"depth of mind" is a correct and usable phrase in written English.
It can refer to the strength of someone's mental capacity or internal thought processes. For example, you could say, "He was a great leader due to his impressive depth of mind."
In shot after shot, made through windows and doors, the director suggests a society under surveillance, shunting hurts and desires into ever-deeper recesses, from the street to the back office, from the courtyard to the closed doors of home to the depths of mind revealed in dreams (and he films a superb one).
Alexis de Tocqueville described Blackstone as "an inferior writer, without liberality of mind or depth of judgment".
You can start, move on, and then continue re-thinking it (starting gives it a place in the "depths" of your mind -- an inventive part of your mind) and then going back to it, to do more, so you won't get too bogged down, but it will have priority for the subconscious mind to work on it!
Chances are, if you were a comedy fan in 2004, the theme music of Peep Show's first series can still be heard looping somewhere in the depths of your mind, branded onto your brain by multiple nights of falling asleep with it on (again), only to be awoken by "Pip Pop Plop" looping for eternity on the DVD menu screen.
They have the good taste, cultural depth and independence of mind to see the absurdity of their condition.
Patients and families; husbands and wives; parents and children and colleagues and friends: because while they try, they will never understand the depth and breadth of mind and body required of a nurse.
I was not asleep for this, merely busy trying to mine the murky depths of my mind for song ideas.
I sought to press home the advantage, evoking memories from his political past that I hoped he would continue, somewhere in the depths of his mind, to treasure.
He invented his revolutionary way of painting, in which he dredges enigmatic forms from the depths of his mind to create coloured universes of inner space, a cosmos of sex and death, in Paris in the 1920s.
The thing is, I don't think I could reach the depths of my mind with a gold-ribbed hare's ear nymph on a floating line, even a bead-head nymph.
But when he returned to Switzerland, he said, the American space program was in a lull so he turned to plumbing the depths of the mind instead, and became a psychiatrist.
