The 3D Forward Modeling And Generalized Inverse Matrix Inversion Of Transient Electromagnetic Method

The transient electromagnetic method(TEM)has many advantages,such as flexible response,low volume effect,high horizontal resolution,high efficiency and good economic benefit,this method is widely used in mineral and oil exploration,coal mine disaster prevention,hydro geological investigation and engineering exploration and so on.With the development of instruments,theoretical methods and data processing methods,the application range of TEM is expanding rapidly in many fields.At present,one-dimensional layered inverse algorithm and 2D resistivity imaging way have been developed relatively mature.When the shape and physical parameters of target are complex,1D layed model must be replaced by three-dimensional model which close to the actual geologic target in inversion.Because the Forward is the base of inversion,the response mechanism and anomaly characteristics of complex targets can be studied by using 3D Forward numerical simulation.It has important application value and practical significance to improve the level of application and interpretation accuracy.The TEM numerical simulation method can be divided into time domain method and frequency domain method.The theory of frequency domain method is more complex than time domain method's.The algorithm of frequency domain method is not easy to implement and takes a long time the theory of time domain method is very simple.Comparing with the frequency domain method,time domain FDTD method has obvious advantages.The algorithm of FDTD method is simple and suitable for many electromagnetic problems with complex media and shapes.The main drawback of the FDTD is the low accuracy in the model border.But for the actual application of geological exploration,the precision of target border is not very high.With the development of parallel technology and computer graphics,the FDTD method has a better future.Therefore,the FDTD method is choosed as the 3D forward algorithms in this paper.Since Wang and Hohmann proposed the finite difference algorithm,FDTD has been well applied in the continuous improvement by the follow-up scholars.The disadvantages of this method are mainly in three aspects: first,the calculation of the source requires that the near surface is horizontal,and the distribution of the electrical properties is uniform.It is very difficult to calculate the initial source in many common situations such as the resistivity of ground is inhomogeneous and and terrain is not horizontal,and so on;second,The Dirichlet boundary condition is used in the underground boundary,which usually leads to the calculation area is very large,and the calculation of the magnetic field by the upward continuation method will affect the accuracy of the calculation results;third,The FDTD algorithm uses triplet loop in space and single loop in time to calculate the propagation process of electromagnetic fields underground,the computation time is very long.In this paper,different solutions are adopted to solve the above problems:(1)The source emission loop of TEM is discretized directly to the ground grid,and a certain thickness of air layer is added above the ground surface.The active Maxwell difference equation and the thin wire model are used to calculate the field source.This directly calculates the field source method can avoid the restriction of Wang's algorithm.It is not only suitable for the half space but also for the whole space.(2)The CPML absorbing boundary is used to truncate the big computational space into a small space,which greatly reduces the number of nodes.The distribution of the CPML boundary parameters is optimized to absorb the low frequency electromagnetic wave ofTEM.(3)By using the matrix calculation instead of the multi loop method,the computational speed is improved greatly,but the memory consumption is increasing rapidly;the dielectric constant of the added air is modified to increase the step size and reduce the number of iterations.In the case of keeping the stability of calculation,the computational efficiency is further improved.The complex geological objects are modeled by the body sculpture method,and the material space is defined to calculate the background and the geological model together.The accuracy of the proposed algorithm is verified by comparing the analytical solution with the FDTD numerical results.Due to the ramp time,the early response of TEM is different from the analytical solution.By using the improved CPML parameter distribution,the calculation accuracy can meet the actual requirements in the case of more than 105 iterations.The influence of different ramp time and waveform on the early response is studied to analyse the early response characteristics,which can be used as a reference for the inversion of actual transient electromagnetic method.The 3D FDTD algorithm is used to calculate the TEM response of many kinds of combinations geoelectric model,such as plate,spherical and anisotropic plate under homogeneous earth,layered strata,anisotropic strata,topography and other background.And the forward simulation of the whole space transient electromagnetic method is carried out.The conclusions can provide reference and support for the quantitative interpretation of the data.The generalized inverse matrix method is used to inverse the low resistance plate model.The result showed that the spatial position of plate is very accurate and the apparent resistivity has small deviation.The inverse results are closed depends on the initial values of parameters and accuracy of background response,the extraction method of anomaly needs further improvement.Probability tomography is a fast algorithm for the inversion of apparent longitudinal conductivity in TEM.The tomography results can determine the approximate spatial position of the anomalous body,but the resolution of border is low.