A Time Domain Full Waveform Inversion Of GPR Based On Modified PRP Conjugate Gradient Method

The full waveform inversion of ground penetrating radar(GPR)is a nonlinear least square optimization method for inversion of underground electrical parameters by making full use of the travel time,amplitude and phase information of radar recorded waveforms.The optimal model is obtained by using the corresponding optimization method to continuously reduce the residual between the forward simulation data and the measured data,and finally the distribution of electrical parameters with high resolution in the underground is obtained.The local optimization method is usually used to solve the full waveform inversion problem,the conjugate gradient method is most commonly used,while the PRP conjugate gradient method(Polak-Ribiere-Polyak)is recognized as the numerical results compare good method,but the method in the process of iteration might away from the optimal solution in an infinite loop falling into local minimum value,and may produce to the objective function in the process of iteration rising algorithm search direction and lead to instability,this paper deals with the revision,the revised method than the traditional method in the search direction a,This one contains more information on objective function gradient,when this coefficient is equal to zero,and the traditional PRP conjugate gradient method,and the revised method and quasi-newton algorithm has similar structure and properties,so the revised method not only retained the advantages of the traditional methods,and on the calculation accuracy and convergence speed close to the quasi-newton algorithm,and under the condition of the exact line search,this method possesses global convergence,effectively solved the problem of the traditional method rising search direction.In this paper,the Maxwell equation in two-dimensional TM mode is simulated by high-order staggered grid finite-difference time-domain modeling,and theinfluence of boundary reflection is eliminated by using the absorbing boundary condition of uniaxial anisotropy perfectly matched layer.The gradient is obtained by the method of zero delay cross correlation between the positive wave field and the residual wave field,and the parameters of the model are perturbed along the search direction by the objective function.Compared with the traditional exact line search method,the method of finding the extreme value of the objective function to determine the maximum Uber length can obviously reduce the number of forward modeling.For the full waveform inversion of ground penetrating radar(GPR),the single parameter inversion of dielectric constant and conductivity and the simultaneous inversion of two parameters are carried out based on the modified PRP conjugated gradient method,and it can be seen from the inversion results.The results of single parameter inversion are closer to the real model in shape and value of abnormal body than those of simultaneous inversion of two parameters,which is due to the fact that more parameters are involved in simultaneous inversion of two parameters.The coupling between different parameters affects the accuracy of the inversion results,but the two-parameter inversion results can provide more information on the electrical parameters of the underground target.Then the two-parameter full waveform inversion based on the three optimization methods is carried out.Because the radar records are more sensitive to the shallow layer,the inversion results of the three optimization methods in the shallow layer are better than those in the deep layer.Compared with the inversion results of the three optimization methods,we can find that the inversion results of the three optimization methods are better than those of the deep layer.The inversion results of the PRP conjugated gradient method are slightly better than those of the gradient method,while the inversion results of the modified PRP conjugated gradient method are better than those of the former two,especially in the deep layer.In addition,the objective function convergence speed of the modified PRP conjugated gradient method is faster.The inversion accuracy is higher.