Study On Underground Electromagnetic Forward Modeling Based On CN-FDTD

Electromagnetic calculation is the main method to study the electromagnetic properties of complex targets.As the foundation of electromagnetic computing,forward modeling directly affects the effect of inversion and imaging.Therefore,it is of great significance to carry out electromagnetic forward modeling research.An improved Crank-Nicolson finite-difference time-domain(FDTD)algorithm was proposed to solve the problem of low efficiency for numerical computation of fine structures.By studying the FDTD algorithm and Crank-Nicolson theory,the full-space 3D electromagnetic finite-difference time-domain algorithm was derived by using the principle of central difference and antecedent and antecedent substitution calculation.Based on Crank-Nicolson difference scheme of discrete,the Maxwell curl equations of finite difference form of space location of the split,set all physical quantities have nothing to do with the Z coordinate,namely the Z direction of the first order partial derivative is zero,combined with two-dimensional finite-difference time-domain algorithm of TM and TE wave equation,is derived with second order accuracy of Crank-Nicolson finite-difference time-domain equation,thus can reduce the dimension of a data calculation,greatly improve the computing efficiency of forward modeling.The three-dimensional space model of water-bearing fault and water-rich goaf was constructed,and the computing efficiency of FDTD algorithm,CN-FDTD algorithm and the improved CN-FDTD algorithm was compared.Compared with the traditional FDTD algorithm,the efficiency of the improved CN-FDTD algorithm is improved by 21.9%,memory ratio by 24.4%,and memory ratio by 74.7%,and memory ratio by 32.6%.Compared with the model,the average error and the maximum error of the distance between the target body and the receiving position of the water-rich area shown by the forward simulation are 0.69%and 0.78%respectively.The forward simulation results are in high agreement with the model.The simulation results show that the improved CN-FDTD algorithm can be applied to the study of the distribution law and response characteristics of three-dimensional electromagnetic components in underground full-space,and can effectively improve the computational efficiency when solving multi-scale electromagnetic problems of fine structure,which is of great significance to the subsequent researches on electromagnetic inversion and multi-dimensional imaging.