Research On Multi-scale Waveform Inversion Method Of Ground Penetrating Radar

Ground Penetrating Radar(GPR)is favored by many industries and used in environmental,hydrological and engineering geophysics because of its convenient operation,high work efficiency and ability to depict complex near-surface structures.With the development of economy and society,the application range of ground penetrating radar is more and more extensive,and the technical requirements for ground penetrating radar are getting higher and higher.Traditional ground penetrating radar imaging methods are based on ray tracing theory,such as travel time inversion and maximum amplitude inversion in the first cycle.Conventional tomographic results based on the above-described ray techniques often only have limited resolution,mainly because only a small portion of the information contained in the radar data(ie,the first arrival time and the maximum amplitude of the first period)is utilized in the inversion..In order to achieve improved resolution and achieve quantitative interpretation of physical properties of underground media,waveform inversion technology has been introduced into the field of ground penetrating radar and has gradually become a research hotspot.In the field of geophysics,waveform inversion technology was first applied to seismic exploration and development,and a set of waveform inversion scheme based on wave equation was formed.In this paper,a vector matrix waveform inversion scheme for ground penetrating radar(GPR)based on Maxwell equations is presented.At present,the research of ground penetrating radar(GPR)waveform mainly focuses on full waveform inversion in time domain based on traditional objective function,and inversion using all information of radar wave.Although high resolution inversion results can be obtained by inversion of all information,it also faces high nonlinearity in the inversion process,which makes the inversion fall into local minimum.In order to solve the non-linear problem of traditional full waveform inversion,the most commonly used method is to provide a relatively accurate initial model for waveform inversion,but since the underground is unknown,how to provide the initial model to avoid falling into the local minimum is a hot spot in waveform inversion research.In this paper,the traditional time domain full waveform inversion technique which achieves certain results in the field of ground penetrating radar is realized.The gradient and step-size formulas of ground penetrating radar waveform inversion are deduced again by deriving the objective function.The forward simulation of the model is realized by using the CPML absorbing boundary of high order finite difference in time domain,and the convergence of the objective function is achieved by using the conjugate gradient method in the iteration process.After validating the inversion theory with synthetic data,two sets of data collected at different geographic locations are inverted by full waveform inversion technique in time domain.Before the beginning of the inversion process,the radar signal should be processed,and the actual data should be converted into two-dimensional data and source wavelet estimation.After realizing the inversion of cross-hole radar data by using time domain full waveform inversion technique,this paper extends the time domain waveform inversion technique to the ground acquisition radar data inversion.The frequency components of the forward data and the forward data are decomposed by the filter.In the iterative process,different frequency components are inverted according to the law from low frequency to high frequency,and a set of iterations in the time domain is constructed.Multi-band multi-scale inversion strategy for domain decomposition.The multi-scale strategy can effectively avoid the high nonlinear problems faced when inversion using inaccurate initial models and reduce the dependence on the initial model.Through multi-band multi-scale strategy,this paper inverts the groundpenetrating radar synthetic data collected in the time domain,and separately inverts the dielectric constant and conductivity.In recent years,the research on ground penetrating radar data waveform inversion has gradually become a research hotspot in the radar field,and it is also a research difficulty.In order to explore the possibility of using the waveform inversion technique to realize the ground data inversion of ground penetrating radar,this paper proposes a phase waveform inversion method and uses the phase integral multi-scale inversion strategy to invert the synthetic data of ground-penetrating radar acquired by the ground.When constructing the ground penetrating radar phase waveform inversion objective function,the amplitude spectrum and the phase spectrum of the actual observation data and the forward data are respectively obtained by Fourier transform(FFT),and the amplitude spectrum of the actual observation data is used instead of the synthesized data amplitude spectrum,that is,Normalize the amplitude of the observed data and the forward data to eliminate the influence of the amplitude and achieve the purpose of inverting the phase.Phase waveform inversion restores the same radar information as full-wave inversion.The phase waveform inversion does not need to know the amplitude of the source wavelet,and the amplitude is difficult to estimate when processing the actual data;the phase integral multi-scale inversion strategy-allows for a poor initial mode,which is a waveform inversion for lacking a priori information is very important.In the field of seismic waveform inversion,the envelope fluctuations and attenuation of seismic records are considered to carry ultra-low frequency(ie,the frequency below the lowest frequency in the source spectrum,ULF)signals,which can be used to estimate the long-wave velocity structure.Envelope inversion can then be used to recover the low wavenumber components of the medium(smooth background)so that the initial model dependence of the waveform inversion can be reduced.In this paper,the envelope waveform inversion concept is introduced into the field of ground penetrating radar,and the envelope operator of the actual observation data and forward data is obtained by Hilbert transform.Using the properties of the Hilbert transform,we separate the phase and amplitude information in the time domain.Through the method of derivation and the concept of virtual vector source,the gradient formula of envelope waveform inversion is deduced in detail,and the optimal step size is given.By analyzing the spectrum of the signal,it is determined that the envelope signal has the ability to restore the low-frequency information of the signal.The envelope waveform inversion has lower nonlinearity,is not sensitive to the selection of the initial model parameters,and has the ability to suppress local minimum.The synthetic data demonstrates that the envelope objective function has the ability to invert low frequency missing cross-hole radar data.After determining the ability of envelope objective function to suppress local minimum,this paper combines envelope objective function with source-independent cross-hole radar waveform inversion,and constructs a source-independent waveform inversion theory based on envelope objective function.The gradient and step-size formulas of time-domain waveform inversion independent of source wavelet are derived in detail by derivation method,and the simultaneous inversion of dielectric constant and conductivity is realized.According to the filtering characteristics of convolution wave field and by changing the center frequency of forward source wavelet in inversion process,a multi-scale inversion strategy with envelope source-independent waveform inversion is developed.The complex and time-consuming process of source wavelet estimation is avoided in the process of inversion.When processing actual data,each waveform obtained by source wavelet estimation often differs greatly.Usually,the final source wavelet is estimated by extracting the average of several source wavelets,which brings uncertainty to inversion and brings adverse effects on convergence.Envelope source-independent waveform inversion avoids the process of source wavelet estimation and restrains the high nonlinearity of conventional source-independent wavelet waveform inversion.In this paper,the waveform inversion method with envelope source-independent is validated by synthetic data,and the actual data are successfully inverted by this method.At the end of this paper,two-dimensional distribution maps of objective functions are calculated for different objective functions.By observing the two-dimensional distribution map,we can understand the inversion ability of each method for the initial model with different physical parameters,the law of parameter selection of the initial model,and the characteristics of each method.By comparing the two-dimensional distribution patterns,smoothness and complexity of the objective functions of different methods,we can understand the non-linearity of different methods,which has certain guiding significance for the construction of multi-scale inversion methods.