Study On 2.5D Numerical Modeling For Transient Electromagnetic Method By Finite Element Method With Topography

The transient electromagnetic method(TEM),which is sometimes called time-domain electromagnetic method(TDEM),is widely used in mineral and oil exploration as well as water exploration,engineering and environment geophysics exploration.The most widely used data processing methods are based on one-dimensional model due to the complication of the electromagnetic responses.The three-dimensional data processing methods are not utility since the forward and inversion codes are computationally very demanding.Thus the 2.5-D problem is introduced into the TEM forward and inversion research.Representing a 3-D source over a 2-D geoelectric model is the so-called 2.5-D problem in which the conductivityσ,dielectric permittivityεand magnetic permeabilityμof the 3-D geoelectric model are invariant along the strike direction.The 3-D problem can be converting into 2-D problem in Fourier domain by applying the Fourier transform to the electromagnetic field with respect to the strike direction. Thus the computing time is reduced compare to the real 3-D problem.And it is more accurate than pure 2-D problem since the source and geoelectric model are three-dimensional.In order to simulate the surveys in mountainous areas,the topography should be considered.This paper deals with the forward numerical modeling for central-loop electromagnetic method with topography using finite element method.The paper consists of six chapters.Chapter one is the introduction in which the background and origin of the subject as well as the progress and problems in the forward and inversion problem for electromagnetic method are introduced.The research target and research content are also introduced.In the second chapter,it deals with the numerical modeling for 2.5-D transient electromagnetic method by finite element method.The 3-D time domain electromagnetic problem is converted into 2-D problem in Laplace and Fourier domain by Laplace transform and Fourier transform.Two coupled governing differential equations for along-strike components of the electric and magnetic fields are obtained.The variational approach is used to obtain the finite element equations from the coupled governing differential equations.The along-strike electric and magnetic fields are solved by the finite element equations.The other electromagnetic components are obtained by the along-strike electric and magnetic fields.Finally the time domain electromagnetic components are obtained by numerical Laplace transform inversion and Fourier transform inversion.In the third chapter,the key problems and their solutions in the numerical modeling for 2.5-D transient electromagnetic method with topography are introduced.It includes the numerical inversion of the Laplace transforms and the Fourier transforms,which are the key issues for the numerical modeling for 2.5D transient electromagnetic method,the solution for the generation of the finite element mesh with topography,the computation method for the all time apparent resistivity defined by both vertical magnetic field and its derivative.In the fourth chapter,it deals with the 1-D transient electromagnetic forward and inversion problem.The formulas of the homogeneous half space electromagnetic responses in Laplace transform and Fourier transform domain with a rectangle loop source under ground are introduced.The apparent vertical conductance interpretation method,which can identify the layers clearly,is introduced into the one-dimensional linear inversion for generating initial earth model.The model parameters are given through the characters of the apparent depth-apparent vertical conductance curves,accomplished with the apparent depth-apparent resistivity curves and apparent depth-smoking-ring resistivity curves.The inversion results show that this inversion approach converges fast and can reduce the affect by equivalence.In the fifth chapter,several forward examples are shown,including 1-D and 2-D models as well as 2-D model with topography.Finally,chapter six arrives at some conclusions.The remaining problems of the 2.5-D numerical modeling for transient electromagnetic method and the researches for the 2.5-D forward modeling for electromagnetic method with topography to be done are discussed.