مجله ژئوفیزیک ایران

مجله ژئوفیزیک ایران

برآورد هم‌زمان ساختارهای هموار و بلوکی در وارون‌سازی توموگرافی داده‌های مقاومت ویژه الکتریکی

نوع مقاله : مقاله پژوهشی‌

نویسندگان
1 کارشناسی ارشد ژئوفیزیک، موسسه ژئوفیزیک، دانشگاه تهران، تهران، ایران
2 دانشیار، موسسه ژئوفیزیک، دانشگاه تهران، تهران، ایران
چکیده
توموگرافی مقاومت ویژه الکتریکی روشی برای تصویرسازی ساختارهای زیر سطحی  بر مبنای ویژگی‌های الکتریکی آن ساختار است. توموگرافی الکتریکی در واقع روشی است که می­توان با استفاده از آن توزیع فضایی خاصیت رسانندگی لایه­های زیرسطحی را از طریق عبور یک جریان الکتریکی در­همان فضا تعیین کرد؛ بنابراین در توموگرافی الکتریکی یک جریان الکتریکی به درون زمین ارسال شده و پاسخ زمین نسبت به این جریان برحسب ولتاژ اندازه گرفته می­شود؛ سپس با استفاده از روش‌های عددی حل مسائل وارون غیرخطی و با داشتن حل مسئله پیشرو، مدلی از توزیع رسانندگی زیرسطحی برآورد می­شود. در این پژوهش، حل مسائل وارون برای توموگرافی داده‌های مقاومت ویژه الکتریکی بررسی و مدلی ارائه می­شود که بتواند خصوصیات هموار و لبه‌دار آنومالی و مرزهای لایه‌های زمین را پیش‌بینی کند. دو روش منظم‌سازی تیخنوف و تغییرات کلی، برای حل مسئله وارون مورداستفاده قرار گرفته است. در منظم­سازی تیخنوف از تکنیک گوس نیوتن  و در روش تغییرات کلی از الگوریتم IRLS به‌عنوان یک الگوریتم سریع و کاربردی در به کمینه‌سازی تابع هدف کلی و یافتن مدل نهائی استفاده می­شود. در گام بعدی با هدف برآورد هم­زمان ویژگی­های هموار و بلوکی مدل­های زیر سطحی، یک تابع هدف مشترک براساس ویژگی­های دور روش منظم­سازی تیخنوف و تغییرات کلی ارائه می­شود. عملکرد الگوریتم پیشنهادی ابتدا بر روی مدل‌های مصنوعی مورد ارزیابی قرار می‌گیرد و سپس در داده‌های صحرایی تجزیه‌وتحلیل می‌شود. نتایج عددی نشان می­دهد که روش بهینه­سازی پیشنهادی با در نظر گرفتن هم­زمان ویژگی­های هموار و بلوکی می‌تواند مدلی دقیق‌تر از توزیع رسانندگی الکتریکی زمین را ارائه دهد.
کلیدواژه‌ها

عنوان مقاله English

Simultaneous estimation of smooth and blocky structures in tomographic inversion of electrical resistivity data

نویسندگان English

Pardis Salehi 1
Reza Ghanati 2
1 M.Sc. Graduated, Institute of Geophysics, University of Tehran,Tehran, Iran
2 Associate Professor, Institute of Geophysics, University of Tehran,Tehran, Iran
چکیده English

Electrical resistivity tomography is a non-invasive, near-surface geophysical technique commonly used for creating detailed images of the subsurface. It plays a crucial role in diverse geoscientific fields, such as subsurface resource exploration, environmental and engineering studies, soil characteristics determination, mapping hydrogeophysical properties. Electrical resistivity tomography is a technique that allows the spatial distribution of electrical conductivity (or equivalently resistivity) to be determined by passing an electric current through the Earth subsurface and measuring the Earth's response in terms of electrical voltage. Subsequently, numerical methods are used to solve nonlinear inverse problems and interpret the results. The method's adaptability and precision have made it indispensable in applications ranging from groundwater exploration and contamination assessment to archaeological investigations and infrastructure stability evaluations. Recent advancements in Electrical resistivity tomography technology, including higher resolution imaging and improved inversion algorithms, have further expanded its utility and accuracy in complex geology. In this study, the focus is on achieving a more accurate characterization of the physical properties of the subsurface Earth. The goal is to develop a model that can accurately predict the characteristics of smooth and sharp anomalies as well as the boundaries of subsurface layers. Two regularization methods including Tikhonov regularization and total variation regularization are considered. Tikhonov regularization utilizes the Gauss-Newton technique, while total variation regularization employs the Iteratively Reweighted Least Squares (IRLS) algorithm as a fast and practical approach for minimizing the overall objective function and obtaining the final model. IRLS is an optimization technique commonly used to solve problems where the objective function can be expressed as a weighted least squares problem. Tikhonov regularization leads to a smooth model of subsurface structures, while total variation regularization emphasizes edge enhancement. Since subsurface layers may simultaneously contain smooth and sharp (edge-like) structures, using only one of these methods would result in the loss of the other features. Therefore, to preserve both characteristics, this study proposes a novel strategy based on the simultaneous use of both Tikhonov and total variation regularization within a common objective function to obtain a model of electrical conductivity variations in subsurface layers that closely matches reality. The performance of the proposed algorithm is first evaluated on several synthetic models with different features. Then, its functionality is assessed through its application to field data. Numerical results demonstrate that the proposed approach enables the creation of a model of subsurface electrical conductivity distribution that bears a closer resemblance to subsurface reality.

کلیدواژه‌ها English

Electrical reisitivity tomography
tikhonov regularization
total variation
ill-posedness
IRLS
Gauss-Newton
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