Three-dimensional Frequency-domain Inversion Of Transient Electromagnetic Data From A Rectanglar Large Loop Based On Time-frequency Transformation Method

The rectangular large loop is one of the most widely used devices in transient electromagnetic method.Three-dimensional forward and inversion research have been hot issues both at home and abroad.This paper presents a time-frequency transformation method to achieve the transformations of time-domain signal to frequency-domain response.The three-dimensional frequency-domain nonlinear conjugate gradient inversion of rectangular large loop transient electromagnetic data is achieved by using mature frequency domain data processing technique.In order to achieve the time-frequency transformation,it is assumed that the Fourier transform relationship of the time-frequency response can be expressed as a linear system with the response of the electromagnetic field in the frequency domain to the unknown model and the time response to the right-hand term.The regularized inversion technique is used to solve the problem owing to the singularity of the matrix equation,and the optimal regularization factor is selected by L-curve method.The time-frequency transformation based on regularization inversion technique lays the foundation for the frequency domain interpretation of time domain data.In the process of three-dimensional frequency-domain inversion of rectangular large loop data,three-dimensional forward modeling is performed using a staggered-grid finite difference method.The forward modeling start from the Helmholtz equation for the secondary field.In order to calculate the Green function generated by the rectangular large loop in the background medium,the rectangular loop is divided into an equivalence virtual square loop,and the electromagnetic field response at any point is equal to that generated by each virtual square at the measurement point superposition of electromagnetic response.When using the virtual interface method,the source can be located at any position,and the calculation pointcan be extended to any position in the three-dimensional space outside the boundary of the transmitting loop.The Hankel integral is calculated using direct numerical integration techniques.The Helmholtz equation for the second field overcomes the difficulties of source description and source singularity in numerical simulation.The three-dimensional linear equations are solved by the MUMPS factorization software package,and then the interpolation method is used to obtain the frequency-domain electromagnetic response of the rectangular large loop in the whole space.Three-dimensional forward simulation of transient electromagnetic can be achieved from the rectangular large loop combined with cosine transform.Compared with the results of the predecessors,it is feasible that combining frequency domain three-dimensional forward and cosine transform techniques to compute three-dimensional transient electromagnetic response under the horizontal terrain condition.The model is designed as a low resistivity anomaly embedded in uniform half-space,simulating rectangular large source observation system in full space.estimating the diffusion range of the subsurface induced eddy current field in the early timeto design the observation range outside the rectangle large loop.The numerical modeling shows that:(1)the transient electromagnetic field from the rectangular large loop is diffused in the form of "smoke ring".As the time decays,the "smoke circle" is expanded and the strength is weakened.(2)The borehole transient electromagnetic response is much influenced by the observation position,especially the edge and inside of the abnormal body.The voltage profile curve is greatly change in the vicinity of the abnormal body,and the medium time channel appear to phenomenon of changed the sign.(3)For shallow engineering geophysical exploration,the influence of the shape of the source should be fully considered in the process of interpretation and processing of transient electromagnetic data.Frequency-domain three-dimensional inversion is performed by means of nonlinear conjugate gradient inversion(NLCG).In the nonlinear inversion process,it is not necessary to explicitly calculate and store the sensitivity matrix.Only compute the product of the sensitivity matrix with a vector,requiring only one forward and one transposed forward.Simple and complex models inversion test are desginedrespectively.The inversion results of the synthetic data show:(1)The nonlinear conjugate gradient method has the global convergence property,which can give the geophysical information such as the position,size and resistivity of the underground electrical anomaly accurately.(2)The multi-source observation system has different electromagnetic coupling for different parts of the anomaly.The observed data has more abundant underground anomaly information,and the three-dimensional inversion effect is obvious.(3)Stability of three-dimensional frequency-domain inversion of nonlinear conjugate gradient with rectangular large loop is confirmed,compared with the three-dimensional inversion results and the theoretical model.In order to adopt the above-mentioned frequency domain three-dimensional inversion technique,the following pre-processing work is needed for the field-measured transient electromagnetic data from rectangular large loop:(1)filter and turn-off time correction for the transient electromagnetic data,then the induced electromotive force(emf)data under the ideal step emission waveform condition are obtained.(2)emf is converted into the time domain magnetic field required for time-frequency tranformation using the integrated relationship between emf and the time domain magnetic field.(3)Using the regularization inversion technique to complete the time-frequency transformation,and obtain the real and imaginary data of the frequency-domain electromagnetic response required for three-dimensional inversion.(4)Three-dimensional inversion based on complex magnetic field data using nonlinear conjugate gradient(NLCG).The spatial distribution of the resistivity obtained by the three-dimensional inversion is consistent with the actual geological model of the survey area.The three-dimensional inversion of the transient electromagnetic measured data from rectangular large loop collected at the eastern of the Qinshui Basin,Shanxi Province,China.In this paper,the nonlinear conjugate gradient inversion technique is used to the three-dimensional frequency-domain interpretation of the transient electromagnetic data from rectangular large loop.Regularization inversion technique realized the transformation from transient electromagnetic data to the frequency domain and combined the frequency domain nonlinear conjugate gradient method,which providing a new idea is for the transientelectromagnetic three-dimensional inversion,and a new way for the three-dimensional interpretation of the field transient electromagnetic data.