On Resolution Matrices

Abstract Solution appraisal, which has been realized on the basis of projections from true medium to solution, is an essential procedure in practical studies, especially computer tomography. The projection operator a linear problem or its approximation nonlinear resolution matrix for solution (or model). Practical applications can be used quantitatively retrieve resolvability medium, constrainability parameters, and relationship between factors study system. A given row vector parameter quantify resolvability, deviation expectation, difference that neighbor main-diagonal element, row-vector sum, neighboring elements vector, respectively. length should estimated although it may unreliable when unstable (e.g., due errors). Comparatively, lengths are column vectors observation-constrained parameters reliable this instance. Previous studies have generally employed either direct hybrid as model matrix. inversion with damping general Tikhonov regularization) Gramian symmetric). using zero-row-sum regularization matrices higher-order regularizations) one-row-sum but not stochastic When two appear iterative inversions, they rather gradient improvement immediately after iteration. Regardless, their resultant inversions surface-wave dispersion remain similar those solution. influenced by various study, derived only observation matrix, whereas matrices. limitations imply appropriateness questionable applications. Here we propose new complete overcome limitations, all errors) (inverse non-inverse) incorporated. Insights above ensuring appropriate application appraise model/solution understand system, also important improving