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The phrase "a given depth" is correct and usable in written English.
It can be used in contexts where you are specifying a particular depth that has been established or defined for a purpose, such as in scientific, technical, or mathematical discussions.
Example: "The experiment was conducted at a given depth to ensure consistent results across all trials."
Alternatives: "a specified depth" or "a defined depth".
Exact(60)
The getLevel method returns, for a given depth, a new, flat MeterSequence.
Together, they enable the system to compensate SA at a given depth.
Currents also can be measured by drifting floats, either at the surface or at a given depth.
Exact expressions of the masses of water leaving a given depth are also derived for the three cases.
Specific yield determines the volume of water loss per unit area necessary to lower the water table by a given depth.
The getLevelSpan method returns, for a given depth, the time span of each node as a list of start and end values.
This makes it very challenging to determine the color of a given depth pixel or the depth of a given color pixel.
We now have at our disposal some algorithms that succeed in quantifying FHR and fetal movements with a signal from a given sensor at a given depth.
For the fine-over-coarse layered soils of LS and LSL, water and nitrate were uniformly distributed at a given depth in the top layer soil.
This increased range straggling for a given depth results in a reduction of the local current density and consequently in a more pronounced in situ defect annealing.
A purposely designed single-particle-injector was used to impulsively introduce fuel particles one at a time at a given depth into the fluidized bed.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com