Magnetotelluric Data Reconstruction Based On Radial Basis Function

In the collection of magnetotelluric measured data,due to the restrictions of topographical conditions or the influence of humanistic noise,data at certain locations cannot be collected or the data quality of individual measurement points is not ideal,resulting in some measurement points,The lack of frequency point data leads to inaccurate final inversion model,and it is impossible to obtain accurate interpretation and description of underground structures.In order to solve the above problems,this paper proposes a method of magnetotelluric transfer function reconstruction based on radial basis functions.The thesis expands from the radial basis function interpolation theory,discusses and solves the solution when the interpolation function appears singular matrix,improves the accuracy of the interpolation result,and adaptively determines the shape parameter of the Gaussian function according to the local density of the sample point.The correction was made,and the basis function interpolation polynomial was established,and the regularized least squares method was used to solve the underdetermined equations to obtain the interpolation result,which avoided the problem of the radial basis function not being able to fit the polynomial function or overfitting the data,and finally realized Reconstruction method of magnetotelluric transfer function based on radial basis function.The synthetic data of the theoretical model and the calculation examples of the measured data show that the method is suitable for the magnetotelluric measurement of dense networks.Choosing appropriate shape parameters and regular term coefficients can effectively improve the reconstruction effect during data reconstruction.The decisive factor influencing the reconstruction results is the selection of sample points;further,the transfer function of the missing data after reconstruction and the transfer function of the missing data without reconstruction are respectively carried out in three dimensions.Inversion comparison shows that the former is closer to the original inversion result model without missing data.The method proposed in this paper has a certain practical value for the reconstruction of magnetotelluric transfer function,and can effectively reduce the impact of missing data at measurement points and frequency points caused by terrain influence or low signal-to-noise ratio on the three-dimensional inversion results.