GNGTS 2017 - 36° Convegno Nazionale

640 GNGTS 2017 S essione 3.2 The proposed MATLAB inverse algorithm applies the LSQR method to the least-squares formulation of the Tikhonov problem (Jacobsen et al ., 2003) (2) starting from (3) in which K is the Kernel matrix, L is the depth weighting matrix for the problem, y is the vector of SP observed data and the regularization parameter λ controls the weight between the residual and smoothing norms and introducing the QR factorization (4) The solution is obtained in the form (5) where (6) The columns of the matrix V span the subspace V , and the columns of the matrix W span the subspace W . V and W are the two subspaces in which the solution is splitted: the residual Fig. 1 - Sketch of the experimental setup showing the location of depth SP data points (upper right) and the position of surface data points (lower right), the iron bar installed during placement of sand (upper left) and patterns of ferric staining of pore fluid and sand below the phreatic surface at the conclusion of the study (lower left).