Research on regularized inversion algorithms of one-dimensional magnetotelluric data

In order to solve the ill-posed problem of magnetotelluric inversion,regularization is the main application method at present. Regularization is to add a stable functional to the objective functional of data,so as to obtain the stable solution of ill-conditioned problem. In order to effectively improve the non-uniqueness and instability of solutions in magnetotelluric inversion,the least square smoothing constraint inversion algorithm and homotopy regular inversion algorithm are proposed to solve these problems. Among them,homotopy regular inversion algorithm has the advantage of good convergence in solving nonlinear problems. This algorithm combines homotopy idea with Tikhonov regularization idea to construct inversion objective functional. Different from the existing achievements in the selection of regularization factors in magnetotelluric one-dimensional regularization inversion algorithm,both regularization algorithms use Morozov deviation principle to determine the regularization factors. In order to verify the robustness of the two algorithms,the theoretical data can be inverted after adding random Gaussian noise,and the model parameters can also be inverted basically. The results show that the two algorithms have good robustness. Considering that homotopy regularization algorithm is applied to magnetotelluric one-dimensional inversion for the first time,it further inverts the measured data. Inversion data comes from a measured point in Huapichang geothermal field,Jilin Province,and the inversion results are compared with Bostick inversion and Occam inversion results. The inversion results of homotopy regularization algorithm are more consistent with the actual exploration results,which shows that homotopy regularization algorithm has higher accuracy in the processing of magnetotelluric measured data. The results of an example show that the two algorithms are effective and can improve the ill-posed problem of magnetotelluric inversion。