Simultaneous iterative reconstruction technique: Physical interpretation based on the generalized least squares solution

The Simultaneous Iterative Reconstruction Technique is a very suitable technique for inverting large sparse linear systems, since it is iterative and does not need the whole matrix to be stored in the internal computer memory. It was designed for medical tomography, but is nowadays commonly used in seismic tomography. We propose to analyze this inversion technique, which has nevertheless a few drawbacks, such as inconsistency and the introduction of nonphysical, a priori information into the solution resulting from an implicit rescaling of the problem. The introduction of a damped version of the original algorithm and the study of its relationship with the generalized least squares algorithm Tarantola and Valette , 1982 enables us to explain the physical behavior of the method. The damped algorithm appears to be more efficient than the original one because it allows us to control the inversion. There are two main options: (1) a fast convergence with, unfortunately, nonphysical, a priori information in the solution and (2) complete control of the a priori information, but at the expense of the convergence speed. Finally, we show how to compute the resolution matrix and an approximation of the estimated model covariance, without passing through memory‐consuming matrix inversions.