基于有限差分的瞬变电磁三维数值模拟
发布时间：2019-04-24 12:28
【摘要】：近年来,瞬变电磁仪的研制取得了巨大突破,使得我们能够采集到高精度的野外数据,但是目前我们对瞬变电磁法的理论研究还不够深入,资料处理、反演解释水平不高,不能很好发挥瞬变电磁法的优势。尤其在反演方面,一维反演仍然是最常用的手段,二维、三维反演依然处于起步阶段,使得我们无法将瞬变电磁法应用于地下复杂的三维地质构造的研究中去。为了更好地发展三维反演技术,就必须充分了解瞬变场在地下三维复杂介质中的响应特性,为此,本文针对回线源瞬变电磁法的时域有限差分(FDTD)三维数值模拟进行了如下研究：首先采用YEE(1966)交错网格方案和Wang Hohmann(1993)提出的改进的DuFort-Frankel方案对均匀网格剖分下Maxwell方程的FDTD离散形式进行了推导。激励源采用软源直接注入的方式施加,即源所在网格,需要在无源媒质的Maxwell方程组右端项中加入源电流密度,将其修改为有源情况下的方程。这种以软源直接注入来施加激励源的方式克服了Wang Hohmann以均匀半空间解析解作为初始时刻电磁场值的局限性,可以模拟无法计算解析解的任意复杂三维模型的瞬变电磁响应。其次本文还研究了边界条件的设置、稳定性条件及数值色散等问题。并给出了适用于多种回线源装置(中心回线、重叠回线、大定回线源),任意激励源激发的瞬变电磁法三维有限差分数值模拟程序。分别计算了均匀半空间瞬变场解析解、水平层状模型数字滤波解,并将它们和本文给出的FDTD解进行了对比分析。结果表明,均匀半空间解析解、水平层状模型数字滤波解与FDTD解的整体相对误差均在可以接受的范围内,平均相对误差达到4%以内。之后针对一系列复杂三维模型的瞬变电磁响应进行了数值模拟,最终通过快速反演证明本文给出的三维FDTD解精度高、结果稳定,能适应三维复杂介质的数值模拟。最后以本文得出的瞬变电磁理论为基础,对山西朔州安家岭露天煤矿的实际野外瞬变电磁勘探数据进行了处理,绘制了各测线视电阻率拟断面图,并利用现有的一维反演软件IX1D进行了反演解释,最终推断得到了地下三维空间下的煤层采空区赋存状态,并且结果得到了实际地质资料的验证。
[Abstract]:In recent years, the development of transient electromagnetic instrument has made a great breakthrough, so that we can collect high-precision field data, but at present our theoretical research on transient electromagnetic method is not deep enough, the data processing, the level of inverse interpretation is not high. The advantage of transient electromagnetic method can not be brought into play well. Especially in inversion, one-dimensional inversion is still the most commonly used means, two-dimensional, three-dimensional inversion is still in its infancy, which makes it impossible for us to apply the transient electromagnetic method to the study of the complex underground three-dimensional geological structure. In order to better develop 3D inversion technology, it is necessary to fully understand the response characteristics of transient field in underground 3D complex medium. In this paper, the finite-difference time-domain (FDTD) three-dimensional numerical simulation of loop source transient electromagnetic method is studied as follows: firstly, the improved DuFort-Frankel scheme proposed by YEE (1966) staggered grid scheme and Wang Hohmann (1993 is used to simulate uniformity. In this paper, the FDTD discrete form of the Maxwell equation is derived. The excitation source is directly injected into the soft source, that is, the source is in the grid, and the source current density is added to the right end of the Maxwell equation system of the passive medium, and the source current density is modified to the equation in the active case. This method overcomes the limitation of Wang Hohmann using uniform half-space analytical solution as the initial time electromagnetic field value, and can simulate the transient electromagnetic response of any complex three-dimensional model which cannot be calculated by analytical solution. Secondly, the setting of boundary conditions, stability conditions and numerical dispersion are also studied. A three-dimensional finite difference numerical simulation program of transient electromagnetic method for multiple loop source devices (center loop, overlapping loop, large definite loop source) and arbitrary excitation source is also given in this paper. The analytical solutions of the transient field in homogeneous half-space and the digital filtering solutions of the horizontal layered model are calculated and compared with the FDTD solutions given in this paper. The results show that the global relative errors of the analytical solution of the homogeneous half-space, the digital filtering solution of the horizontal layered model and the FDTD solution are all within acceptable range, and the average relative error is less than 4%. Then the transient electromagnetic response of a series of complex three-dimensional models is numerically simulated. Finally, it is proved by fast inversion that the three-dimensional FDTD solution presented in this paper has high accuracy, stable results and can adapt to the numerical simulation of three-dimensional complex medium. Finally, on the basis of the transient electromagnetic theory obtained in this paper, the actual field transient electromagnetic survey data of Anjialing opencast coal mine in Shuozhou, Shanxi Province are processed, and the quasi-sectional diagrams of the apparent resistance rates of each line are drawn. The existing one-dimensional inversion software IX1D is used to carry out the inversion interpretation. Finally, the occurrence state of coal seam goaf in underground three-dimensional space is inferred, and the results are verified by the actual geological data.
【学位授予单位】：中国地质大学(北京)
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.325
本文编号：2464447
[Abstract]:In recent years, the development of transient electromagnetic instrument has made a great breakthrough, so that we can collect high-precision field data, but at present our theoretical research on transient electromagnetic method is not deep enough, the data processing, the level of inverse interpretation is not high. The advantage of transient electromagnetic method can not be brought into play well. Especially in inversion, one-dimensional inversion is still the most commonly used means, two-dimensional, three-dimensional inversion is still in its infancy, which makes it impossible for us to apply the transient electromagnetic method to the study of the complex underground three-dimensional geological structure. In order to better develop 3D inversion technology, it is necessary to fully understand the response characteristics of transient field in underground 3D complex medium. In this paper, the finite-difference time-domain (FDTD) three-dimensional numerical simulation of loop source transient electromagnetic method is studied as follows: firstly, the improved DuFort-Frankel scheme proposed by YEE (1966) staggered grid scheme and Wang Hohmann (1993 is used to simulate uniformity. In this paper, the FDTD discrete form of the Maxwell equation is derived. The excitation source is directly injected into the soft source, that is, the source is in the grid, and the source current density is added to the right end of the Maxwell equation system of the passive medium, and the source current density is modified to the equation in the active case. This method overcomes the limitation of Wang Hohmann using uniform half-space analytical solution as the initial time electromagnetic field value, and can simulate the transient electromagnetic response of any complex three-dimensional model which cannot be calculated by analytical solution. Secondly, the setting of boundary conditions, stability conditions and numerical dispersion are also studied. A three-dimensional finite difference numerical simulation program of transient electromagnetic method for multiple loop source devices (center loop, overlapping loop, large definite loop source) and arbitrary excitation source is also given in this paper. The analytical solutions of the transient field in homogeneous half-space and the digital filtering solutions of the horizontal layered model are calculated and compared with the FDTD solutions given in this paper. The results show that the global relative errors of the analytical solution of the homogeneous half-space, the digital filtering solution of the horizontal layered model and the FDTD solution are all within acceptable range, and the average relative error is less than 4%. Then the transient electromagnetic response of a series of complex three-dimensional models is numerically simulated. Finally, it is proved by fast inversion that the three-dimensional FDTD solution presented in this paper has high accuracy, stable results and can adapt to the numerical simulation of three-dimensional complex medium. Finally, on the basis of the transient electromagnetic theory obtained in this paper, the actual field transient electromagnetic survey data of Anjialing opencast coal mine in Shuozhou, Shanxi Province are processed, and the quasi-sectional diagrams of the apparent resistance rates of each line are drawn. The existing one-dimensional inversion software IX1D is used to carry out the inversion interpretation. Finally, the occurrence state of coal seam goaf in underground three-dimensional space is inferred, and the results are verified by the actual geological data.
【学位授予单位】：中国地质大学(北京)
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.325
【参考文献】
相关期刊论文 前1条
1 张玉良;马安丽;;瞬变电磁法在基岩找水中的应用[J];地下水;2010年04期
，本文编号：2464447
本文链接：https://www.wllwen.com/kejilunwen/diqiudizhi/2464447.html
