时域瞬变电磁法三维有限差分正演技术研究

瞬变电磁法应用广泛,三维数值模拟是研究复杂地质模型异常响应规律的重要技术手段之一,也是反演的基础.目前瞬变电磁数值模拟的不足主要有两个方面:第一,场源是在地表水平、浅层介质均匀的条件下计算的,限制了应用范围;第二,地下边界采用Dirichlet边界条件,导致计算空间很大,耗时较长.针对上述问题,在三维正演时,场源采用有限长细导线模型,在Maxwell有源差分方程中直接加入电流密度进行计算.在地表面加入空气层,避免了复杂的向上延拓计算,也可以对地形影响下的响应规律进行分析.在空气边界和地下边界均采用CPML吸收边界条件,并改进了CPML的参数分布,能够吸收空气介质和大地介质中的低频电磁波而反射误差极小,在满足计算精度的条件下可以有效减小节点数量.对循环迭代方法进行优化,将计算域、CPML区域和场源的空间循环统一转化为矩阵方式,加快了计算速度,但是空间消耗增大了约4~5倍.采用三维有限差分正演算法对均匀半空间模型、层状模型和地形模型进行了计算,并与解析解进行了对比验证.

Three-dimensional finite difference forward modeling of the transient electromagnetic method in the time domain

The transient electromagnetic method (TEM) is widely used in many fields, Three-dimensional numerical simulation is one of the important approaches to study the abnormal response of the complex geological model as well as the foundation of inversion. There are two main problems in the numerical simulation of this method. First, the source is calculated under the condition that the surface is horizontal and near the surface of the ground is homogeneous, which limits the scope of application. Second, the underground boundary are given Dirichlet boundary conditions so that the calculated space is large and time-consuming. To solve these problems, a finite length thin-wire model is used in three-dimensional forward modeling, so the current density can be calculated directly in the Maxwell difference equation. On the ground surface, the air layer is added to avoid the complicated upward continuation calculation, and the response of the terrain can be analyzed. On the air boundary and underground boundary CPML an absorbing boundary condition is used to replace the Dirichlet boundary. The parameter distribution of CPML is improved, which can absorb the low-frequency electromagnetic waves in the air medium and the earth medium, and the reflection error is very small. This method can effectively reduce the number of nodes in the condition satisfying the accuracy of calculation. The multi-iteration calculations of the computation domain, the CPML region and the source are optimized and replaced by the matrix method. The computation speed is accelerated by the matrix mode, but the space consumption is increased by about 4~5 times. The three-dimensional FDTD algorithm is used to calculate the homogeneous half space model, the H-type interlayer model and different terrain models, and their results are compared with the analytical solution.