Transient Electromagnetic Multiresolution Migration Imaging Method For Grounded Sources

Nowadays,the geophysical requirements of deep exploration are getting higher and higher,and the traditional data interpretation methods need to be changed and innovated accordingly.The current main interpretation method of transient electromagnetic(TEM)is to give resistivity information of subsurface medium,and the portrayal of geological interface and tectonic features is weak.To address this problem,this paper presents a complete imaging system based on the multiresolution TEM diffusion field data,then calculates the corresponding virtual wavefield,and finally realizes the multiresolution prestack migration imaging using the finite difference technique.For 3D forward modeling of transient electromagnetics,this paper makes innovations from two aspects: improving calculation efficiency and improving resolution.The transient electromagnetic response during OFF-TIME can be written as a system of first-order ordinary differential linear equations without considering the transmitted waveform.The traditional way of solving is to use difference instead of differentiation,which requires several matrix decompositions and hundreds of times backward substitutions during the whole procedure,which is computationally inefficient.For the direct solver,SAI-Krylov subspace technology is introduced in this paper,which greatly improves the solving efficiency.However,the memory requirements of the direct method will increase exponentially with the growth of the number of grids,so it is necessary to develop the Krylov subspace technology based on the iterative method.Because the order of the coefficient matrix is too large and sparse,the basis vector matrix of the Krylov subspace can be constructed using the preprocessed conjugate gradient(PCG)method.By combining the conjugate gradient method with the Krylov subspace technique and the optimization parameters,the 3D forward modeling of large-scale grids can be well solved.However,when the order of the subspace is too large,it still poses a great challenge to the above solution strategy.As a result,this work has proposed an adaptive residual-time(ART)restarting polynomial Krylov method.The algorithm is based on a reliable residual stopping criterion and a restarting mechanism that can effectively solve the orthorectification problem for large-scale grids.On the other hand,traditional transient electromagnetic detection is dominated by square waves,which have more low-frequency harmonics,leaving the resolution of transient electromagnetic detection to be further improved.This paper uses differential pulses as the transmitting waveform,which is not affected by low-frequency components,and the effective frequency components are mainly focused around the main frequency,which can effectively improve the TEM detection resolution.Furthermore,differential pulses with various pulse widths have unique dominant frequencies,which correlate to different detection depths.As a result,several differential pulses can be transmitted in field detection,enabling high-quality TEM images from shallow to deep.The virtual wavefield can be further calculated to improve the detection resolution after obtaining the transient electromagnetic diffusion field.It is well known that the solution of transient electromagnetic virtual wave fields is a serious ill-posed problem,and it is difficult to obtain stable and accurate virtual wave fields using conventional algorithms.To address this challenge,the precise integration method(PIM)is adopted in this paper to solve the stable conversion of the TEM diffusion field to a virtual wave field.This method greatly reduces the difficulty of solving ill-conditioned linear equations by transforming the solution of highly ill-conditioned linear equations into an integral process.In addition,the integral step length increases exponentially by 2,which has high computational efficiency on the premise of ensuring accuracy.On this basis,based on the idea of norm equalization,the coefficient matrix is preprocessed before calculating the virtual wave field.This strategy can effectively optimize the solving process and improve the accuracy of the virtual wave field.The applicability of the proposed method is further improved by studying the corresponding relationship between the virtual time and the diffusion field time,the selection criteria of discrete points and the optimized step length of the precise integration method,and setting reasonable termination iteration conditions.According to the results of typical geoelectric models,the proposed method has high accuracy,good resolution,and anti-noise performance.Compared with the preconditioned regularized conjugate gradient(PRCG)method,the computational efficiency of the proposed method is improved by about 4 times.The relative error is less than 5%,while the maximum relative error of PRCG can reach40%-50%,and the accuracy can be increased up to 10 times.In terms of resolution and stability,it also shows good performance.To further improve the resolution,the multiwindow sweep time wavefield inverse transformation technology is introduced in this work.When solving the virtual wavefield,a small sweep time window could successfully extract shallow anomaly information,whereas a large sweep time window can effectively obtain deep anomaly information.The interface information from shallow to deep could be acquired by correlating and superimposing virtual wave fields at different scanning time windows.After the TEM virtual wave field is obtained,the pre-stack migration imaging technology can be introduced to obtain the structural characteristics of geological targets.The finite difference migration imaging method plays an important role in the field of seismic exploration because it can better adapt to the model of strong lateral velocity variation.Therefore,this paper introduces finite difference migration imaging technology into the interpretation of the TEM virtual wave field.First,the direct wave in the virtual wave field is eliminated,and the virtual wave field containing only the stratum reflected wave is obtained.Then,based on the wave equation in the time domain,this paper reversely extrapolates the first-order approximation equation of the upward traveling wave and obtains the recursive formula of the wave field in the time-space domain.After solving the wave field of underground space,deconvolution technology is used to weaken the waveform broadening effect and improve the longitudinal resolution of the geological interface,to obtain more accurate depth information of the geological interface.Finally,the proposed method is validated using a typical 3D geological model and field data.The migration imaging results correspond well with known geological data,demonstrating the efficacy of the finite difference migration imaging approach for identifying electrical interfaces and formation characteristics.