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اثر تخمین نوفه در وارون سازی داده‌های توموگرافی مقاومت ویژه الکتریکی | ||
| فیزیک زمین و فضا | ||
| مقاله 5، دوره 49، شماره 1، خرداد 1402، صفحه 75-95 اصل مقاله (1.92 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22059/jesphys.2022.342440.1007428 | ||
| نویسندگان | ||
| یسری آزادی1؛ رضا قناتی* 2 | ||
| 1گروه فیزیک زمین، مؤسسه ژئوفیزیک، دانشگاه تهران، تهران، ایران. رایانامه: yosraazadi@ut.ac.ir | ||
| 2نویسنده مسئول، گروه فیزیک زمین، مؤسسه ژئوفیزیک، دانشگاه تهران، تهران، ایران. رایانامه: rghanati@ut.ac.ir | ||
| چکیده | ||
| تصویر‌سازی دوبعدی الکتریکی تحت عنوان توموگرافی مقاومت‌ویژه الکتریکی از طریق تعریف و حل یک مسئله وارون غیرخطی انجام میشود. در اغلب موارد داده‌های حاصل از برداشت صحرائی به‌دلیل ایده‌آل نبودن دستگاه‌های اندازه‌گیری، شرایط نامناسب برداشت، خطاهای اپراتوری و شرایط زمین‌شناسی، دارای نوفه هستند. آگاهی از توزیع آماری و مقادیر نوفه به‌دلیل ویژگی‌های خاص مسئله وارون می‌تواند نقش محوری در وارون‌سازی مقاومت‌ویژه الکتریکی ایفا کند. به‌طوری‌که برآورد درستی از مقادیر نوفه، مانع برازش بیش از حد و کمتر از حد داده‌های محاسباتی و داده‌های صحرائی در حین وارون‌سازی میشود. در واقع برازش نامناسب (برازشی که مقدار پارامتر خیلی بیشتر یا کمتر از یک باشد) منجر به ایجاد بی‌هنجاری‌‌های کاذب یا از دست دادن جزئیات مهم در مدل وارون نهایی میشود؛ بنابراین برآورد صحیح از سطح نوفه داده‌های صحرایی از طریق مدل‌های ریاضی و یا تکنیک‌های صحرایی با هدف تخمین مدلی نزدیک به واقعیت زمین ضرورتی اجتناب‌ناپذیر است. در این مقاله برای ارزیابی نقش برآورد سطح نوفه داده‌های صحرایی در خروجی مدل‌های وارون، ماتریس وزنی داده‌ها که متشکل از سطح نوفه در هر داده است از طریق دو روش هم‌پاسخی و برانبارش و در قالب آرایه ونر محاسبه میشود. نتایج مدل‌سازی‌های عددی بر‌روی داده‌های مصنوعی و صحرائی نشان می‌دهد که تخمین صحیح ماتریس وزنی داده‌ها منجر به برآورد مدل‌های مقاومت‌ویژه نزدیک به واقعیت زمین میشود. | ||
| کلیدواژه‌ها | ||
| خطای برانبارش؛ خطای هم‌پاسخی؛ تخمین سطح نوفه؛ تفاضل محدود؛ توموگرافی مقاومت ویژه الکتریکی (ERT)؛ وارون‌سازی غیرخطی | ||
| عنوان مقاله [English] | ||
| Influence of noise estimation on Electrical Resistivity Tomography Data Inversion | ||
| نویسندگان [English] | ||
| Yosra Azadi1؛ Reza Ghanati2 | ||
| 1Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran. E-mail: yosraazadi@ut.ac.ir | ||
| 2Corresponding Author, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran. E-mail: rghanati@ut.ac.ir | ||
| چکیده [English] | ||
| Electrical resistivity tomography is a simple, cost-effective, and highly practical method for surveying near-surface properties. Today, this method is widely used in the discovery and exploitation of water resources, archeology, and environmental and hydro-geophysical studies (such as estimating the hydrogeological parameters of the aquifer). In electrical resistivity imaging, according to the purpose and location of data collection, the electrodes are placed in specific arrays, and data collection is performed. The collected data (potential distribution or apparent resistivity) is then transformed into a distribution of actual electrical resistivity values using inverse modeling methods. Imaging requires defining and solving a nonlinear inverse problem. In this strategy, we optimize the objective function, which consists of fitting field and theoretical data. First, the physics of the problem (forward model) is presented by solving Poisson's equation with the finite difference numerical solution method. An accurate and efficient forward calculation is the basis of most processes of the inversion. Calculation of resistivity forward responses is carried out using simulation of the current flow into the earth’s surface through solving Poisson’s equation. In this contribution, a finite-difference algorithm is applied to discretize the simulated models, restricted by a mixed boundary condition. One of the merits of the finite-difference method over the other methods is its well-known ability to quickly approximate the solutions for any arbitrary and complex structure models. The finite-difference method is relatively fast compared with the finite-element method. However, to include a general topography, the finite-element method becomes a better selection despite being computationally expensive. The partial differential equations governing the resistivity problem are obtained by using the principle of conservation of charge and the continuity equation. The inverse problem is then solved by linearizing the problem in different iterations. A significant part of this research is how to perform inverse modeling of electrical resistivity data. The formulation and solution of the forward and inverse problem in this dissertation have been programmed in MATLAB and part of the program has been written in the C language to increase the computing speed. The field data is noisy due to the non-ideal measuring instruments, improperly filed conditions, operator errors, and geological conditions. Noise values can play a pivotal role in the inversion of electrical resistivity due to the special properties of the inverse problem. A proper estimation of field measurements noise level prevents over- or under-fitting of the calculated data and field data during inversion. Improper fitting (i.e., fitting where the value of the parameter is much more or less than one) leads to creating an artifact or loss of important details in the final inverted model. In this paper, to deal with the effect of noise level on the ERT inversion results, two methods of reciprocity error method and stacking error method have been used. The results of numerical modeling show that the appropriate estimation of the noise level leads to the estimation of subsurface resistivity models close to the ground reality. We also provide a comparison between the inversion results obtained with the presence of noise level and those derived without including the weighting matrix into the objective function. | ||
| کلیدواژه‌ها [English] | ||
| Electrical resistivity tomography (ERT), Finite difference, Noise level estimation, Non-linear inversion, Stacking error method, Reciprocity error method | ||
| مراجع | ||
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