Computing tomographic resolution matrices using Arnoldi’s iterative inversion algorithm

Resolution matrices are useful in seismic tomography because they allow us to evaluate the information content of reconstructed images. Techniques based on the multiplicity of equivalent exact formulas that may be used to define the resolution matrices have been used previously by the author to design algorithms that avoid the need for any singular value decomposition of the ray-path matrix. An explicit procedure is presented for computing both model and data resolution matrices using Arnoldi’s algorithm for iterative inversion in seismic tomography. Arnoldi’s method differs from the Lanczos scheme by including explicit reorthogonalization of basis vectors. Some convenient notation is introduced to permit ready comparison of Arnoldi’s method with the Lanczos approach. Arnoldi’s method requires greater storage of basis vectors but completely overcomes the lack of basis vector orthogonality, which is the major practical limitation of the Lanczos method.