为衰减地质雷达数值模拟时因截断区域厚度或者参数影响产生的倏逝波,提出了一种利用复频移完美匹配层(complex frequency shifted perfectly matched layer,CFS-PML)作为吸收边界,并结合频域高阶有限元算法(higher order finite element...为衰减地质雷达数值模拟时因截断区域厚度或者参数影响产生的倏逝波,提出了一种利用复频移完美匹配层(complex frequency shifted perfectly matched layer,CFS-PML)作为吸收边界,并结合频域高阶有限元算法(higher order finite element method,HO-FEM)求解电磁总场分量分布情况的新方法.该方法改善了截断域介质本构张量矩阵的特性,利用矩阵频移参量α吸收倏逝波,提高掠射角处吸收性能.数值实验结果表明,与传统PML相比,结合CFS-PML的HO-FEM方法精度得到明显提高,反射误差额外降低10~30 dB,节省了17%~30%的计算时间.此外,该方法能应用于复杂地质结构模型的电磁总场计算,为地质雷达数值模拟提供了一种新的方法.展开更多
This study used the stable and convergent Dufort-Frankel method to differentially discretize the diffusion equation of the ground-well transient electromagnetic secondary field.The absorption boundary condition of com...This study used the stable and convergent Dufort-Frankel method to differentially discretize the diffusion equation of the ground-well transient electromagnetic secondary field.The absorption boundary condition of complex frequency-shifted perfectly matched layer(CFS-PML)was used for truncation so that the low-frequency electromagnetic wave can be better absorbed at the model boundary.A typical three-dimensional(3D)homogeneous half-space model was established and a low-resistivity cube model was analyzed under the half-space condition.The response patterns and drivers of the low-resistivity cube model were discussed under the influence of a low-resistivity overburden.The absorption boundary conditions of CFS-PML significantly affected the low-frequency electromagnetic waves.For a low-resistivity cube around the borehole,its response curve exhibited a single-peak,and the extreme point of the curve corresponded to the center of the low-resistivity body.When the low-resistivity cube was directly below the borehole,the response curve showed three extreme values(two high and one low),with the low corresponding to the center of the low-resistivity body.The total field response of the low-resistivity overburden was stronger than that of the uniform half-space model due to the low-resistivity shielding effect of electromagnetic waves.When the receiving-transmitting distance gradually increased,the effect of the low-resistivity overburden was gradually weakened,and the response of the low-resistivity cube was strengthened.It was affected by the ratio of the overburden resistivity to the resistivity of the low-resistivity body.展开更多
文摘为衰减地质雷达数值模拟时因截断区域厚度或者参数影响产生的倏逝波,提出了一种利用复频移完美匹配层(complex frequency shifted perfectly matched layer,CFS-PML)作为吸收边界,并结合频域高阶有限元算法(higher order finite element method,HO-FEM)求解电磁总场分量分布情况的新方法.该方法改善了截断域介质本构张量矩阵的特性,利用矩阵频移参量α吸收倏逝波,提高掠射角处吸收性能.数值实验结果表明,与传统PML相比,结合CFS-PML的HO-FEM方法精度得到明显提高,反射误差额外降低10~30 dB,节省了17%~30%的计算时间.此外,该方法能应用于复杂地质结构模型的电磁总场计算,为地质雷达数值模拟提供了一种新的方法.
基金This work was supported by China Postdoctoral Science Foundation(No.2022M723391)the Science and Technology Innovation Project of Higher Education in Shanxi Province(No.2019L0754)+1 种基金the Central Guiding Local Science and Technology Development Fund Project(No.YDZJSX2021B021)Shanxi Province Basic Research Plan General Project(No.202203021221294).
文摘This study used the stable and convergent Dufort-Frankel method to differentially discretize the diffusion equation of the ground-well transient electromagnetic secondary field.The absorption boundary condition of complex frequency-shifted perfectly matched layer(CFS-PML)was used for truncation so that the low-frequency electromagnetic wave can be better absorbed at the model boundary.A typical three-dimensional(3D)homogeneous half-space model was established and a low-resistivity cube model was analyzed under the half-space condition.The response patterns and drivers of the low-resistivity cube model were discussed under the influence of a low-resistivity overburden.The absorption boundary conditions of CFS-PML significantly affected the low-frequency electromagnetic waves.For a low-resistivity cube around the borehole,its response curve exhibited a single-peak,and the extreme point of the curve corresponded to the center of the low-resistivity body.When the low-resistivity cube was directly below the borehole,the response curve showed three extreme values(two high and one low),with the low corresponding to the center of the low-resistivity body.The total field response of the low-resistivity overburden was stronger than that of the uniform half-space model due to the low-resistivity shielding effect of electromagnetic waves.When the receiving-transmitting distance gradually increased,the effect of the low-resistivity overburden was gradually weakened,and the response of the low-resistivity cube was strengthened.It was affected by the ratio of the overburden resistivity to the resistivity of the low-resistivity body.
