The 3D Forward Research Of Ground-tunnel Long Offset Transient Electromagnetic

The main purpose of this paper is to solve the problem of three-dimensional forward of Ground-Tunnel Long Offset Transient Electromagnetic.Time domain electric dipole field is calculated through the frequency domain to the time domain method.In solving the three-dimensional electromagnetic field of the frequency domain of the galvanic source,the method that separate the primary field and the secondary field is used.The generalized variational principle is used to get variation of the double-rotation equation of the secondary field derived.Secondary field is calculated by the finite element method.One dimensional forward for frequency domain uniform half-space use Hankel transform to achieve,The Hankel transform filter coefficients are obtained by Fourier transforming of known transformation pairs.In order to obtain the background field of the frequency domain,the formula of the uniform half-space electric dipole field is deduced.the electric dipole field is divided into two parts of general and special solution.When the emission source is located on the ground surface,The expression of the components of the uniform half-space only existing ascending wave in the air and descending wave on underground is derived.we further derive the component expression,and then get the component expression base on cosine transform filter algorithm.calculating the frequency domain and the time domain response,we verify the correctness of the forward result in the frequency and time domain respectively.Based on the double rotation electric field equation of the secondary field separated,the generalized variational principle is used to variate the secondary field on the left side of the equation and the background field on the right side of the equation to derive the stiffness matrix expression of each part of the equation.For calculation of sparse matrix,this paper uses a stable complex conjugate gradient algorithm.In order to accelerate the iterative convergence,a preprocessing matrix of LDLT decomposition is introduced.Finally,the total field signal is frequency-time transformation.The above three-dimensional forward theory formula is deduced,and the forward parameters are set.The three-dimensional forward of time domain is carried out and the results of forward are analyzed.In the study of the three-dimensional anomaly response feature of the Ex component,the anomalous characteristics of the two models of low resistance and high impedance are studied.(1)The same horizontal position,the receiving point in different depth tunnels(2)The receiving point at the same level of depth,is in different position along the Y-axis direction;(3)At the same horizontal position,multichannel curve is in different tunnel depth;(4)At the same horizontal plane,the multichannel curve is located in below and edge of the anomalous body;(5)For the plane distribution characteristics,diffusion variation characteristics of Ex component electric field is studied at eight different times.