Scattering And Transmission Of Low Frequency Electromagnetic Waves In Inhomogeneous Media

With the popularity of logging while drilling(LWD)and measurement while drilling(MWD)technology in logging engineering,the key issues: high-speed transmission of measurement signals,fast and efficient interpretation and evaluation of logging data have become the focus of academic research.The essence of these technical problems is the scattering and transmission of electromagnetic waves in inhomogeneous media.Due to the complex inhomogeneity of the background medium,numerical modeling and theoretical analysis of the electromagnetic problems therein become more complicated.Moreover,due to the multipath effect caused by the background of the inhomogeneous medium,it will interfere with the wirelessly transmitted signal and greatly reduce the quality of the received signal.The work of this paper focuses on the research of wireless transmission of signals between top and bottom of the well,as well as the efficient numerical modeling and imaging algorithm research of electromagnetic induction logging technology.First of all this paper introduces the numerical modeling method used in the study of forward modeling problems in the background of inhomogeneous media.The numerical mode matching(NMM)method is used to solve the two-dimensional forward problem,and its principle and solution process are introduced in detail.For the threedimensional forward problem,the volume integral equation is first established,and then the method of moments is used to solve the problem.The main process is given in this paper.Because the traditional numerical mode matching method is inferior in solving electromagnetic problems in low-loss and lossless medium.In this paper,the split-field perfectly matching layer(PML)has been combined with NMM method to improve the accuracy of the solution.By deducing the condition that the cylindrical electromagnetic wave shoots on the interface of the PML without reflection,the design scheme of the electrical parameters of the PML is given,and finally the high-precision solution of the electromagnetic problem in the low-loss and lossless medium is realized.Then,facing the challenges when wirelessly transmitting the LWD and MWD signal underground,the idea of using multi-relay cooperative wireless transmission has been proposed in this paper.In the relatively weak contrast layer,the multi-relay cooperative transmission strategy of storage and in-phase re-transmitting is used.This method draws on the principle of the traveling wave array in the homogeneous medium,and realizes the approximate in-phase superposition of the multi-channel signals transmitted by different relays at the receiving position.It reduces the interference between multi-channel signals.For the stratum with strong contrast,an adaptive field focusing cooperative transmission strategy is proposed.This method needs to perform a pre-test first,and then according to the principle of reciprocity,realizes the signals transmitted by different relays superimposed in phase at the receiving location when the stratum electrical parameters are unknown.The multi-relay cooperative wireless transmission method can make up for the weakness of the underground signal transmission distance not far enough.Moreover,while uploading or downloading signals,the signal strength of the reverse transmission can be suppressed to reduce the interference of the reverse transmission signal to the forward transmission signal,thereby further improving the quality of the received signal.In this paper,the NMM method combined with the PML proposed above is used to numerically model the multi-relay cooperative transmission scheme of LWD and MWD signals,and the effectiveness of the proposed multi-relay cooperative transmission method in different stratum environments is verified.In order to realize the efficient inversion of formation electrical parameters using electromagnetic induction logging data,this paper proposes a new scheme for efficient inversion based on volume integral equation.In the new scheme,the homogeneous medium background Green's function is used as the integral kernel of the volume integral equation,and all other regions different from the homogeneous medium are treated as scatterers.The efficiency of the algorithm is greatly improved by avoiding calculating the Green's function of the inhomogeneous medium background.Moreover,the increase in the number of scatterers does not increase the number of unknowns to be inverted,and the number of unknowns to be inverted is the same as the number of unknowns to be inverted in the case of using an inhomogeneous medium background.Then,based on the new scheme,this paper proposes three inversion strategies.The first two strategies have the advantages of strong stability and fast iterative convergence.The third strategy has the advantages of both,and is more suitable for solving electromagnetic inverse scattering problem with noise interference.The numerical examples are used to verify the advantages of the new scheme for solving the electromagnetic inverse scattering problem in complex environments,and compare the advantages and disadvantages of different inversion strategies.In addition,for the case of noise interference in the actual inversion problem,this paper proposes a new iterative strategy based on the Born iterative method for solving the inversion problem with noise interference.In the new iterative strategy a new parameter,balance factor,is introduced.The influence of different values of the balance factor on the performance of the algorithm is studied.A calculation formula for determining a relatively good balance factor is given in the case where the signal-to-noise ratio of the measured signal is known to be received.Through analysis and numerical verification,the new iterative strategy can achieve faster convergence speed while ensuring iterative convergence.Moreover,it can also be combined with the new inversion scheme proposed above to efficiently solve the electromagnetic Inverse scattering problem in the inhomogeneous medium background.Finally,this paper proposes a subspace-based variational Born iterative method,which combines the subspace-based optimization method with the variational Bonn iterative method.In the new method,the total field approximation accuracy inside the scatterer is higher than the approximation accuracy of the total field in the variational Bonn iterative method,which makes the new method have faster convergence speed and better quality of the image than the variational Bonn iterative method.