Measures of resolution in global body wave tomography

Abstract

The resolution of tomographic images is most often evaluated through synthetic tests: the inversion algorithm used to derive the image itself is applied to a synthetic data set having the same source-station geometry of the real one, but theoretical travel times computed from a chosen "input model" (e.g., a checkerboard). The similarity between input model and solution of the synthetic test, used as a measure of resolution, has the major shortcoming of depending on the choice of the input model. Conversely, the similarity of the "model resolution matrix" (R) to the identity matrix is a rigorous measure of resolution that does not depend on any input model, but has the drawback of being computationally heavy. In the past decade, several authors have devised complicated algorithms for the approximate or iterative derivation of R. I show here that parallel Cholesky factorization of At · A (A being the matrix that identifies the linear inverse problem), feasible on shared-memory multiprocessor servers, provides an efficient way of determining both least squares solutions and resolution matrices in global tomography. I apply this procedure in an evaluation of the resolution of mantle structure from a global P-wave travel time data set.