Interesting question - I have looked for it, but haven't found it for large faults with complicated histories. If the faults are small (enough to be idealized as dislocations in elastic medium) then displacement-length scaling relationships probably apply to depth as well, but propagation/growth rate might be different in the slip direction than in the slip-normal direction, so it might matter what kind of faults you're interested in. For bigger faults (e.g. plate boundary faults) I don't know of any observational or theoretical constraints.
Please share if you find more!
Christie