| The electromagnetic(EM)exploration has been successfully applied to many fields such as resource and energy exploration,geological hazard assessment,and hydrological,engineering and environmental geological investigation,which are closely related to the national property.It is well known that undulating terrain has a great influence on EM exploration,therefore the corresponding forward and inversion under undulating terrain conditions are always topical and difficult studies in this field,even though certain advancements have been obtained in recent years.However,these researches were carried out in the open domain of half-space.The accurate and efficient EM imaging studies of objects with bending surfaces such as cylinders,ellipsoids,and dams in the closed or semi-open domains are still extremely rare.With the expansion of EM imaging to the application fields such as biomedicine,forestry,and material testing,the 2.5-dimensional resistivity imaging of cylindrical objects is widely introduced to the non-invasive testing of growing trees and medical imaging of human organs.Nevertheless,the problem that the current field excited by a point source on the surface of a cylinder is very different from that of the traditional undulating terrain has not been well solved,leading to the fact that many EM imaging results are obtained by using the experimentally acquired empirical formulas to correct the resistivity data or basing on the numerical calculations that are developed for the half-space condition.The ground-penetrating radar(GPR)of cylindrical objects can achieve relatively high accuracy,but using this method can be quite difficult to quantitatively analyze the electrical parameters.Successful three-dimensional resistivity images of dams and ellipsoidal objects such as human brains have not been achieved yet.Therefore,the study of accurate and efficient EM imaging of objects with bending surfaces has great theoretical significance and application value.For the 2.5-dimensional resistivity imaging of cylindrical objects,the selection of the wavenumber is associated with the accuracy of the forward modeling and is thus directly related to the accuracy of resistivity tomography.The optimization wavenumber selection is derived based on the analytic potential solution of an infinitely long homogeneous cylindrical model with the point source being on the surface.Since the direct and accurate analytic potential solution of an infinitely long homogeneous cylindrical model is not available,most studies directly use the wavenumbers derived from the half-space condition.In this thesis,a 2.5-dimensional unstructured finite element numerical simulation of an infinitely long homogeneous cylindrical model is implemented to systematically analyze the effect of the optimization wavenumber corresponding to the half-space condition on the forward modeling of the cylindrical objects,and the results show that it can cause large errors.We then employ a fitting method to explicitly solve the inverse Fourier transform of the wavenumber domain and derive the approximate analytical potential solution on the cross-section where the point source is located.Based on those researches,the optimization wavenumber selection algorithm and the geometric factor are re-derived.Laboratory experiments of the cylindrical objects were carried out and the measured field data proved that the new optimization wavenumber could improve the accuracy of the 2.5-dimensional forward modeling of the cylindrical model.Based on the new optimization wavenumber sequence,the accurate and complete resistivity forward and inversion for the cylindrical model are developed.The resisti vity tomography of the synaptic data has achieved good results.In the meanwhile,the inversion results of the experiment data of the cylindrical models are in good agreement with the actual model,which proves that the algorithm proposed in this paper is accurate and reliable.In order to quantitatively and simultaneously inverse the geometrical and electrical parameters of a cylindrical model by GPR,we study the full-wave inversion of the cylindrical objects.The cylindrical Green’s functions and the far-field model are firstly combined to solve the radar response of a cylindrical model,based on which the influences of the radius,conductivity,and relative permittivity of a cylinder on the radar response are analyzed,laying the foundation for the full-wave inversion of the cylindrical objects.Then,we design six sets of experiments detecting cylindrical objects with different parameters,use the far-field model to perform antenna correction on the radar signal,and achieve the full-wave inversion of cylindrical objects in combination with the far-field model for the first time.The results show that the fullwave inversion can inverse the radius and the relative permittivity simultaneously,but cannot obtain the radius and conductivity simultaneously,because the radar wave responses of these two parameters are coupled to each other.The current distortion on the bending surfaces of dams and ellipsoids is relatively large.For the detection of dams,two-dimensional resistivity profiles along the top or slope of the dam are usually obtained.Obtaining accurate images of the dangers hidden inside the dam is uneasy under this condition.The resistivity imaging of the human brain,breast,and other approximate ellipsoid organs is also dominated by twodimensional algorithms,which makes it difficult to identify lesions inside the human body.In this thesis,three-dimensional resistivity imaging is performed for both models.Firstly,efficient and accurate finite element numerical simulations of the objects with bending surfaces are achieved using Gmsh for unstructured mesh generation of the models.Secondly,fast and accurate three-dimensional resistivity imaging of dams as well as ellipsoidal models are obtained by exploiting the favourable condition that the transmitting and receiving electrodes can be placed randomly on the surfaces of the ellipsoidal objects and dams,which are closed or semi-open domain surfaces. |
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