Forward Modeling And Inversion Of Induced Polarization Parameters From Time-domain Airborne EM Data

Airborne electromagnetic(AEM)method has the advantages of low cost,high speed and no need for ground personnel to approach.It has been widely used in the exploration of minerals,oil and gas,groundwater and geothermal resources.With the continuous expansion of the applications of AEM method,high requirements are put forward for the interpretation of airborne EM data.Inversion methods have been developed from early imaging to one-dimensional(1D)inversions,until the recent rapid development of three-dimensional(3D)inversions.In recent years,the sign reversal phenomenon often happens in the time-domain airborne EM signal acquired from the frozen soil areas and sulfide-bearing underground.This phenomenon is caused by the induced polarization(IP)effect of underground medium.The inversion based on the real resistivity model cannot interpret this kind of data,which brings difficulties to the data interpretation of time-domain airborne EM method.Therefore,it is necessary to develop the inversion method of airborne data by taking into account of IP effect.Due to the complex coupling relationship between the IP parameters and the large sensitivity difference between the parameters,the inversion has serious non-uniqueness and instability,which brings great challenges to the inversion of IP parameters.In this paper,we introduce the Pearson correlation coefficient in statistics to realize inversions of resistivity and polarizability parameters based on the Pearson correlation constraint.At the same time,the deep learning method is used to estimate the time constant and frequency correlation coefficient,so that a small range of constraints can be set for the two parameters,and we can create conditions for simultaneous inversion of four IP parameters.In this paper,the Pearson correlation constrained inversion method and deep learning strategy are combined to reduce the multiplicity of IP parameters inversion and improve the inversion stability,which has important guiding significance for time domain airborne electromagnetic induced polarization data inversion and interpretation.In this paper,firstly,based on Maxwell's equation and frequency-time conversion technique,the Helmholtz equation satisfied by the secondary field in frequency-domain is discretized by staggered grid finite difference method,and the linear equations are solved by quasi minimum residual method(QMR).Further,the real resistivity in traditional EM is replaced by frequency time conversion and the Cole Cole model to realize 3D time-domain AEM forward modeling for induced polarization response.In addition,in order to understand the characteristics of airborne EM responses with IP effect and effectively identify IP anomalies in airborne EM data,we carry out forward calculation for different combinations of IP parameters,and systematically analyze the influence of IP parameters on airborne EM responses in time-domain.This will increase our understanding of airborne EM induced polarization response in time-domain,so as to lay a foundation for induced polarization data inversions.In this paper,based on the 3D forward algorithm,three-dimensional inversion of airborne EM data with IP in time-domain is realized based on Gauss Newton method,and the effects on inversions from IP parameters are analyzed.The inversion results show that the resistivity inversion is the best,followed by the polarizability,the frequency correlation coefficient is worse than the polarizability,while the inversion of the time constant is the worst.In addition,the effects of different regularization factors on the inversion parameters are compared.The results show that the inversion is relatively good when the initial regularization factor is large,but the inversion needs more iterations to converge,so the convergence is slow.Pearson correlation coefficient in statistics is a statistical index to describe the closeness of correlation between variables,which reflects the degree of linear correlation between them.In order to reduce the non-uniqueness of IP parameter inversions,this paper uses the idea of structural similarity and introduces the Pearson correlation coefficient in statistics to construct the correlation between resistivity and polarizability parameters.For that purpose,we introduce the correlation into the inversion objective functional to realize 3D inversion of time-domain airborne EM data based on the Pearson correlation constraint.Through the experiments on the theoretical models with Pearson correlation constraint and Gauss Newton inversion,the inversion results show that the distribution of the polarizability obtained by the Gauss Newton method is more divergent,while based on the Pearson correlation constraint inversion,because of the correlation constraints of resistivity and polarizability,the transverse and longitudinal distribution of the polarizable abnormal body are relatively focused,which is better than the Gauss Newton method The inversion results are closer to the true model.In addition,the resistivity inversion results are improved compared with Gauss Newton method with the resistivity inversion results closer to the real model.In order to obtain more prior information and reduce the probability of inversion into local minimum,this paper explores the use of deep learning technology to predict the parameters of Cole-Cole model.Different IP parameters and forward responses are used as training sets to train CNN2 D,LSTM,and CNN2 D + LSTM neural networks,and the corresponding neural network models are obtained,the predicted results of these neural network models are compared.The results show that CNN2 D +LSTM model has faster convergence and more stable predicted results than CNN2 D and LSTM models.On this basis,we further combine in this thesis the Pearson correlation constraint with the deep learning method for estimating IP parameters to establish a joint inversion strategy to improve the effectiveness of multi-parameter inversions.For this,we first use deep learning to estimate IP parameters,and then set a smaller constraint range of time constant and frequency correlation coefficient according to the estimated IP parameters.Then,based on the Pearson correlation coefficient,we invert the resistivity and polarizability from time-domain airborne EM data under the constraints of time constant and frequency correlation coefficient.The model experimental results show that the inverted resistivity and polarizability constrained by the Pearson correlation are very close to those when inverting the data using true time constant and frequency correlation coefficient.Finally,in order to further verify the effectiveness of our time-domain inversion strategy for multiple IP parameters proposed in this paper,we carry out 3D inversion of the AEM survey data with IP effect.For the sake of comparison,we also carry out1)the inversion of EM data with negative responses omitted without considering IP effect;2)the inversion of EM data with negative response included without considering IP effect;3)the inversion of EM data with negative response included but without considering IP effect.The results show that the inverted layer when considering IP effect is more continuous and the interface is clearer.Furthermore,the inversion considering IP effect can better fit the survey data,which shows the necessity of inversion considering IP effect.It is expected that the research results of this paper will play an active role in the inversion of airborne EM data in areas with obvious IP effect.