A non-linear truncated SVD variance and resolution analysis of two-dimensional magnetotelluric models

Details A non-linear truncated SVD variance and resolution analysis of two-dimensional magnetotelluric models A non-linear truncated SVD variance and resolution analysis of two-dimensional magnetotelluric models

May 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007geoji.169..435k&link_type=abstract

Geophysical Journal International, Volume 169, Issue 2, pp. 435-447.

Astronomy and Astrophysics

Astronomy

3

Magnetotellurics, Model Resolution, Model Variance, Non-Linearity, Svd, Tsvd

Scientific paper

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.

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