Three resolution matrices for the underdetermined inverse problem presented in Fig. 1. Panels (b), (d) and (f) are the normalized matrices corresponding, respectively, to the panels (a), (c) (e). The matrix in (c,d) is an identity matrix. The matrices are calculated by the SVD of (a,b) the G matrix and its inverse, (c,d) the A matrix and its inverse and (e,f) the G matrix and the inverse of the A matrix. A is a matrix that combines G and the flatness constraints C among all neighbouring parameters. The weight (λ= 1) is used here. In panel (a), all components of the resolution matrix for parameters, m_i (i= 86–100) are 0 because no information is available for the parameters in the observation matrix G. The extent of the square-like pattern indicates that the related solution parameters should have the same value in this inversion problem. The extent can be taken as the resolution length of the solution parameters. The horizontal red bars in (d,f) of each model parameter are the same as in (b), and indicate the resolution lengths from (a), but are centralized along the diagonal element of the matrix.