مجله ژئوفیزیک ایران

مجله ژئوفیزیک ایران

برآورد عمق بررسی در مدل‌سازی وارون توموگرافی مقاومت ویژه الکتریکی

نوع مقاله : مقاله پژوهشی‌

نویسندگان
1 کارشناسی ارشد ژئوفیزیک، ، گروه فیزیک زمین، موسسه ژئوفیزیک، دانشگاه تهران، تهران،ایران
2 دانشیار، گروه فیزیک زمین، موسسه ژئوفیزیک، دانشگاه تهران، تهران، ایران
چکیده
برآورد صحیح و مناسب عمق قابل‌بررسی در مطالعات توموگرافی مقاومت ویژه الکتریکی هنگام ساخت مدل‌های زمین‌شناسی و هیدروژئولوژیکی از مجموعه داده‌های صحرایی بسیار مهم است؛ زیرا آگاهی از عمق قابل‌بررسی امکان اعتبار سنجی مدل‌های منتج شده از مدل‌سازی وارون را فراهم می‌آورد. عمق ‌بررسی به عمقی اطلاق می‌شود که در عمق های بیشتر از آن داده‌های ژئوفیزیکی سطحی (یا هوابرد) به‌دست‌آمده نسبت به خواص فیزیکی لایه‌های زیرسطحی زمین حساس نیستند. به عبارت دیگر عمقی که در آن تغییرات فیزیکی زیر سطحی تاثیر چندانی در اندازه گیری های ژئوفیزیکی و نیز مدل بدست آمده از مسئله وارون ندارند. در بررسی های توموگرافی مقاومت ویژه الکتریکی، باهدف برآورد توزیع رسانندگی لایه های زیرسطحی، داده ها (مقاومت ویژه ظاهری) وارد یک مسئله وارون غیرخطی می شوند. سپس این مسئله وارون طی یک فرآیند تکراری و تحت قیود فیزیکی مناسب حل می شود. استنباط صحیح از مدل زمین شناسی زیرسطحی با استفاده از توزیع پارامتر فیزیکی مقاومت ویژه الکتریکی از طریق ارزیابی عمق قابل‌اطمینان از مدل منتج شده است. در همین راستا در این مقاله ابتدا رهیافتی برای محاسبه عمق قابل‌بررسی در توموگرام‌های مقاومت ویژه الکتریکی ارائه می شود. همچنین برای بررسی بیشتر از ماتریس حساسیت و نیز شاخص حساسیت به مدل اولیه نیز استفاده می‌شود. نتایج عددی بر روی داده های مصنوعی و واقعی نشان می دهد که نتایج به‌دست‌آمده از هر سه معیار یعنی عمق قابل‌بررسی، ماتریس حساسیت و شاخص حساسیت به مدل اولیه تا حدود زیادی یکدیگر را تائید می کنند. همچنین مشاهده می شود که عدم اطلاعات (داده) کافی منجر به افزایش عدم قطعیت در مقطع وارون شده می‌شود که این موضوع به‌صورت کاهش عمق قابل‌بررسی، کمتر شدن میزان حساسیت و افزایش مقدار شاخص حساسیت به مدل اولیه می شود.
کلیدواژه‌ها

عنوان مقاله English

Estimating depth of investigation in electrical resistivity tomography Inverse modelling

نویسندگان English

Reza Ghanati 1
Fateme Farahmand 2
1 M.Sc. Graduated, Department of Earth Physics, Institute of Geophysics, University of Tehran,Tehran,Iran
2 Associate Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran,Tehran,Iran
چکیده English

Correct and appropriate estimation of the depth of investigation (DOI) in electrical resistivity tomography (ERT) studies is crucial for constructing geologic and hydrological models from field data sets. Understanding the DOI allows for the validation of models resulting from inverse modeling. The investigation depth typically refers to the depth below which surface (or airborne) geophysical data obtained are not sensitive to the physical properties of subsurface layers of the Earth. In other words, it is the depth at which the geophysical techniques used in an investigation become insensitive to subsurface changes. Estimating this depth is essential for resistivity (DC) and induced polarization (IP) investigations when interpreting the models obtained from inverse modeling. This is because the structure beneath it has a greater depth of uncertainty compared to other parts of the inverted model and must be carefully interpreted from a geological perspective. The depth of investigation is influenced by various factors, such as receiver sensitivity, measurement accuracy, operating frequencies, ambient noise level, exploration target characteristics, host rock, and data processing and interpretation techniques. Several resolution indicators can be used to estimate the depth of investigation or to identify possible artifacts in the electrical structures. Understanding the quantitative relationship between survey depth and these factors is crucial for users to achieve their geological objectives, minimize unnecessary survey costs, and uncover meaningful geological features. In electrical resistivity or induced polarization (IP) tomography studies, the data, including apparent resistivity or apparent induced polarization, is used to solve a nonlinear inverse problem. This problem is addressed through an iterative process known as the Occam’s inversion method with appropriate physical constraints to avoid unrealistic subsurface features. Accurate interpretation of the subsurface geological model relies on the distribution of specific physical parameters, such as electrical resistance and chargeability, and enables reliable depth assessment. This study presents an approach to calculate the detectable depth (DOI) in electrical resistivity tomograms. Additionally, the sensitivity matrix (SM) and the sensitivity index to the primary model (SIM) are employed for further investigation. To evaluate the proposed method, a synthetic model and a real dataset are utilized. Numerical results obtained from synthetic and real data demonstrate a strong agreement among all three criteria i.e., DOI, SM, and SIM. It is worth noting that insufficient information (data) leads to increased uncertainty in the inverted cross-section, resulting in a decrease in the DOI index, a decrease in sensitivity, and an increase in the SIM value.
 

کلیدواژه‌ها English

Depth of investigation (DOI), electrical resistivity tomography (ERT), fré
chet derivatives, uncertainty quantification
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