Comparison of Iterative Back-Projection Inversion and Generalized Inversion Without Blocks: Case Studies In Attenuation Tomography

Abstract

Iterative back-projection tomography and generalized inversion without blocks (‘no-block’) are two different inversion techniques developed recently for 3-D studies, and are commonly applied to the inversion of travel-time data. In this study, we compare the two methods and derive one from the other under certain assumptions. We then apply these two methods to the attenuation problem, inverting for the quality factor, Q, of the medium. Usually, travel-time inversion involves large data sets and fine resolution is not possible if generalized inversion is applied. A relatively small data set with little redundancy enables us to apply both techniques with similar resolution. We applied the methods to the data sets obtained for two areas in southern California, the Coso-Indian Wells region and Imperial Valley. The results obtained by the two methods are very similar. Back-projection tomography is a direct and fast method for this type of problem. However, it does not provide formal error estimates and resolution. The no-block inversion requires more computational time, but formal errors and resolution can be directly computed for the final model. Thus, application of the two methods to the same data set enhances the objectivity of the final result.