Research Of Resistivity Inversion Based On Shrinking Landweber Iterative Method

The geophysical inverse problem is a branch of geophysics.Due to the development of the science and technology engineering,resistivity tomography has become an important research content in geophysical inverse problem.For resistivity tomography,the resistivity structure below the surface is inferred by receiving signals.So it can be transformed into an optimization problem.First,we can reconstruct its mathematical model through some method,and then study the mathematical model,finally obtain the structure of the underground resistivity.However,in the application of industrial production,due to the interference of noise and other factors,the inverse problem of resistivity is ill-posed.When we reconstruct its mathematical model,therefore,need to use regularization method,and then use inversion algorithm for solving,the stable approximate solution of the true solution is obtained using MATLAB to get the composition of the resistivity.In this paper,the mathematical model of resistivity is reconstructed by Tikhonov regularization method,and then the resistivity inversion model is solved by the shrinking Landweber iteration method.The Tikhonov regularization and the shrinking Landweber iterative method are the important method to study optimization problems,and they have the good applicability.In addition,this paper briefly describes the proximinal modification Landweber iterative method and compares it with the shrinking Landweber iterative method to verify the inversion effect of the Tikhonov regularization and the shrinking Landweber iterative method.Resistivity tomography is mainly obtained by measuring the test data of the regional.Inversion algorithm was applied to mathematical model to reconstruct the resistivity distribution image.In this paper,the first simulation experiment is based on the resistivity model with the abnormal body with the structure of the four sharp corners.It can show the location of the abnormal body structure when the shrinking Landweber iteration method appling to the resistivity inversion model.In addition,the comparison between the inversion image and the real resistivity image after adding the different noise is verified that the shrinking Landweber iterative method has good anti-noise capability.Then the shrinking Landweber iteration method and the proximinal modification Landweber iteration method is applied to the multiple corners of resistivity model of abnormal body structure.It can be obtained the inversion image respectively under different noise.Compared with the inversion effect of the two iterative methods,it is proved that the shrinking Landweber iterative method has good stability when it is applied to the mathematical model of resistivity.