The cross is analogous to the two-barred archiepiscopal cross used in heraldry to indicate an archbishop, and seems to have been used precisely to indicate an ecclesiastical rank still higher than that of archbishop.
In the past, this design of the cross was often used in ecclesiastical heraldry as a distinctive mark of his office.
It was often merely an artistic device, as use of a staff or crosier was not part of the traditional papal insignia.
[1] However, at least one staff surmounted with a papal cross does exist.
Symbolism connected with the papal powers have been attached to the three crossbars, similar to the symbolism attached to the three bands on the papal tiara.