Non-linear model error and resolution properties from two-dimensional single and joint inversions of direct current resistivity and radiomagnetotelluric data

Abstract

S U M M A R YFor the first time, a comparative analysis of the resolution and variance properties of 2-D models of electrical resistivity derived from single and joint inversions of dc resistivity (DCR) and radiomagnetotelluric (RMT) measurements is presented.DCR and RMT data are inverted with a smoothness-constrained 2-D scheme. Model resolution, model variance and data resolution analyses are performed both with a classical linearized scheme that employs the smoothness-constrained generalized inverse and a non-linear truncated singular value decomposition (TSVD). In the latter method, the model regularization used in the inversion is avoided and non-linear semi-axes give an approximate description of the non-linear confidence surface in the directions of the model eigenvectors. Hence, this method analyses the constraints that can be provided by the data. Model error estimates are checked against improved and independent estimates of model variability from most-squares inversions.For single and joint inverse models of synthetic data sets, the smoothness-constrained scheme suggests relatively small model errors (typically up to 30 to 40 per cent) and resolving kernels that are spread over several cells in the vicinity of the investigated cell. Linearized smoothness-constrained errors are in good agreement with the corresponding most-squares errors. The variability of the RMT model as estimated from non-linear semi-axes is confirmed by TSVD-based most-squares inversions for most model cells within the depth range of investigation. In contrast to this, most-squares errors of the DCR model are consistently larger than errors estimated from non-linear semi-axes except for the smallest truncation levels.The model analyses confirm previous studies that DCR data can constrain resistive and conductive structures equally well while RMT data provide superior constraints for conductive structures. The joint inversion can improve error and resolution of structures which are within the depth ranges of exploration of both methods. In such parts of the model which are outside the depth range of exploration for one method, error and resolution of the joint inverse model are close to those of the best single inversion result subject to an appropriate weighting of the different data sets.

A magnetotelluric investigation of the Scandinavian Caledonides in western Jämtland, Sweden, using the COSC borehole logs as prior information

“…Adding additional Marquardt-Levenberg damping to stabilize the model finding process (Kalscheuer et al 2010), the solution is…”

“…We applied the Emilia inversion package, which has two schemes for 2-D MT inversion: an Occam scheme and a damped Occam scheme (Kalscheuer et al 2010; Appendix A). While the former scheme applies general smoothness constraints, the latter one employs additional Marquardt-Levenberg damping for stabilization.…”

Two-Dimensional Magnetotelluric Modelling of Ore Deposits: Improvements in Model Constraints by Inclusion of Borehole Measurements

“…Under certain assumptions (Kalscheuer et al 2010), the model m kþ1 computed at the ðk þ 1Þth iteration can be related to the unknown true model m true , an optional reference model m r and the noise n contained in the data as…”

“…As model regularisation, smoothness constraints in the form of first-or second-order direct differences or derivatives of model resistivities are employed following Kalscheuer et al (2010). In case of convergence problems, Marquardt-Levenberg damping is employed in addition to smoothness constraints.…”

“…In the 2D smoothness-constrained least-squares inversion used here (Kalscheuer et al 2010), the fit of the forward response of a model m to the field data is measured using the root-mean-square (RMS) misfit RMS ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi In comparison with measurements on the surface, additional entries for the two model cells just above a receiver node need to be included to simulate the Jacobian matrix of borehole measurements. In the subsequent inversion examples, all Jacobian matrices (sensitivities) were computed using the sensitivity equation method (McGillivray and Oldenburg 1990;Rodi and Mackie 2001;Kalscheuer et al 2008).…”