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Non-linear model error and resolution properties from two-dimensional single and joint inversions of direct current resistivity and radiomagnetotelluric data
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
College of Oceanic and Atmospheric Sciences, Oregon State University, USA.
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
2010 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 182, no 3, 1174-1188 p.Article in journal (Refereed) Published
Abstract [en]

P>For 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.

Place, publisher, year, edition, pages
2010. Vol. 182, no 3, 1174-1188 p.
Keyword [en]
Instability analysis, Inverse theory, Numerical approximations and analysis, Electromagnetic theory, Magnetotelluric
National Category
Earth and Related Environmental Sciences
Identifiers
URN: urn:nbn:se:uu:diva-97759DOI: 10.1111/j.1365-246X.2010.04686.xISI: 000280997700006OAI: oai:DiVA.org:uu-97759DiVA: diva2:172818
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Improvement and Assessment of Two-Dimensional Resistivity Models Derived from Radiomagnetotelluric and Direct-Current Resistivity Data
Open this publication in new window or tab >>Improvement and Assessment of Two-Dimensional Resistivity Models Derived from Radiomagnetotelluric and Direct-Current Resistivity Data
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Two-dimensional (2-D) models of electrical resistivity are improved by jointly inverting radiomagnetotelluric (RMT) and direct-current resistivity (DCR) data or by allowing for displacement currents in the inversion of RMT data collected on highly resistive bedrock. Uniqueness and stability of the 2-D models are assessed with a model variance and resolution analysis that allows for the non-linearity of the inverse problem.

Model variance and resolution are estimated with a truncated singular value decomposition (TSVD) of the sensitivity matrix. In the computation of model errors, inverse singular values are replaced by non-linear semi-axes and the number of included eigenvectors is increased until a given error threshold is reached. Non-linear error estimates are verified with most-squares inversions. For the obtained truncation levels, model resolution matrices are computed. For RMT data, non-linear error appraisals are smaller than linearized ones. Hence, the consideration of the non-linearity in RMT data leads to reduced model errors or enhanced model resolution.

The dielectric effect on RMT data is investigated with a new 2-D forward and inverse code that allows for displacement currents. As compared to the quasi-static approximation, apparent resistivities and phases of the impedance tensor elements are found to be significantly smaller and the vertical magnetic transfer function exhibits more distinct sign reversals. More reliable models of electrical resistivity are obtained from areas with highly resistive bedrock, if displacement currents are allowed for. In contrast, inversions with a quasi-static scheme introduce artefactual structures with extremely low or high resistivities.

A smoothness-constrained 2-D joint inversion of RMT and DCR data is presented. The non-linear model variance and resolution analysis is applied to single and joint inverse models. For DCR data, the errors estimated by most-squares inversions are consistently larger than those estimated by the non-linear semi-axes, indicating that DCR models are poorly resolved. Certain areas of the joint inverse models are better resolved than in the single inverse models.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2008. 82 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 572
Keyword
Electromagnetic geophysics, radiomagnetotellurics, direct-current resistivity, displacement currents, dielectric effect, non-linearity, inversion, regularization, two-dimensional model, model variance, model resolution, data resolution
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-9366 (URN)978-91-554-7334-1 (ISBN)
Public defence
2008-12-05, Axel Hambergsalen, Department of Earth Sciences, Villavagen 16, 75236 Uppsala, Sweden, 10:00
Opponent
Supervisors
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2016-05-13Bibliographically approved

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Kalscheuer, ThomasGarcia Juanatey, Maria de los AngelesPedersen, Laust B.

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