This "local Lg" cannot be the real Lg !
The epicentral distances for these seismograms is less than 100 km, Lg should not yet be set-up, much less follow Sg by more than 10 seconds! Indeed, when I analyze the apparent group velocity of the LLg phase, it is extremely slow, on the order of 2 km/sec. It has the correct period for Lg, about 1.5 sec, but its velocity is way too slow!
What is this LLg?
At this time, my best guess is that LLg are surface waves trapped in the low-velocity Paleozoic basin layer. This layer varies in thickness around the Great Lakes, from more than 5 km in parts of the Michigan and Appalachian basins to less than a kilometer over the Cincinnati Arch.