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2009-09-04 – SEMINAR by Thomas Kalscheuer: Error and resolution properties of 2-D resistivity models from the inversion of direct current resistivity and radiomagnetotelluric data

4 September, 2009 (16:00 GMT), 5 Merrion Square, Dublin 2.

Speaker: Thomas Kalscheuer, ETH Zuerich, Switzerland.
Title: Error and resolution properties of 2-D resistivity models from the inversion of direct current resistivity and radiomagnetotelluric data.

Lecture Notes: Link
Archived Talk: Available here

Abstract:

For the first time, a comparative analysis of the resolution and variance properties of twodimensional (2-D) 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 2-D Occam scheme. Model resolution, model variance and data resolution analyses are performed both with a classical linearised scheme that employs the smoothness-constrained generalized inverse from the Occam inversion and a non-linear truncated singular value decomposition (TSVD) scheme. 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. The model error estimates are checked against improved and independent estimates of model variability obtained from a most-squares analysis. In a study with synthetic data, model error and resolution analyses are performed for several cells of the inverse models. For both single and joint inversions, the smoothness-constrained scheme suggests very small model parameter errors (typically a few per cent only) and resolving kernels that are spread over several cells in the vicinity of the investigated cell even for near-surface structures. For the TSVD scheme, the model variability of RMT problems estimated from non-linear semi-axes is confirmed by the most-squares inversion in an average sense. In contrast to this, most-squares error estimates of the DCR problem are consistently larger than error estimates from non-linear semi-axes except for the smallest
truncation levels. Therefore, error estimates of models obtained from DCR data should be computed with the most-squares inversion rather than from non-linear semi-axes. The nonlinear 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 improves error and resolution of both resistive and conductive 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, model error and resolution estimates 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.