We introduce an annotation scheme and corpus study to investigate the use of base and target components of analogies in tutorial dialogues. We present the development of the scheme and test its final form on a corpus of one-to-one tutorial dialogues on computer science, for which we achieve over 0.77 multirater inter-annotator agreement. We then annotate data from the same corpus to investigate the use of semantic wave structures from Legitimation Code Theory in tutoring, and we find a regular adherence to semantic wave structures in explanations which use analogies. We further identified different semantic wave shapes and show their distributions. We conclude that semantic waves and the novel characterisation of analogical explanations in tutorial dialogues reported in this investigation can be useful tools for both the analysis of human tutorial dialogue and future implementation of tutorial dialogue systems.