Study On Stochastic Medium Inversion Method Preserving Autocorrelation Structure

It is widely recognized that the near-surface media is characterized by strong heterogeneity,and often shows dramatic and complex changes in corresponding internal physical and chemical properties.Ground penetrating radar(GPR)impedance inversion methods could obtain the physical parameters of the near-surface media and further investigate its spatial heterogeneity.Research has shown that the traditional GPR impedance inversion methods based on homogeneous layered model failed to obtain satisfactory results when there exists extreme lateral variations of near-surface media.The spatially distributed physical property parameters within near-surface media usually change randomly and can be characterized by a spatial autocorrelation function.Thus,this type of statistically-derived model can be named as stochastic medium model with certain autocorrelation structure.Compared with the traditional homogeneous and layered media models,the stochastic medium model with certain autocorrelation structure can describe the heterogeneity within near-surface media more accurately and completely.Thus,it is quite necessary to develop an effective GPR impedance inversion method based on stochastic media theory.However,the previous GPR impedance inversion methods based on stochastic medium model usually establish a stochastic medium model as the initial model in advance,then under the constraint of borehole data they continuously modify the model(such as electromagnetic wave velocity)to fit the GPR data until obtaining inversion results that fully fit the GPR data.According to the theory of stochastic medium,the inherent autocorrelation structure of the stochastic medium model will be destroyed if modifying the stochastic medium model directly during the inversion process.Owing to the problem of non-uniqueness,the inversion results may not conform to the actual situation(e.g.,the inversion results lack local details).To solve the above problems,a new stochastic medium inversion method preserving autocorrelation structure has been proposed in this paper.On the basis of ensuring that the autocorrelation structure is always maintained in the process of modeling and inversion,GPR impedance inversion is performed under the constraints of the borehole data and its corresponding autocorrelation.The proposed inversion method could obtain spatial heterogeneity of physical properties and hydrogeological parameters,it then provides reliable and highresolution imaging results for near-surface geophysical exploration.To estimate the uncertainty of the inversion results,we can apply the methodology many times using different random seeds and then evaluate the uncertainty by statistically analyzing the obtained inversion results.There are two key points in the proposed inversion method: one is how to estimate the autocorrelation structure information from the existing data,and the other is how to maintain the autocorrelation structure information during modeling and inversion.Focusing on the above two points,the main research contents and results are as follows:(1)By extending the previous 2D estimation approach to 3D,the mathematical relation between the 3D autocorrelation of the high-frequency subsurface electromagnetic wave velocity distribution and that of the corresponding 3D depth-migrated GPR reflection image has been derived.Based on the deduced mathematical relation,I proposed the method of estimating 3D correlation structure from GPR reflection data based on Monte Carlo strategy.Acting as part of autocorrelation structure,the estimation results can be further used for stochastic medium modeling and inversion.(2)The Fast Fourier Transform Moving Average(FFT-MA)simulation method can establish stochastic medium model with specific autocorrelation structure.To generate stochastic medium model constrained by the borehole data,the ordinary kriging based FFT-MA conditional simulation algorithm has been investigated in this paper.The designed algorithm could build conditional simulation results(models)conformed to borehole data and specific autocorrelation structure.Furthermore,modifications can be brought to one or many random numbers to create new conditional realizations without altering the simulated autocorrelation structure.(3)By blending the designed conditional simulation algorithm,simulated annealing(SA)algorithm and the GPR impedance inversion method,the stochastic medium inversion method preserving autocorrelation structure has been proposed in this paper.SA optimization strategy is performed to perturb random numbers from global to local to obtain new conditional simulation results without changing the autocorrelation structure,and the new conditional simulation results will then be used for GPR impedance inversion until the termination of the SA algorithm is achieved.Furthermore,a constrain item of autocorrelation calculated from borehole data has been added to the traditional objective function.This means that two conditions must be satisfied when accepting the iterative conditional simulation results in the inversion process: the Metropolis criterion must be met and the autocorrelation of the conditional simulation results at test borehole must fit that of the data at test borehole quite well.(4)Two improved strategies are brought to the traditional simulated annealing algorithm to promote the efficiency of the proposed stochastic medium inversion method.The first one is to set the length of Markov chain dynamically,and this process will avoid too many ineffective attempts during the inversion procedure.And the second one is to introduce error-feedback mechanism,this process could modify the random number of the poorly matched area according to the residual(associated with fitting the GPR data).In addition,the GPUs parallel computing technique is utilized to improve the efficiency of proposed inversion method.(5)The inversion results for 2D synthetic and field data show that the proposed inversion method could obtain the heterogeneous structure of the porosity(or electromagnetic wave velocity)of the near-surface media on the basis of keeping the autocorrelation structure.By using different random numbers to obtain a certain number of inversion results,the uncertainty of the inversion results can also be estimated.