وارون‌سازي محتواي آب سيگنال سونداژ تشديد مغناطيسي، مطالعه موردي نينه محلات، ايران مركزي

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

روش سونداژ تشديد مغناطيسي تنها روش ژئوفيزيكي است كه به‌طور مستقيم به مولكول‌هاي آب زيرسطحي حساس مي‌باشد. با استفاده از وارون‌سازي داده‌هاي سونداژ تشديد مغناطيسي مي‌توان اطلاعات مهمي از قبيل ضخامت و عمق لايه آبخوان، محتواي آب و در شرايطي مناسب، ميزان رسانندگي هيدروليكي لايه آبدار را به‌دست آورد. اين روش به‌شدت به اندازه و نوع نوفه حساس است؛ لذا تخمين پارامترهاي سيگنال و نيز وارون‌سازي آن حساسيت بالايي دارد. وارون‌سازي داده‌هاي سونداژ تشديد مغناطيسي يك مسأله بدوضع مي‌باشد و نمي‌توان با استفاده از روش‌هاي مستقيم آن را حل كرد. به‌همين دليل استفاده از روش‌هاي منظم‌سازي در وارون­سازي سونداژ تشديد مغناطيسي امري اجتناب‌ناپذير است. روش‌هاي متعددي جهت حل مسأله وارون سونداژ تشديد مغناطيسي پيشنهاد شده است. رهيافت هندسه ثابت و رهيافت هندسه متغير، همراه با بهره‌گيري از روش‌هاي مختلف بهينه‌سازي تابع هدف از جمله اين روش‌ها است. در اين مقاله از رهيافت هندسه ثابت و اعمال منظم‌سازي تيخنوف همراه با قيدهاي مناسب، جهت وارون‌سازي و مدل‌سازي پيشرو استفاده شده است. خروجي حاصل از داده‌هاي مصنوعي، و داده‌هايي از ايران و آلمان به‌عنوان داده‌هاي كم آب و پرآب، نتايج قابل قبولي از تغييرات محتواي آب نسبت به عمق و به‌كار‌گيري روش ارائه شده نشان مي­دهد.

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.