selichot - Change from Kail Erech to Kail Melech in Selichos

Nusach Ashkenaz and Ashkenazi Nusach Sefard both start Selichos with Kail Erech Apayim prior to the first Hashem Hashem, and then for the rest of Selichos say Kail Melech Yoshaiv prior to Hashem Hashem. Why do we only say Kail Erech the first time? Why the change after the first time? Why not Kail Melech all the time?

Answer

This idea may have an earlier source, but I found in the Nit'ei Gavriel (Rosh HaShana, ch. 2, fn. 33) that the recitation of the 13 middos causes HaShem to move to His throne of mercy (see also Rosh HaShana 17b), which is why all subsequent recitations are preceded by "Kail Melech Yoshaiv" ("Lord King who sits on the Throne of Mercy").