Data Processing And Interpretation Of GPR Based On Mode Decomposition In F-x Domain

Ground penetrating radar(GPR)is a commonly used engineering geophysical method,and it is one of the effective methods for shallow earth exploration.Its principle is to use the propagation of high-frequency electromagnetic waves in underground media,and then analyze and interpret the characteristics of received electromagnetic waves to derive the underground structure and physical properties of the underground medium.However,the signal received by GPR is non-stationary and non-linear,the conventional Fourier transform cannot process the signal accurately and efficiently.Therefore,Empirical Mode Decomposition(EMD),Ensemble Empirical Mode Decomposition(EEMD),complete set empirical mode decomposition(Complete Ensemble Empirical Mode Decomposition,CEEMD)and Variational Mode Decomposition(VMD)can be used to process the radar signal in f-x domain.Decompose the signal into multiple intrinsic mode functions(IMFs),In this way,signals in different frequency bands are decomposed into different IMF components,then select the IMF components that meet the conditions to achieve the effect of denoising.This article details the basic principles of these four methods and verify its correctness through analog signals and forward modeling.Through the processing and interpretation of measured GPR data,the advantages and disadvantages of the four methods in GPR data processing are compared and analyzed.In 1998,Huang et al.proposed EMD method.EMD method is to decompose a signal into multiple IMF components,and then further select and process them.But EMD method has many problems,such as serious modal aliasing.In 2009,in view of the many problems of the EMD method,Wu and Huang proposed EEMD method.EEMD is a new method that has been improved based on EMD method.It is consistent with the basic principles of the EMD method.The difference is that before the EMD decomposition,a certain proportion of Gaussian white noise is added to the signal to be processed.The problem is that the proportion and the number of averages of Gaussian white noise cannot be determined accurately.In 2011,based on the problems of the EEMD method,Torres proposed a new improved algorithm,the CEEMD method.In the decomposition process of the CEEMD method,specific noiseis added at each stage,and different IMF components are obtained through the uniqueness of the residual.However,there are still problems such as lack of mathematical foundation and long calculation time.In 2014,Dragomiretskiy K.proposed the VMD method.The VMD method is not consistent with the theoretical basis of the first three methods.The VMD method determines the IMF component parameters by determining the optimal solution of the variational model.The definition and meaning of the IMF component is different from the previous method.However,the VMD method cannot independently set the penalty factor and the number of IMF components,at the same time,the end effect occurs from time to time.In ground penetrating radar data processing,common methods are based on Fourier transform.Such as one-dimensional filtering,two-dimensional filtering,inverse filtering and so on.Performing Fourier transform of the ground penetrating radar data in the t-x domain along the t axis can obtain the data in the f-x domain;The signal in the t-x domain is subjected to Fourier transform on the t-axis and the x-axis simultaneously to obtain the signal in the f-k domain.Compare and analyze signal processing methods in f-k domain and f-x domain,and focus on signal processing in f-x domain.The f-x domain processing and modal decomposition method are combined to overcome the shortcomings of traditional processing methods.In order to verify the correctness of the four methods of EMD,EEMD,CEEMD,and VMD,an analog signal and a forward model were established,and the four methods were used to process them.Compare the processing results of the four methods to verify the accuracy of the four methods when processing signals.At the same time,by analyzing and comparing the results of processing IMF components,the advantages and disadvantages of the four methods and the advantages of processing characteristic signals are summarized.Subsequently,these four methods are used to process the measured GPR data.Through comparative analysis of the results,the advantages,disadvantages,and application of the four methods in processing GPR data are discussed.