(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) 有色金屬成礦預(yù)測教育部重點(diǎn)實(shí)驗(yàn)室，長沙 410083；
3. 中南大學(xué) 資源勘查與環(huán)境地質(zhì)研究院，長沙 410083)
摘 要: 以旋轉(zhuǎn)交錯(cuò)網(wǎng)格(RSG)差分為基礎(chǔ)，實(shí)現(xiàn)探地雷達(dá)(GPR)在非均勻突變介質(zhì)中的正演數(shù)值模擬。通過利用旋轉(zhuǎn)交錯(cuò)差分算子，將雷達(dá)波場各場分量設(shè)置在非均勻突變介質(zhì)的基本單元中，單元內(nèi)同一物性參數(shù)定義在同一位置，將對(duì)角線方向上物性參數(shù)差分值的線性組合來計(jì)算坐標(biāo)軸方向上的物性參數(shù)差分值，針對(duì)非均勻特征變化劇烈的網(wǎng)格區(qū)域，算法中的單元網(wǎng)格形式不再需要進(jìn)行插值，擴(kuò)寬了數(shù)值穩(wěn)定性條件的限制。推導(dǎo)了適合于探地雷達(dá)的旋轉(zhuǎn)交錯(cuò)網(wǎng)格差分格式及TMy極化模式下的更新方程組，實(shí)現(xiàn)了均勻介質(zhì)和非均勻突變介質(zhì)中的TMy雷達(dá)波場的數(shù)值模擬，并分別從解析解、模擬剖面和波場快照的角度，與標(biāo)準(zhǔn)交錯(cuò)網(wǎng)格差分算法進(jìn)行了對(duì)比。結(jié)果表明，在模擬非均勻特征明顯的介質(zhì)時(shí)，旋轉(zhuǎn)交錯(cuò)網(wǎng)格算法可以選取更大的時(shí)間步長，數(shù)值色散程度控制更好，提高了模擬效率和成像精度，可更有效地指導(dǎo)非均勻突變介質(zhì)中探地雷達(dá)數(shù)據(jù)的解譯。
關(guān)鍵字: 旋轉(zhuǎn)交錯(cuò)網(wǎng)格；標(biāo)準(zhǔn)交錯(cuò)網(wǎng)格；探地雷達(dá)；正演模擬；數(shù)值色散
（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,
Central South University, Changsha 410083, China;
3. Institute of Resources exploration and Environmental Geology, Central South University, Changsha 410083, China）
Abstract:Based on the rotated staggered grid finite-difference, forward simulation in inhomogeneous media with strong discontinuities for ground penetrating radar (GPR) was implemented. By using the rotating staggered difference operator, the GPR wave field components and other physical parameters were distributed in the elementary cells of RSG, in which all field components of one physical property were located at one elementary unit in computational domain, then the difference of field components and physical parameters along the coordinate axes were calculated by using the linear combination value of them across the diagonal coordinate axes, no averaging of elementary cell was needed even in grids-domain with strong heterogeneities, which relax the limitation of the numerical stability condition. The rotated staggered grid finite difference scheme for GPR and the corresponding update equations was deduced in TMy polarization mode, then the numerical simulation of GPR wave field in TMy polarization mode was implemented, in addition, the comparation between the standard staggered grid and RSG was presented from three respects of the analytic solutions, the simulated sections and the field snapshots. The results show that with the more relaxed limitation of the numerical stability condition and the better controlling of numerical dispersion degree, the RSG difference algorithm improves the efficiency and accuracy of simulation, which can effectively guide the GPR data inversion and interpretation in the inhomogeneous media with strong heterogeneities.
Key words: rotated staggered grid; standard staggered grid; ground penetrating radar; forward modeling; numerical dispersion
