Three-dimensional Forward Modeling Of Transient Electromagnetic Based On Crank-Nicolson Difference Method

The finite-difference time-domain(FDTD)algorithm is one of the main time-domain transient electromagnetic three-dimensional forward modeling method,but it must be limited by the influence of Courant stability conditions.The mesh size is strictly limited by the time step size,and the FDTD algorithm is affected by the Yee cell structure.The mesh meshes currently studied can only use structured meshes with non-uniform and multi-resolution meshes,but the length-to-width ratio of the mesh cannot be increased indefinitely.Therefore,the mesh size is small and can meet the accuracy requirements.However,the calculation time increases sharply and the detailed description is complicated because the model becomes larger.In the case of an abnormal body,the meshing size is small,and the time step is small,the calculation time is sharply increased,and the calculation efficiency is low.In order to solve the problem,this paper studies the three-dimensional Crank-Nicolson finite-difference algorithm for transient electromagnetic in the Cartesian coordinate system,and overcomes the Courant stability condition.Based on the Maxwell equations of passive and active conditions,the recursive formula of Crank-Nicolson finite difference time domain in Cartesian coordinates is derived.The conjugate gradient method is used to solve the electric and magnetic field values,and the Crank-Nicolson finite difference time domain algorithm is combed.I write Crank-Nicolson time domain finite difference algorithm program,and it provides the basis for the study of transient electromagnetic three-dimensional forward modeling.In order to verify the accuracy of the Crank-Nicolson finite-difference time-domain algorithm.Firstly,compared with the analytical solution of uniform half-space,it is found that the two curves are basically coincident and meet the accuracy requirements.Secondly,the three-layer classical layered models(A,H,K,Q)are built,comparing the results of the 3D CN-FDTD forward simulation with the analytical solution;then designing the uniform half-space containing the 3D low-resistance anomaly model,and the result is compared with the integral equation method,the multi-resolution grid time-domain finite difference method and Wang Comparison of time domain finite difference algorithms.On the basis of satisfying the calculation accuracy.the appropriate time step is selected to analyze the calculation efficiency.Two-layer and three-laver models with three grid numbers are designed.Comparing the calculation time and analyzing the acceleration ratio,it is found that the transient electromagnetic three-dimensional CN-FDTD algorithm can significantly improve the calculation efficiency.According to the three-dimensional CN-FDTD algorithm of transient electromagnetic,this paper analyzes the transient electromagnetic response of three different geological bodies.Firstly,some typical constructions,low-resistance body,parallel low-resistance body,single high-resistance body and parallel high-resistance body,is simulated and analyzed.Secondly,the transient electromagnetic response characteristics of low-resistance and high-resistance anomaly are studied.Then,three-dimensional complex vertical contact is studied,and its response at different offsets are investigated.TEM response characteristics of different receiving points in valleys,trench tops and complex terrain are investigated.Finally,TEM response of trenches,trench tops and complex terrain along terrain simulation is investigatedIn this paper,TEM three-dimensional Crank-Nicolson finite-difference time difference algorithm is studied by theoretical research,algorithm development,accuracy verification,efficiency comparison and numerical simulation,which provides a basis for future complex terrain models and 3D inversion.