# مدل‌سازی سه‌بُعدی مقاومت ویژه الکتریکی و قُطبش القایی به روش اجزای محدود در آرایش الکترودی مستطیلی

نوع مقاله : مقاله تحقیقی‌ (پژوهشی‌)

نویسندگان

دانشکده مهندسی معدن و متالورژی، دانشگاه یزد، ایران

چکیده

آرایش مستطیلی یکی از آرایش‌های الکترودی است که کاربرد زیادی در تحقیقات ژئوالکتریک و قُطبش القایی دارد. هدف از این آرایش محدود کردن مناطق وسیع به‌خصوص در اکتشاف کانسارهای سولفیدی است. برخلاف کاربرد وسیع آن کمتر به مدل‌سازی و اعتبارسنجی نتایج حاصل از آن پرداخته شده است.
یک مدل سه‌بُعدی مقاومت ویژه الکتریکی و قُطبش القایی برای برداشت های ژئوالکتریک با آرایش مستطیل و با استفاده از روش اجزای محدود در نرم‌افزار کمسول اسکریپت (COMSOL Script) توسعه داده و به زبان مطلب (MATLAB) برنامه‌نویسی شد. مدل‌سازی قُطبش القایی در حوزه بسامد مستقیما با حل عددی معادلات ماکسول صورت پذیرفت. از مدل کل-کل(Cole-Cole)  برای تعیین رابطه مقاومت ویژه الکتریکی و ثابت دی‌الکتریک نسبی با بسامد استفاده شد. نتایج نشان می‌دهد تفسیر کیفی که با استفاده از نقشه مقاومت ویژه الکتریکی ظاهری و درصد اثر بسامد به‌دست آمده، زمانی صحیح است که بی‌هنجاری زیرسطحی ابعاد بزرگ، عمق کم و رسانایی زیادی داشته باشد. تعیین ضخامت توده رسانا در جهت قائم و تشخیص جهت قرارگیری توده رسانا با نقشه‌های مقاومت ویژه ظاهری و قُطبش القایی به‌دست آمده از برداشت با آرایه مستطیل، امکان‌پذیر نیست. همچنین، نتایج نشان می‌دهد که تفسیر کیفی روش مقاومت ویژه الکتریکی نتایج بهتری در ارتباط با هندسه بی‌هنجاری، نسبت به قُطبش القایی نمایش می‌دهد.

کلیدواژه‌ها

عنوان مقاله [English]

### 3D Modeling of resistivity and IP data for rectangle array using Finite Element Method

نویسندگان [English]

• Zahra Falsafin
چکیده [English]

Rectangle array is widely used in resistivity and induced polarization (IP) studies. The purpose of this array is to restrict the wide areas especially in the exploration of sulfide minerals. On the contrary to the wide application of this array, less attention has been paid to the results of modelling and true estimates. The interpretations are normally qualitative.
A 3D resistivity and IP model was developed for the geoelectric surveys with a rectangle array. We used the COMSOL environment to solve the DC-resistivity and Maxwell’s equations by the finite element method. Codes were programmed in Matlab language.
A common geometry of the model space was used for both resistivity and IP modelling. In the rectangle array, two current electrodes were located in a large distance and different potentials were measured on the profiles parallel to the current electrodes. Our model was formed by a homogeneous half space (a large block with dimensions 800 × 800 × 500 m3, with a resistivity of 400 ohm.m). Two current electrodes with a 200-m distance were located on the surface. Non-polarizing electrodes were located in a 5-m distance. The two measuring electrodes were moved on the profiles (parallel to the current electrode direction). Nine parallel profiles were located symmetrically on each side of the current electrode direction. Each profile had a 40-m length. The distance between the profiles was 5 m. The electrode configuration could be changed in the model. IP and resistivity anomalies could be created from different blocked locations in the subsurface (into the half space). The blocks near the potential profiles had small dimensions. The block sizes increased as the depth increased. We calculated the geometrical factor for the half-space. Apparent resistivity for each dual potential electrode was calculated from different potentials measured during the code execution and its geometry factors.
We compared the results from different anomalies by sensitivity Δρa/Δρi, where Δρa is the difference between the apparent resistivity of the anomaly and the homogeneous half-space (400 ohm.m) and Δρi is the difference between the resistivity value of the half-space and the anomaly in block number i.
Frequency domain IP was calculated directly from Maxwell's equations. Block scheme of the model done in the modelling space resistivity were used here. There was a resistivity value for each subsurface block in the resistivity model while there were a resistivity and a dielectric value for each block in an IP model. Resistivity and dielectric values of each block are functions of the frequency. We used the Cole-Cole model in order to calculate the resistivity and dielectric values in each frequency. Four intrinsic Cole-Cole parameters (DC-resistivity, chargeability, time constant and frequency relaxation) were considered for each block. During the frequency changes, these parameters were constant. Finally, apparent resistivity and percentage frequency effect (PFE) maps were calculated in a frequency range of 0.1 to 12000 Hz.
In this research, we studied the effect of size, depth and overburden thickness of the subsurface anomalies. The geoelectrical effects of vertical and horizontal anomalies were investigated. The impact of the potential electrode separation was also verified. The results showed that the qualitative interpretation using the apparent resistivity and appearent percentage frequency effect (PFE) maps was correct when anomaly had remarkable dimensions, a small depth and a high conductivity. The apparent-resistivity map reflected the effect of conductive and polarisable anomalies better than the PFE map.

کلیدواژه‌ها [English]

• Induced Polarization
• Electrical resistivity
• Finite element method
• rectangle Array
• modelling
• COMSOL script
• Cole-Cole model
• percent frequency effect