3D FDTD Modeling And LBFGS Inversion Of Transient Electromagnetic Induced Polarization Data

In the actual exploration,the late TEM data often appear negative(anti sign)phenomenon,and the existing research thinks that the negative response is the reflect of IP effect.At the same time,considering that the 3D model is more in line with the actual underground situation,and the processing and interpretation of the current measured data lack of practical 3D forward inversion technology of transient electromagnetic,this paper chooses to add IP effect into the 3D forward modeling,and carry out the research of 3D forward modeling of transient electromagnetic considering IP effect and 3D inversion of transient electromagnetic without IP effect.In order to improve the calculation efficiency and avoid the disadvantage of converting the frequency domain response to the time domain response(In order to ensure the calculation accuracy,it takes a lot of time to calculate the response of dozens of frequencies,especially in the case of multi-source,the time consumption is greater),the 3D forward modeling uses the finite difference time domain method to directly simulate the transient electromagnetic response in the time domain.The excitation source adopts trapezoidal wave processed by switch function,and the transmitting coil is placed on the edge of the grid.Starting from the Maxwell equations in passive medium,deduces the difference dispersion form of Maxwell equations in passive medium by the finite difference time domain method,and then deduces the difference dispersion form of Maxwell equations in active medium,which realizes the 3D transient electromagnetic without exciting effect Forward.Compared with the response results of overseas mature Aarhus Inv program,the correctness of 3D forward algorithm is verified.In order to consider the IP effect in the FDTD calculation,the time domain Cole-Cole model is needed.After Laplace transform of Cole-Cole model in frequency domain to time domain,two kinds of solutions of Cole-Cole model in time domain can be obtained by using numerical filtering algorithm and analytical solution method(frequency correlation coefficient takes special value): numerical filtering solution expression and analytical solution expression.Two expressions of time domain Cole-Cole model are introduced into the 3D forward modeling to realize the 3D forward modeling of transient electromagnetic in time domain considering the IP effect.Establish a uniform half space IP model,used to compare the three-dimensional response with the calculation results of Aarhus Inv program to verify the correctness of the 3D forward algorithm of time domain transient electromagnetic considering IP effect.In the 3D inversion,the Limited-memory Quasi Newton(L-BFGS)inversion method and the regularized objective function are used.In the inversion process,the solution of Jacobian matrix is the most important.In order to solve this problem,we use the electromagnetic migration imaging method to calculate the gradient of the target function directly and quickly,avoiding the calculation and storage of Jacobian matrix in time domain.After obtaining the Jacobian matrix(the gradient of the objective function)in the time domain,the iterative resistivity model is updated by using the L-BFGS inversion process,and a time-domain transient electromagnetic three-dimensional inversion program without IP effect is built.Then,a three-dimensional inversion example of the synthesized data of the theoretical model is given.The result shows that the program has the preliminary inversion ability,but needs further debugging and improvement.