Many techniques have been established that perform tomographic reconstructions of the acoustic velocity profile of a solid object. A SIRT technique was selected as a particular one that was able to handle arbitrary sampling geometries and to incorporate a raybending correction. In this paper, these modifications to the basic algorithm are presented. A fast approximate raybending correction, suitable for use on personal computers, is given based on discretization of the raypaths, and the use of a graph-searching algorithm to obtain the minimum time path. The performance of the algorithm is evaluated in the field of seismic frequencies, imaging an area of backfill in an irregularly shaped rock pillar in a hard rock mine.