'much greater depth' is correct and usable in written English.
You can use it when referring to a comparison between two different levels of something. For example, "He has a much greater depth of knowledge on the subject than I do."
After great labor, wr realized that China was at a much greater depth than we had anticipated.
Because the strings are longer in a grand piano, you get a much greater depth, control and volume of sound.
It needs greater char without and much greater depth of flavour within, though the bearnaise is serviceable.
So you want the soil loosened to a much greater depth than those two inches of topsoil the builder may have left you".
By spooling out these themes over dozens of episodes, the series is able to explore them in much greater depth than the old zombie films ever could.
Johnson made his bat talk for 64 runs on the first day but he spoke in much greater depth and volume with ball in hand yesterday.
More usually, however, the lower layers of the air are stirred by motion over the rough ground, so the cooling is distributed through a much greater depth.
As for the larger statue, which was 180 feet tall, Mr. Emmerling said its much greater depth - about 40 feet - made it much more difficult to restore.
With this project they were invested in what was happening, because they'd imagined they were the character from the beginning, that they were able to describe how they were feeling in much greater depth.
And younger writers like Martin McDonagh, whose play "The Beauty Queen of Leenane" won four Tony Awards in 1998, set their plays on ground that Mr. Murphy covered in much greater depth decades ago.
But I was contemplating a point that Fellman explores in much greater depth about the way that myths and legends become part of the culture, and are themselves used to politicize certain values, what are called "family values".
