The Electromagnetic Prospecting Robust Inversion Of One-Dimensional Stratified Medium

GPR (Ground Penetrating Radar) and high frequency electromagnet are frequently used geophysical methods in surveying terrene shallow of engineering field. It opens up a vast range of prospects in Hydrogeology, Engineering Geology, Archaeology, Geological Investigation, Military Investigation and other field. Inverse simulate technology is one of the important contents in GPR (Ground Penetrating Radar) field. The interpretation of GPR pictures, judgment and inversion are all depended on dielectric properties. The study of dielectric properties is the base of GPR development and the key of abstracting useful information from GPR pictures as much as possible. So it has great significance of improving GPR interpreting accuracy and abstracting crucial information to obtain dielectric parameter of medium mode by means of inversion. Therefore, the forward modeling algorithm and inverse modeling have practical meaning.Geophysical inverse problem is nonlinear and ill-posed in general. The nonlinearity arises because:1. The data functional that gives the synthetic response may be nonlinearly related with the model parameters,2. The cost functional chosen may be nonlinear in nature and/or3. Both the data and cost functionals are nonlinear in nature.In addition, the presence of noise in data even complicates the problem of nonlinearity to an extent so that the nature of nonlinearity becomes hard to decipher. In addition to the problem of nonlinearity, the problem of ill-posedness often arose which affects the robustness of the numerical scheme significantly. Therefore, in the context of geophysical inversion the aim is, with a given data set, to design numerically stable yet robust algorithm in delineating a model that would describe the data set meaningfully.The main purpose of this paper is to do inversion of electromagnetic investigation, mainly referring to One Dimensional Magnetotelluric simulation so that it could make a foundation of the theory interpretation and practical application. Due to the frequency range and investigating characteristic of high frequency electromagnet, the traditional electromagnetic method no longer has any effect. Therefore, using the improved forward modeling algorithm to inverse is one of the problems to be solved.The computation of forward model in inversion method is the most time-consuming method. From the time-consuming factors in forward model, the size of model and the precision and speed of forward model method determine the computing time of forward model. Adopting high density sampling filter method to compute forward response function-polarization ellipticity, we compute algorithm through adjusting parameter and selecting Sampling Interval to realize Hankel Transform Algorithm, response computation for Electric Doublet, the standard of fast computing speed and high computing accuracy. In traditional magnetotellurics forward theory, Sampling Interval is10 . But it can not satisfy the accuracy of radar detecting frequency range. Adjust parameter M and Sampling Interval- ln10100 . After computing the filtering coefficients, the coefficients then are used into Hankel integration. By contrast to other algorithms, the high density sampling algorithm has a large superiority. The algorithm solves the problem of losing accuracy in the traditional filtering coefficients, and also avoids the problem of losing efficiency in the Chave's Gauss integration. Compared to other methods; it could improve the inversion efficiency.We adopt a robust descent type algorithm for geophysical inversion through adaptive regularization to inverse the underground medium parameter. Steepest descent method was proposed by French mathematician Cauchy (1847).It has inspiration for other computation and occupies a commanding position in the optimization algorithm. Steepest descent direction of functions is negative gradient direction. When descent direction is positive associate close to the negative gradient direction, the descent speed is low. Only the case that the descent direction and negative gradient direction is the same, can guarantee the sequence to descend in the fastest speed. Steepest descent method can guarantee convergence, but convergence rate is low. Although the Steepest descent direction is the most fast descending direction of objective function from the local convergence, it is not the best direction from the global convergence, which makes searching route swing to and fro and low convergent speed.The adopted improved method-steepest descent method is to improve insufficiency and make convergence from the whole range. Therefore, it makes improvements in the direction vector and the step size. First, for the direction vector, we choose it though adaptive regularization and make sure that satisfy Wolfe theorem, the theorem assure that it is convergent in global. We now minimize F~ through Polak–Ribiere form of CG technique. I have adopted Armijo's method in determining step length. So we solve the global minimum problem, and making the medium parameters convergence in global .Forever, the precision of inverse and the rate of convergence improved. In this paper, we inverse with the 1 D layer model to validate the precision of inverse and the rate of convergence. In contrast ,the error of the inversion result of the least squares method is too large for the resistivity,dielectric constant and deeps .It says that it convergence to the local minimum because lock the information .But the improved steepest descent method have a better robust than the least squares method ,does not convergence to the local minimum.This paper makes a full investigation of the adopt inversion method and develops a program of 1 D inverse algorithm suited to high frequency electromagnet. High density sampling filter method combined with steepest descent method based on adaptive regularization is the pioneering point of this paper and paves the way for future development in this field. By contrast with other methods of inversion, our method has the better robust; it is a key in this paper. Our study in this paper mostly on 1 D layer medium, the adopt algorithm is the same with the 2 D and 3 D medium, but the 2D or 3D modeling and inversion will not be within the scope of the studies in this paper, it will be the work for the future.