Yao et al. (1999) and Berryman (2001b) provide methods for calculating the a posteriori covariance for iterative methods based on SVD. For a thorough description of the methods I refer to these papers. The principle is as follows; each iteration provides one extra vector in the solution space. After K iterations these K vectors are used for calculating the a posteriori covariance. As a consequence, if more iterations are performed, not only the approximated inverse but also the a posteriori covariance becomes more accurate. Figure 9b,c shows a posteriori covariance matrices for M=33 model parameters obtained by respectively CG and LSQR. Both matrices resemble the real a posteriori covariance matrix (Fig.9a). Note that both methods compute the complete covariance matrix, so also the non diagonal elements.