See the discussions especially by N. Bookides, who has worked on the site with C. Williams for years. N. Bookides and J. E. Fischer, “The Sanctuary of Demeter and Kore on Acro-Corinth,” Hesperia 41 (1972), pp. 283–331; N. Bookides and R. S. Stroud, Demeter and Persephone in Ancient Corinth (Princeton: ASCSA, 1987).