基于全空间初始场源的半空间TEM三维FDTD正演

Half-space TEM 3D FDTD forward modeling based on whole-space initial field

传统TEM三维FDTD正演,受相邻网格步长比例和最大与最小网格步长比例限制,难以模拟小尺度和多尺度模型;对于基于半空间初始场源的正演,多采用向上延拓的地空边界处理方法,难以处理带地形模型和航空探测模型.针对以上问题,提出了基于全空间初始场源的半空间TEM三维FDTD正演方法.首先,给出了正演方法,其中初始场源采用发射电流关断后某时刻的均匀全空间电磁场,地空边界处理采用设置空气层的方法,在初始场源计算中电阻率参数采用发送回线下方大地电阻率值,在初始时刻和时间步长计算中电阻率参数采用发送回线上方空气电阻率值.然后,建立了半空间均匀介质模型、半空间含低阻层模型和半空间含低阻三维块体模型,开展了正演计算,并将计算结果与其他方法结果进行了对比,验证了方法的可靠性.之后,采用控制变量法分析了网格步长和时间步长与稳定性和计算量的关系,结果表明:相邻网格步长比例为2时仍然可以取得稳定可靠的结果,最大与最小网格步长比例未发现存在限制.基于此性质,可以用较少的网格数量构建很大的模型,从而减小计算量,提高计算精度,且适用于小尺度、大尺度和多尺度模型的模拟.最后,给出了带地形模型、航空探测模型和多尺度模型的模型算例,验证了方法的适用性.提出的正演方法具有稳定性好、计算效率高、适用范围广的优势,实现了全空间正演和半空间正演的统一,适用于多领域(巷道、隧道、带地形的地面、航空探测等)和广尺度(小尺度、大尺度和多尺度)正演.

Traditional TEM 3 D FDTD forward modeling is limited by the proportion of adjacent grid steps and the proportion of maximum and minimum grid steps, which is difficult to simulate small-scale and multi-scale models. Besides, the method based on half-space initial field adopts the ground air boundary processing method of upward continuation, which is difficult to deal with the terrain model and airborne model. To solve the above problems, half-space TEM 3 D FDTD forward modeling based on whole-space initial field is proposed. Firstly, method is given. Uniform whole-space electromagnetic field at an initial time after emission current turn off is used as the initial field. Air layer is used to deal with the ground air boundary. In the initial field calculation, the resistivity parameter adopts the earth resistivity value below the transmitting loop. In the initial time and time step calculation, the resistivity parameter adopts the air resistivity value above the transmitting loop. Then, the half-space uniform medium model, the half-space model with low resistivity layer and the half-space model with a 3 D block are established. Forward calculations are carried out, and calculation results are compared with those of other methods. Results show that the calculation results of the proposed method are consistent with those of other methods. Furthermore, stability and calculation amount of the proposed method are analyzed. Results show that stable and reliable results can be obtained when the adjacent grid step scale is 2. The ratio of maximum and minimum grid steps is not found to be limited. Therefore, a large model can be built with a small number of grids, so as to reduce the amount of calculation and improve the calculation accuracy, and suitable for the simulation of small-scale, large-scale and multi-scale models. Finally, forward modeling examples of the terrain model, the airborne model and the multi-scale model are given, which illustrate the applicability of the method. The proposed method realizes the unity of whole-space forward modeling and half-space forward modeling, and can be used to a wide range of detection fields, including roadway, tunnel, ground with terrain, airborne detection and multi-scale model.