3D Modeling Of Transient Electromagnetic Data Using Mimetic Finite Volume And Rational Krylov Space Methods

Precise detection of complex electrical targets is a leading-edge topic in transient electromagnetic(TEM)research,in which the interpretation and inversion method is playing an important role.However,at present,the forward algorithm has still not been well solved,which becomes the main bottleneck in the development of the interpretation method.To solve this problem,this thesis is trying to set up a framework for 3D modeling of TEM data,and developing a set of an accurate,stable,efficient and flexible algorithm.The main innovative work is as follows:(1)To solve the modeling problem of the TEM method under the assumptions of different types of configuration and different types of geophysical models,the mimetic finite volume method was used to discrete the space domain.Based on the idea of “mimetic operator,” we obtain discrete forms of differential operators and then give out different methods for computing the initial fields corresponding to the circular loop source,ground wire source,and complex loop source.(2)To improve the computational efficiency of the time integration,the rational Krylov space algorithm with single repeated poles is used.Based on the error analysis theory,an alternative single repeated pole optimization search method is proposed;and then the magnetic responses are obtained efficiently by combing the use of the rational Arnoldi algorithm and LU decomposition technique.The model calculation results show that the algorithm is reliable,accurate,and is much more efficient than that of the conventional implicit time-stepping methods.(3)To overcome the difficulties in dealing with the time domain response calculation in the case of arbitrary anisotropic media,another rational Krylov algorithm based on the electric field is proposed,and the effects of arbitrary anisotropic media on the responses of ground-airborne TEM data is discussed.(4)To modeling of the on-time TEM responses with rational Krylov methods,the exponential quadrature rule and trapezoidal quadrature rule are used,and then the magnetic field can be represented as a matrix function.The accuracy and universal applicability of the algorithm are verified with typical theoretical waveforms and realistic waveforms.Through the study of the above works,a set of the transient electromagnetic 3D forward algorithms was finally formed with high accuracy,strong stability,high efficiency and strong applicability.These algorithms can be used for the development of a 3D inversion algorithm.In addition,they can also be used to simulate 3D complex models with different types of TEM configurations,therefore provide useful tools for understanding the physical laws of the TEM responses to the 3D models and give out guidelines for optimal designing of TEM configurations.The mimetic operators formed in this thesis can also be applied to the simulation of other types of EM problems.