LHCb VELO software alignment, Part I: the alignment of the VELO modules in their half boxes

Software alignment of the Vertex Locator (VELO) is a critical stage of the LHCb alignment strategy. This note presents a demonstration of a potential algorithm to satisfy the requirements of this stage. A fast track-based software alignment procedure is described. This method is based on non-iterative least squares fitting. The first step of the algorithm, the alignment of the VELO modules in their half-boxes, is fully described and results obtained with simulated events are presented and discussed. The approach described in this document, and the tools developed, are also applicable to the alignment of the other LHCb sub-systems and the global relative alignment of the sub-detectors.