基于ADI-S-FDTD的低频天地波传播综合建模及预测

Spatial medium characteristics of the earth-ionosphere system are key factors that affect the low frequency (LF) sky-surface wave propagation. FDTD prediction models have proven to be of higher accuracies than that of the analytic method as the medium distribution is complex. However, the traditional FDTD method is facing difficulty in dealing with the models which have random characteristics at the same time. The computing resources can hardly meet the needs for the FDTD codes should be run thousands of times. In this work, a new hybrid method—alternating direction implicit stochastic FDTD (ADI-S-FDTD) is to be constructed by combining the advantages of the stochastic FDTD (S-FDTD) and the leapfrog alternating direction implicit FDTD (leapfrog ADI-FDTD) methods together. The ADI-S-FDTD is to be taken as the fundamental method for the integrated modeling of the LF sky-surface wave propagation. An efficient scheme how to obtain the statistical properties of the field strength loss and time delay through one simulation is to be studied. The influences of the complex earth, atmosphere and ionosphere will all be taken into account. Aiming at the problem that the correlation coefficient approximations affect the variance accuracy much, the correlation coefficients’ fitting and inversion of the random variables are to be studied based on the Monte Carlo method. For the long distance propagation prediction cost too much computational resource, several methods and techniques are combined innovatively with ADI-S-FDTD together, mainly including: (1) the analytical methods; (2) Segmented Long Path Propagation, Moving Window techniques; (3) MPI+OpenMP+CUDA three-level parallel techniques. By applying the strategies above, the accuracy and efficiency of the model algorithm will be significantly improved again, and the computational cost will be reduced further. Deterministic and stochastic two models are to be adopted to validate the ADI-S-FDTD algorithm, respectively. Then, the LF sky-surface wave propagation properties in the real earth-ionosphere systems are to be studied. The work is expected to provide more theory basis for the LF radio wave applications in many fields.

地—电离层中空间媒质是影响低频电波传播特性的关键因素，传统FDTD预测模型能克服解析方法在处理媒质具有复杂分布特性时精度低的局限，但当其同时具有随机特性，数千次仿真是计算资源难以容忍的。项目拟采用随机FDTD结合Leapfrog ADI-FDTD的方式，提出交替方向隐式随机FDTD（ADI-S-FDTD）新方法，对低频天地波传播进行综合建模，研究通过一次仿真得到同时包含地层、空气层及电离层影响的电波统计特性的高效方案。针对算法中随机量相关系数近似影响方差精度的问题，研究基于蒙特卡罗方案的相关系数拟合与反演；针对算法长距离传播预测应用，研究与解析方法、与分段长距离、滑动窗、MPI+OpenMP+CUDA三级并行等多种技术相结合策略，再次大幅提高算法精度与效率，减少资源占用。采用确定和随机两种模型验证算法有效性。对实际地—电离层中电波传播特性进行预测分析，为天地波的联合应用提供理论依据。

地—电离层中空间媒质是影响低频电波传播特性的关键因素，项目以地波绕射理论、天波“波跳”理论为基础，跟踪国际上FDTD新近研究成果，将Leapfrog ADI-FDTD与随机FDTD方法相结合，针对天地波传播机理、天地波综合建模、随机FDTD方法中相关系数拟合、长距离传播预测技术、随机模型验证等问题进行了深入研究，取得了一系列成果：（1）引入球面校正因子和高程转换技术对积分方程方法进行改进，解决其与其它经典算法在光滑路径模型下预测结果不一致的问题，改进算法更适合考虑地球曲率影响下复杂长距离地面及空中地波传播特性的求解；（2）基于分步离散混合傅立叶算法实现了双向窄角、宽角抛物方程方法，在该方法中引入方向性因子的影响，解决了在近轴、高仰角过渡区域电波传播预测及后续数值模型中馈源及空间场验证问题；（3）提出基于交替方向隐式随机FDTD（ADI-S-FDTD）方法的天地波传播综合建模方案，通过一次仿真即可得到同时包含地层、空气层及电离层影响的电波统计特性，该方案对于具有二维复杂尺度结构、随机变化的传播模型特性求解具有高效、高精度的优势；（4）采用与抛物方程方法、分段长距离、滑动窗、多级并行等技术相结合的策略，大幅提高算法精度与效率，减少资源占用，并在项目研究过程中进一步提出了将数值方法与“波跳”理论相结合的新方案，借助天地波分离技术对天波进行“分区”、“分跳”修正，再由修正后的各跳天波对观测点信号进行合成重构；（5）对复杂地—电离层中低频电波传播特性进行预测分析，重点研究了罗兰-C信号水下色散、海岸效应、地—电离层波跳现象；（6）依据合作单位试验平台对天、地波信号的长期监测数据，对定点区域天地波信号时变特性、扰动量级、电离层反射高度、模型参数反演等问题进行了初步探讨。本项目研究成果可为天地波的联合应用、水下及空间导航授时应用拓展提供一定理论依据。

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