Art wrote:
"---yet I am not finding any documented proof other than emperical
work."

As usual, Terman has answers. See page 882 of his 1955 opus: "Effect of
Ground on the Directional Pattern of Ungrounded Antennas - Image
Antennas."

It`s in the book; math, diagrams, tables, as needed to imagine what
happens.

Best regards, Richard Harrison, KB5WZI