(長安大學(xué) 地質(zhì)工程與測繪學(xué)院，西安 710054)
摘 要: 地形的起伏嚴(yán)重影響著電磁場分布，在實(shí)際資料處理中，研究地形起伏對電磁場的畸變規(guī)律可使電磁勘探解釋更加準(zhǔn)確可信。采用任意四邊形網(wǎng)格剖分求解區(qū)域，實(shí)現(xiàn)起伏地形2.5維電偶源有限元正演算法，推導(dǎo)波數(shù)域電磁場耦合微分方程，通過基于等參單元的雙二次插值將連續(xù)函數(shù)的微分離散化；采用一維非零元素緊縮存儲(chǔ)，利用大規(guī)模稀疏矩陣并行求解器PARDISO求解，得到電偶源激發(fā)下二維地電斷面的波數(shù)域電磁場響應(yīng)。然后通過選取適當(dāng)?shù)牟〝?shù)進(jìn)行傅里葉反變換，獲取空間域電磁場響應(yīng)，對正演中的關(guān)鍵問題，如波數(shù)的選擇、場源參數(shù)的選取以及輔助場的計(jì)算等進(jìn)行了分析和研究，為提高正演計(jì)算的精度和速度提供了理論保證。驗(yàn)證該算法的正確性和高效性，分別對山丘和山谷等典型地形進(jìn)行了數(shù)值計(jì)算，分析起伏地形的電磁場響應(yīng)規(guī)律。
關(guān)鍵字: 電偶源；等參單元；起伏地形；數(shù)值模擬
（School of Geology Engineering and Geomatics, Chang’an University, Xi’an 710054, China）
Abstract:The topography seriously affects the distribution of electromagnetic field, and the study on distortion law of topography for the electromagnetic field can make the electromagnetic interpretation more accurate and reliable in the actual data processing work. The electric dipole source electromagnetic field finite element algorithm of 2.5D rugged topography was studied by using arbitrary quadrilateral mesh generation for computational domain. Firstly, the electromagnetic coupled differential equations in wave number domain was deduced, and continuous function was discretized based on the isoparametric element of interpolation, the wave number domain electromagnetic response is obtained for the two dimensional geoelectric section by a nonzero element compact storage and large-scale parallel sparse matrix solver PARDISO. The electromagnetic field space response is got by choosing appropriate wave number of the inverse Fourier transform. The forward key problems, such as the selection of wave number, source selection and the auxiliary field solution, were analyzed and studied, which provide a theoretical guarantee for improving the computation precision and speed. The correctness and high efficient of the algorithm were verified. Finally, the electromagnetic response characteristics of the trapezoidal hill and valley were analyzed.
Key words: electric dipole source; isoparametric element; ridge terrain; numerical simulation
