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A non-linear truncated SVD variance and resolution analysis of two-dimensional magnetotelluric models
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.
2007 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 169, no 2, 435-447 p.Article in journal (Refereed) Published
Abstract [en]

A novel approach to assess variance and resolution properties of 2-D models of electrical resistivity derived from magnetotelluric measurements is presented. Based on a truncated singular value decomposition (TSVD) scheme on a local subspace, it partly takes the non-linearity of the inverse problem into account. The TSVD resolution and variance analysis is performed on a single cell at a time. A variance threshold is selected and the resulting model resolution is determined. As an improvement over existing schemes, non-linear semi-axes are introduced to describe the non-linear confidence surface in the directions of the model eigenvectors and they replace the inverse singular values entering into the standard expression of model variances. The model variance of the cell considered is estimated from the sum of squares of the non-linear semi-axes up to the given variance threshold. This, in turn, gives the truncation level of the TSVD and the row of the model resolution matrix belonging to the considered cell can be computed from the model eigenvectors of the TSVD. The information contained in the resolution matrix is condensed to easily comprehensible measures like the centre of resolution and horizontal and vertical resolution lengths.The validity of our non-linear model variance and resolution estimates is tested with a most-squares technique which gives an improved estimate of model variability.A synthetic model with a conductive block in a homogenous half-space is analysed. TSVD analyses for model cells on the upper edge of the block and outside the block illustrate how the truncation process works. Typically, the linear and non-linear semi-axes are almost equal up to a certain singular value number, after which the non-linear semi-axes increase much less than the linear semi-axes. This important result indicates that the resolution of 2-D magnetotelluric models is significantly better than previously suggested by linear schemes for the computation of model variance and resolution properties. A field example from the Skediga area (Sweden) shows that the electrical resistivity distribution of sand and gravel formations which are only laterally bounded by conductive clay lenses is relatively well resolved whereas there is little resolution for the transition between the sand and gravel layer and the basement under a clay cover.

Place, publisher, year, edition, pages
2007. Vol. 169, no 2, 435-447 p.
Keyword [en]
magnetotellurics, model resolution, model variance, non-linearity, SVD, TSVD
National Category
Earth and Related Environmental Sciences
Identifiers
URN: urn:nbn:se:uu:diva-97757DOI: 10.1111/j.1365-246X.2006.03320.xISI: 000245675000006OAI: oai:DiVA.org:uu-97757DiVA: diva2:172816
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, ThomasPedersen, Laust B.

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