(1. 中南大學(xué) 地球科學(xué)與信息物理學(xué)院，長沙 410083；
2. 中南大學(xué) 地球科學(xué)與信息物理學(xué)院 有色金屬成礦預(yù)測教育部重點實驗室，長沙 410083)
摘 要: 為了進一步減小截斷邊界對探地雷達(GPR)數(shù)值模擬精度的影響、提高復(fù)雜GPR地電模型數(shù)值模擬的精度，采用具有良好寬頻帶吸收特性的單軸各向異性完全匹配層(UPML)吸收邊界條件與有限單元法(FEM)相結(jié)合的算法來模擬GPR波在復(fù)雜地電模型中的傳播。從GPR滿足的波動方程出發(fā)，利用伽遼金法導(dǎo)出二維GPR有限元方程。然后，對UPML區(qū)域滿足的兩個頻率域旋度方程采用傅里葉變換，推導(dǎo)GPR時間域有限元波動方程及其求解方法，并建立相應(yīng)的GPR數(shù)值模擬算法。應(yīng)用以上算法編制的程序?qū)蓚€復(fù)雜GPR地電模型進行了正演模擬，得到了相應(yīng)的雷達剖面圖。模擬結(jié)果表明：UPML吸收邊界條件能夠?qū)財噙吔缣幍膹娏曳瓷洳ㄟM行充分的吸收，大大減弱了截斷邊界處的強反射；FEM能夠?qū)?fù)雜的GPR地電模型進行高精度的模擬。基于UPML吸收邊界條件的FEM算法能夠?qū)?fù)雜的GPR地電模型進行快速、高效的模擬。
關(guān)鍵字: UPML；吸收邊界；探地雷達；數(shù)值模擬；有限單元法
（1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;
2. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education,
School of Geosciences and Info-Physics, Central South University, Changsha 410083, China）
Abstract:To decrease the influence of truncation boundaries on the GPR numerical simulation precision availably and improve the precision of complex GPR geo-electric model numerical simulation, the FEM, combined with the UPML boundary condition that is good for absorbing broadband, was used to simulate the propagation of GPR wave in complex GPR geo-electric model. Firstly, starting from wave equation satisfying the GPR, Galerkin method was employed to deduce the two-dimension GPR FEM equation; then, based on the two frequency-domain curl equations which conformed in the UPML field, the GPR time-domain FEM wave equation and its solution were deduced by Fourier transform in details, and then the corresponding GPR simulation algorithm was set up. Finally, the program that was compiled by above algorithms was used to forward model the two complex GPR geo-electric models, and two profile maps of the forward models were obtained. The simulated results demonstrate that UPML boundary condition can fully absorb the super-strong reflection wave on the truncation boundaries, and greatly weaken the strong reflection of truncating boundaries. FEM can simulate complex GPR geo-electric model high accurately. Using the FEM algorithm based on UPML boundary condition can simulate the complex GPR geo-electric models quickly and efficiently.
Key words: UPML; ground penetrating radar; numerical simulation; finite element method
