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The phrase "determine the depth" is grammatically correct and can be used in written English.
It means to measure the distance or extent from the surface to the bottom of something. Example: The team used sonar equipment to determine the depth of the ocean at that specific location.
Exact(60)
He said last week that the state of the economy during the next few months will determine the depth of dissatisfaction among voters in November.
This was an entirely unscientific experiment, but here is what we learned: Responsibility and time, not gender, determine the depth of the bond with a child.
Near Hook Mountain, a tall stone outcropping on the west bank a mile north of Nyack, the bosun dropped a line with a lead sinker to the bottom, to determine the depth just as Hudson's crew did (two fathoms, or about 12 feet, akin to what Jouet recorded).
"HMS Echo will have a pretty accurate fathometer - an echo sounder - to determine the depth.
Water level is sensed to determine the depth of the water in the tank.
Auger electron spectroscopy (AES) was used to determine the depth profile of the implanted nitrogen.
We could not determine the depth of the arc Moho below ECr10 because clear Moho reflections were not observed.
Then, assuming some profile of the substrate etching, it is possible to determine the depth of the formed nanoholes.
However, in principle, the latter could be used to determine the depth dependence of bioirrigation intensity directly.
A non-destructive ultrasonic inspection was carried out to determine the depth of the exfoliation corrosion damage.
Time-of-flight and conventional forward recoil spectrometry were used to determine the depth profile of the deuterated component.
More suggestions(17)
ascertain the depth
delineate the depth
determine the gravity
determine the intensity
determine the comprehensiveness
determine the thoroughness
determine the length
determine the severity
determine the breadth
determine the completeness
determine the width
calculate the depth
establish the depth
determine the magnitude
determine the degree
discuss the depth
determine the extent
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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