The phrase "depth at which" is a perfectly acceptable and commonly used phrase in written English.
For example: The depth at which the water had reached was alarming.
We considered the depth at which they started gliding as a proxy to their depth of neutral buoyancy.
The depth at which women talk to and about each other is invaluable to me.
Bow planes, if fitted, are used principally to control the depth at which the craft runs.
In practice, the depth at which it is barely visible is noted.
The company was allowed to keep drilling, however, down toward the depth at which it would begin the fracturing.
Russia is not capable of sending divers to the 350-foot depth at which the Kursk now lies.
The indentation depth at which the substrate starts to deform plastically is sensitive to indenter geometry.
Scientists believe that the depth at which meltwater enters the ocean can affect global ocean circulation and, in turn, climate.
Depth depthcontrol Depth control allows the user to specify the depth at which each object is placed within a frame.
A simple formula to predict the depth at which wells drilled with seawater are prone to breakouts is derived.
The depth of the evaporation front influences the rate of salinisation and the depth at which salt accumulates.
