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معکوسسازی خطی دو‌بعدی دادههای الکترومغناطیس زمینی حوزه فرکانس با چشمه مصنوعی در محدوده عدد القاء کوچک | ||
| فیزیک زمین و فضا | ||
| مقاله 4، دوره 48، شماره 3، آذر 1401، صفحه 557-573 اصل مقاله (4.22 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22059/jesphys.2022.334600.1007385 | ||
| نویسندگان | ||
| حسینعلی قاری* 1؛ رامین ورفی‌نژاد2 | ||
| 1استادیار، دانشکده مهندسی معدن و متالورژی، دانشگاه یزد، یزد، ایران | ||
| 2دانش‌آموخته دکتری، گروه فیزیک زمین، مؤسسه ژئوفیزیک، دانشگاه تهران، تهران، ایران | ||
| چکیده | ||
| به‌منظور بازسازی مقاطع رسانایی الکتریکی زیرسطحی با استفاده از دادههای ژئوالکترومغناطیس حوزه فرکانس تحت شرایط عدد القاء کوچک، یک الگوریتم مدلسازی معکوس تکراری در دو بعد از طریق رویکرد معادلات انتگرال خطی در محیط برنامهنویسی MATLAB توسعه داده شده است. الگوریتم معکوسسازی حاضر بر اساس یک مدلسازی پیشرو خطی دو‌بعدی بنا نهاده شده است که برای حل این مسئله پیشرو از راه‌حل عددی بهجای شیوه تحلیلی استفاده میشود. از قابلیتهای این الگوریتم خطی، محاسبه کرنل تنها در یک مرحله و استفاده از آن در تمام تکرارها میباشد که باعث افزایش سرعت محاسبات میشود. ورودی این فرایند معکوسسازی، مقادیر رسانایی الکتریکی ظاهری میباشند. برای بهینهسازی تابع هدف از شیوه کمترین‌مربعات وزن داده‌شده با حضور منظمسازی و همچنین اعمال قید، از طریق تابع وزن‌دهی عمقی، استفاده شده است که از شدت عدم‌یکتایی و ناپایداری آن کاسته شود. در این تحقیق، مقدار اولیه پارمتر منظمسازی با استفاده از بیشنه مقدار ماتریس عملگر پیشرو حاصل و سپس بهینه میشود. الگوریتم مذکور قادر به معکوسسازی در دو حالت منفرد و توأمان آرایههای همصفحه افقی و همصفحه قائم میباشد. صحت این الگوریتم با استفاده از دادههای حاصل از دو مدل مصنوعی، مدل اول شامل یک آنومالی در دو حالت افقی یا قائم و مدل دوم شامل چهار آنومالی با ابعاد و موقعیتهای مختلف، و همچنین دادههای مربوط به یک دایک ضخیم در آفریقای جنوبی ارزیابی میشود. دادهها از طریق شرایط دستگاههای EM31، EM34 و EM38 شبیهسازی یا برداشت شدهاند. نتایج معکوسسازیها کارآیی روش را در حد مطلوب نشان میدهند. | ||
| کلیدواژه‌ها | ||
| ژئوالکترومغناطیس حوزه فرکانس تحت شرایط عدد القاء کوچک؛ مدلسازی پیشرو؛ معادلات انتگرال خطی؛ معکوسسازی توأمان؛ تابع وزن‌دهی عمقی | ||
| عنوان مقاله [English] | ||
| 2D Linear inversion of ground-based controlled-source electromagnetic data under a low induction number condition | ||
| نویسندگان [English] | ||
| Hosseinali Ghari1؛ Ramin Varfinezhad2 | ||
| 1Assistant Professor, Faculty of Mining and Metallurgical Engineering, Yazd University, Yazd, Iran | ||
| 2Ph.D. Graduated, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran | ||
| چکیده [English] | ||
| Low-induction-number frequency-domain geoelectromagnetic (LIN-GeoFEM) instruments are ground conductivity meters that use a small coil transmitter (Tx) and one coil receiver (Rx). This coil–coil system is designed to propagate alternating electromagnetic fields through the earth at small Tx–Rx separations and low frequency and receive the EM field coupling in the shallow subsurface to provide direct measures of the apparent electrical conductivity. This measured property is a complicated average of spatially distributed localized electrical conductivities in the subsurface. Instruments capable of operating as LIN FEM instruments include the EM38, EM31, and EM34 (Geonics Ltd., Mississauga, ON), the DUALEM instruments series (DUALEM, Inc., Milton, ON), the GEM instrument series (Geophex Ltd., Raleigh, NC) and CMD series (GF Instruments, s.r.o.). The Tx and Rx coils can be oriented relative to each other and the earth's surface. Orientations considered in this study are horizontal coplanar (HCP) (both coils lie flat on the ground) and vertical coplanar (VCP) (coils are upright and coplanar). The range of LIN FEM instruments applications for environmental and hydrologic characterization and monitoring is large and increasing. The LIN-GeoFEM applications are industrially feasible as long as there is a reasonably fast algorithm that is accurate enough to invert the survey data. Furthermore, forward modeling plays a key role in the inversion procedure. The linear integral equation (IE) method is a powerful tool in EM forward modeling for geophysical applications, especially for simple background conductivity structures. The main advantage of the IE method in comparison with the finite difference (FD) and finite element (FE) methods is its fast and accurate simulation of the response for models with compact 2-D or 3-D bodies in a layered background. The main limitation of the IE method is that the background conductivity model must have a simple structure to allow for an efficient Green’s function calculation. Fortunately, the most widely used background models in LIN-GeoFEM explorations are those formed by horizontally homogeneous layers. A main issue is that the EM field integral equation is nonlinear. However, an approximate linear equation is obtained for the electromagnetic induction at low induction numbers using the Born approximation. A 2D forward modeling code for LIN-GeoFEM is developed based on the integral equation (IE) method. Here, a linear relation between model parameters and apparent conductivity values is proposed. The 2D problem is obtained from 3D using numerical integration along the y-axis (strike direction) from minus infinity to infinity. So, the linear approximation is applied to the 2D inversion of LIN measurements. We use a damped minimum length solution using depth weighting to solve this problem iteratively. Thus, we obtain a better estimate of conductivity in a few iterations. Using this 2D linear inversion or imaging technique, we can produce reasonably good results of inverting jointly and individually VCP and HCP for low and moderate conductivity contrasts. To validate the algorithm, we consider two 2D synthetic scenarios and field data acquired on a thick conductive dyke in the Bloemfontein Nature Reserve region in South Africa. The first synthetic scenario consists of one 3 W.m conductive horizontal or vertical prism immersed in a 100 W.m resistive host. In this example, the recovered models from the inversion of the HCP (VMD) and VCP (HMD) data show good results for the vertical and horizontal prism, respectively. The second scenario simulates four 20 W.m conductive vertical and horizontal prisms in a 100 W.m resistive background. The recovered conductivity from the inversion of the VCP data has the weakest results, especially in the case of vertical prisms. In the conductivity section from the inversion of HCP data, the existence of the four anomalous bodies is evident. However, the image obtained from the joint inversion of HCP and VCP data has generated useful information about the true model in all recovered models. The result of jointly inverting VCP and HCP field data confirms the presence of the dyke as a zone of low conductivities. | ||
| کلیدواژه‌ها [English] | ||
| Low-induction-number frequency-domain geoelectromagnetic, forward modeling, linear integral equations, joint inversion, depth weighting | ||
| مراجع | ||
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