瞬变电磁时域有限差分正演模拟

发布时间：2018-04-26 02:13

本文选题：瞬变电磁 + 时域有限差分　；参考：《长安大学》2015年硕士论文

【摘要】：当前,瞬变电磁不仅广泛应用在石油、金属等矿产资源勘查领域,而且还广泛应用在探测采空区、探测基岩等工程领域。相比瞬变电磁实际应用的发展速度,其处理解释的技术却相对落后,一方面是由于本身瞬变电磁的复杂性,另一方面是由于计算机硬件的落后所致。随着计算硬件的快速发展,使较准确地瞬变电磁场的正演模拟成为可能。而研究瞬变电磁正演模拟对瞬变电磁的资料处理及解释来说至关重要,正演模拟也是为进一步研究瞬变电磁方法反演打下基础。目前,瞬变电磁正演模拟的主要方法有:有限差分法,有限元法,积分方程法等。本文采用时域有限差分法,以二维情况下为例,本文介绍了Yee元胞模型[4],一步步推导出了显式的和无条件稳定的电磁场方程差分格式,讨论近似加载源的方式,讨论了地空边界以及地下边界的解决方案,给出比较合适的自适应迭代步长建议。在上述研究基础上,使用C++完成了程序的编写,图形显示主要采用python加matplotlib实现。主要的难点在于地空边界条件的处理上。首先将非均匀网格剖分的地表场值用三次样条插值插成成均匀网格,然后对其作傅里叶正变换,乘以延拓因子后做傅里叶逆变换。过程中所涉三次样条插值及快速傅里叶变换分别采用的是开源的GSL和FFTW3[32,33]。通过均匀半空间解析解与有限差分数值解对比验证了算法的正确性,并完成了电性线源层状介质模型,直立和倾斜的低阻板状体模型,双直立低阻板状体及低阻覆盖层等模型的正演模拟。同时,利用三维有限差分计算了多个模型,正演模拟的结算结果表明,时域有限差分法在TEM中的应用是一种有效地正演方法。
[Abstract]:At present, transient electromagnetism is widely used not only in the exploration of petroleum, metal and other mineral resources, but also in the engineering fields of detecting goaf and bedrock. Compared with the development speed of the practical application of transient electromagnetic, the technology of processing explanation is relatively backward. On the one hand, it is due to the complexity of transient electromagnetism itself, on the other hand, it is caused by the backwardness of computer hardware. With the rapid development of computing hardware, it is possible to simulate the transient electromagnetic field accurately. The study of transient electromagnetic forward modeling is very important to the processing and interpretation of transient electromagnetic data, and the forward simulation is also a foundation for further research on transient electromagnetic method inversion. At present, the main methods of transient electromagnetic forward modeling are: finite difference method, finite element method, integral equation method and so on. In this paper, the finite difference time domain (FDTD) method is used to illustrate the Yee cell model [4]. The explicit and unconditionally stable difference scheme of electromagnetic field equations is derived step by step, and the approximate loading source is discussed. In this paper, the solutions of the ground and air boundary and the underground boundary are discussed, and a more suitable adaptive iterative step size proposal is given. On the basis of the above research, the program is written with C, and the graphic display is mainly realized by python and matplotlib. The main difficulty is to deal with the boundary conditions of the ground and air. The surface field values of non-uniform meshes are interpolated into uniform grids by cubic spline interpolation. Then Fourier positive transformation is performed on them and then Fourier inversion is performed after multiplying them with continuation factors. The cubic spline interpolation and fast Fourier transform are open source GSL and FFTW3 respectively. The correctness of the algorithm is verified by comparing the analytical solution of uniform half-space with the numerical solution of finite difference. The layered dielectric model of electrical line source and the low-resistance plate model of vertical and inclined are completed. Forward modeling of double vertical low resistance plate and low resistance overlay. At the same time, several models are calculated by using 3D finite-difference method. The results of forward simulation show that the finite-difference time-domain method is an effective forward modeling method in TEM.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.325

【参考文献】