–2) 179–191.

Jiang, C., Shang, X., Lin, T. and lint J., 2017, Quasi-2D block inversion of large-scale surface nuclear magnetic resonance profile data using a laterally constrained model, Geophysics, 82, DOI:10.1190/geo2015-0455.1.

Kim, H. J. and Kim, Y., 2011, A unified transformation function for lower and upper bounding constraints on model parameters in electrical and electromagnetic inversion. Journal of Geophysics and Engineering, 8, 21-26.

Krylov, V. I., 1962, Approximate calculation of integrals, translated by A. H. Stroud. Macmillan, New York.

Larsen, J. J., 2016, Model-based subtraction of spikes from surface nuclear magnetic resonance data. Geophysics, 81, DOI: 10.1190/geo2015-0442.1.

Legchenko, A., 2005, Improved modelling of the magnetic resonance signal in the presence of shallow aquifers. Near Surface Geophysics, 3, 121-130.

Legchenko, A., 2007, MRS measurements and inversion in presence of EM noise. Boletin Geológico y Minero, 118 (3): 489-508.

Legchenko, A., 2013, Magnetic Resonance Imaging for Groundwater. John Wiley & Sons.

Legchenko, A., Beauce, A., Guillen, A., Valla, P. and Bernard, J., 1997, Natural variations in the magnetic resonance signal used in PMR groundwater prospecting from the surface. European Journal of Environmental and Engineering Geophysics 2, 173-190.

Legchenko, A. and Shushakov, O., 1998, Inversion of surface NMR data, Geophysics, 63 (1), 75–84.

Legchenko, A. and Valla, P., 1998, Processing of surface proton magnetic resonance signals using non-linear fitting, Journal of Applied Geophysics, 39, 77–83.

Mohnke, O. and Yaramanci, U., 2000, Inversion of Surface-NMR amplitudes and decay times examination of smooth and block inversion.Proceedings of the 6th Meeting of Environmental and Engineering Geophysics.

Mohnke, O. and Yaramanci, U., 2002, Smooth and block inversion of surface NMR amplitudes and decay times using simulated annealing, Journal of Applied Geophysics 50 (1–2) 163–177.

Müller-Petke, M. and Yaramanci, U., 2008, Resolution studies for magnetic resonance sounding (MRS) using the singular value decomposition. J. Appl Geophys, 66, 165–175.

Müller-Petke, M. and Yaramanci, U., 2010, QT inversion—comprehensive use of the complete surface NMR data set. Geophysics, 75, WA199–WA209.

Müller-Petke, M., Dlugosch, R. and Yaramanci, U., 2011, Evaluation of surface nuclear magnetic resonance-estimated subsurface water content, New journal of physics 13, DOI:10.1088/1367-2630/13/9/095002.

Nabighian, M. N., 1988, Electromagnetic methods in applied geophysics-Theory. SEG.

Perttu, N., 2011, Magnetic Resonance Sounding (MRS) in Groundwater Exploration, with Applications in Laos and Sweden, Ph.D. thesis, Department of Civil, Environmental and Natural resources engineering Luleå University of Technology.

Plata, J. L. and Rubio, F. M., 2008, The use of MRS in the determination of hydraulic transmissivity: the case of alluvial aquifers. J Appl Geophys, 66, 128–139.

Semenov, A. G., Pusep, A. Ju. and Schirov, M. D., 1982, (In Russian) ‘Hydroscope-an installation for prospecting without drilling’ USSR Academy of Sciences, Novosibirsk, USSR.

Semenov, A., 1987, NMR hydroscope for water prospecting, in: Proceedingsof the Seminar on Geotomography. 66–67.

Semenov, A., Schirov, M., Legchenko, A., Burshtein, A. and Pusep, A., 1989, Device for measuring the parameter of underground mineral deposits, Great Britain, Patent 2198540B.

Shirov, M., Legchenko, A. and Creer, G., 1991, A new direct non-invasive groundwater detection technology for Australia.Export.Geophys., 22: 333-338.

Shushakov, O., 1996, Groundwater NMR in conductive water, Geophysics, 61 (4), 998–1006.

Trushkin, D. V, Shushakov, O. A. and Legchenko, A. V., 1995, Surface NMR applied to an electro conductive medium. Geophysical Prospecting, 43, 623–633.

Valla, P. and Legchenko, A., 2002, Surface nuclear magnetic resonance-what is possible, Journal of Applied Geophysics 50, 1–229.

Varian, R., 1962, Ground liquid prospecting method and apparatus, US Patent.

Vouillamoz J. M., Legchenko, A., Albouy, Y. and Bakalowicz, M., 2003, Localization of Saturated Karst Aquifer with Magnetic Resonance Sounding and Resistivity Imagery, Groundwater , 41(5), 578–586.

Weichman, P. B., Lavely, E. M. and Ritzwoller, M., 1999, Surface nuclear magnetic resonance imaging of large systems, Physical Review Letters, 82 (20), 4102–4105.

Weichman, P. B., Lavely, E. M. and Ritzwoller, M. H., 2000, Theory of surface nuclear magnetic resonance with applications to geophysical imaging problems, Physical Review E 62 (1, Part B) 1290–1312.

Weichman, P. B., Lun, D. R., Ritzwoller, M. H. and Lavely, E. M., 2002, Study of surface nuclear magnetic resonance inverse problems, Journal of Applied Geophysics, 50 (1–2), 129–147.

Yaramanci, U. and Hertrich, M., 2007, Inversion of magnetic resonance sounding data, Boltein Geologico y minero, 118 (3), 473-488.

Yaramanci, U. and Legchenko, A., 2005, Magnetic resonance sounding, aquifer detection and characterization, Near Surface Geophysics 3,119–222.

Yaramanci, U. and Muller-Petke, M., 2009, Improvement in inversion of magnetic resonance exploration-water content, decay time, and resistivity, Journal of earth science, 20(3), 592-605.