Analysis Of Low-Frequency Near Field In Inhomogeneous Media And Its Application In Detection

In the analysis of electromagnetic field and its application in detection, the research of low-frequency near field is always challenging and very important in real-life applications. On the one hand, it has broad future and pratical value, such as the application of electromagnetic well-logging problems and investigation of the geophysical structures which have been put into much research effort. On the other hand, the analysis of low-frequency near field has always been a hard zone in numerical computation and analysis. The existing methods have been seriously chanllenged especially when one has to face the large-and multi-scale problems. To deal with these challenges, in this dessertation, these problems are first classified into quasi-static potential field problems and time harmonic field problems based on the physic principle of the near field. And then each kind of problem is handled with different modeling strategy and analysis method. To deal with the time harmonic low-frequency near field problems, this dessertation developed the finite element domain decomposition method combined with tree-cotree splitting strategy and higher order transmission conditions, and then implemented it into the analysis of the forward electromagnetic well-logging problems. Based on the method, the modeling, design and realization of the low-frequency near-field detecting sensors are accomplished easily to gain multi-dimensional information of the earth. Finally, to have a fast inversion of the parameters of3D objects in complex problems, this dessertation proposed a fast3D full-wave inverse method combined with domain decomposition framework based on the research of the existing inverse methods. The inverse method proposed in this dessertation can perform fast inversion of the unknown objects in the low-frequency near-field detection problems.First of all, to model the quasi-static potential field well-logging problems, this dessertation uses scalar finite element method to analysis the quasi-static potential field problems using Laplace equation as the constraint equation, and put forward several important issues in the modeling of quasi-static potential field problems. This dessertation finds out that the traditional far-field truncating boundary condition is no longer suitable for the potential field analysis for the first time and thus put forward a new far-field truncating boundary condition for the real application. Additionally, this dessertation implements another two boundary conditions to optimize the electromagnetic model which are the periodic boundary condition and equal potential field condition. Finally this dessertation build up a unified model both containing the field parameters and circuit parameters and get the numerical result of the slight and important changes of the response for the tools. The numerical results have proved the accuracy and advantage of our proposed quasi-static potential field modeling techniques.At the second part, the vector finite element method and its non-conformal domain decomposition method (NC-FEM-DDM) are developed and optimized for the analysis of the time harmonic field problems. Based on the research of the vector FEM and comparison of basis functions based on different element types, this dessertation introduces a hexahedral hierarchical basis function, which can be very adaptive to the modeling of a complex multi-scale problem and consequently capable of modeling complex low-freqeuncy near field problems. However, in the application of a large-scale problem, the traditional FEM will suffer from large amounts of work load, memory cost and computational time because of its unified modeling strategy, especially when the excitation sources has to move in the need of scanning detection. Additionaly, numerical methods such as FEM will suffer from low-frequency break down and accurarcy loss. To solve the above problems, domain decomposition method is first developed to divide the original problems into several subdomains so that one can compute each subdomain independently and improve parallel efficiency. Then, based on the existing transmission conditions, an improved transmission condition is used to couple fields from different subdomains efficiently. This transmission condition has a more clustered eigenvalue distribution compared with the existing ones and thus it has faster convergence in both high-frequency band and low-frequency band. To solve the low-frequency break down problem, a tree-cotree splitting (TCS) strategy is then applied to eliminate the low-frequency breakdown at very low frequencies. Numerical results of the advanced well-logging problems such as the dielectric scanning tool, directional resistivity logging-while-drilling (LWD) tool, the micro-resistivity scanning tool and the three induction array tool all show an excellent convergence and accuracy obtained with the DDM with TCS at any frequencies.In the low-frequency near-field problems, the analysis and design of the detecting sensors are very important because one need to get multi-dimensional information of the earth. Based on the development and improvement of the NC-FEM-DDM with TCS, series of3D induction sensor arrays have been designed at first. These designs have three orthometric polarized components so that the dip formation and the anisotropic bed can be interpreted. In these designs, the compact wind of the coils greatly shortened the length of the tool and the easy-implementing cancellation of the direct coupling largely improved the signal noise ratio (SNR). Based on the designings, this dessertation accomplished the fabrication, coil winding, system debugging and experiments in the experimental well and finally put out the3D induction array tool. Besides, to gain azimuthal resolution in the investigation, the analytical expression for the electric field of the tilted sensor as magnetic dipole is first derived. The directional component of the dipole was extracted. Then, through the field distribution of single transmitter with different tilt angles and the field distribution of combination of transmitters with different polarizations, clear strategies are illustrated on improving the azimuthal resolution of directional sensors. Based on it, novel transmitter-receiver designs are put forward and modeled using an efficient and accurate finite-element-based domain decomposition method. The results not only testify the designing strategies with better azimuthal resolution, but also indicate that there is still great potential in optimizing the azimuthal resolution of the directional propagation tools.Finally, this dessertation has taken an over view of the existing inverse method to deal with the low-frequency and near-field inverse problems. A fast full-wave inverse scheme is developed combined with a domain decomposition method (DDM) so that the3D objects in complex real-life applications can be easily inversed as well. The division of the solution domain will bring huge advantage in the memory cost, parallel efficiency and computation time. Besides that, the object domain, whose parameters are unknown, is separated from the peripheral devices and outer boundaries so that only the object domain has to be recalculated, which will cut down the redundant computational burden in the inversion compared with other methods based on FEM. This nonlinear inverse scheme is implemented successfully for3-D full-wave problems such as the magnetic induction tomography (MIT) and ground penetrating radar, showing that this method is a robust and efficient3-D full-wave inverse method.