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

Abstract

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.