Two-dimensional single and joint inversion of direct current resistivity and radiomagnetotelluric data: Comparison of non-linear model variance and resolution properties

摘要

For the first time, a comparative analysis of the resolution and variance properties of two-dimensional (2D) models of electrical resistivity derived from single and joint inversions of direct current resistivity (DCR) and radiomagnetotelluric (RMT) measurements is presented. DCR and RMT data are inverted with a smoothness-constrained 2D Occamscheme. After the inversion, model resolution, model variance and data resolution analyses are performed both with a classical linearised scheme that employs the smoothness-constrained generalized inverse fromthe Occaminversion and a non-linear truncated singular value decomposition (TSVD) scheme. In the latter method, the non-linearity of the inverse problems is partly taken into account by replacing the linear semi-axes (i.e. the inverse singular values) in the computation of model variances with non-linear semi-axes that describe the non-linear confidence surface in the directions of the model eigenvectors. The condition that the estimated model variance of the cell considered is not allowed to grow beyond a given variance threshold gives the truncation level of the TSVD and the resolving kernel of the considered cell can be computed from the model eigenvectors. The non-linear model variance estimates are checked against improved and independent estimates of model variability obtained from a most-squares inversion.Synthetic data of a model with conductive and resistive blocks in a host of intermediate resistivity are inverted.Model variance and resolution analyses are performed for several cells. For both single and joint inversions,the smoothness-constrained scheme suggests very small model parameter variances (up to 4%) and relatively spread resolving kernels even for near-surface structures. According to the TSVD scheme, the non-linear semiaxes behave similar for both DCR and RMT data sets. Up to a certain singular value number, the linear and non-linear semi-axes are almost equal and after that the non-linear semi-axes increase much less than the linear semi-axes. While the model variability of RMT problems estimated from non-linear semi-axes is confirmed by the most-squares inversion in an average sense, the most-squares variance estimates of the DCR problem are consistently larger than the variance estimates based on the non-linear semi-axes. The large variability of DCR models as determined solely by the data is at least partly related to the lack of a vertical scale length in DCR models which is an inherent physical property. According to both analyses, the joint inversion improves the resolution of both resistive and conductive structures subject to an appropriate weighting of the different data sets.