An explicit procedure is presented for computing both model and data resolution matrices within a Paige-Saunders LSQR algorithm for iterative inversion in seismic tomography. These methods are designed to avoid the need for an additional singular value decomposition of the ray-path matrix. The techniques discussed are completely general since they are based on the multiplicity of equivalent exact formulas that may be used to define the resolution matrix. Thus, resolution matrices may also be computed for a wide variety of iterative inversion algorithms using the same ideas.
James G. Berryman,
"Tomographic resolution without singular value decomposition", Proc. SPIE 2301, Mathematical Methods in Geophysical Imaging II, (23 September 1994); doi: 10.1117/12.187487; https://doi.org/10.1117/12.187487