Objectives Continuous and dense global navigation satellite system (GNSS) surface deformation data provide an effective tool to invert refined regional surface mass variations. However, the factors influencing the reliability of GNSS inversion results need to be further studied, such as regularization (including the construction of regularization matrix and determination of optimal regularization parameter), observation noise and distribution of GNSS stations.
Methods First, we proposed an improved regularized Laplacian constraint matrix and discussed the adaptability of the generalized cross-validation (GCV) method in selecting the regularization parameter of ill-posed equations for inversion of regional surface mass variations based on the loading Green's function theory. Second, we compared the effects of different constraint matrices and constraint methods on the GNSS inversion results. Third, we further investigated the influences of different noise levels of GNSS vertical displacement, the number and distribution of GNSS stations on the inversion results.
Results (1) The regularized Laplacian matrix in this paper can better suppress the edge effects than the traditional Laplacian matrix. (2) The GCV method can effectively determine the optimal regularization parameter, and the inversion results are in good agreement with those solved by the root mean square error (RMSE) criterion. (3) If there are enough GNSS stations and the observation accuracy is high enough in the studied area, the inversion results will be more reliable. Meanwhile, the accuracy of inversion results for uniformly distributed stations is comparable to that of randomly distributed stations when the number of stations is large enough.
Conclusions The improved regularized Laplacian matrix and the GCV method can improve the reliability of GNSS inversion results, which can guide the inversion of surface mass variations using measured GNSS data.