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The phrase "affect the depth" is correct and usable in written English.
It can be used in contexts where you are discussing how something influences or changes the level or intensity of a particular aspect.
Example: "The type of soil can significantly affect the depth at which the roots of the plants grow."
Alternatives: "influence the depth" or "impact the depth".
Exact(23)
But it can also affect the depth of a district's curriculum, jeopardizing programs in foreign languages, music or art.
However, burrowing crabs affect the depth distribution of polychaete and thus their availability to shorebirds.
Initiator system compositions were varied and shown to affect the depth profile.
The isostatic land uplift also seems to affect the depth of the redox interface in the long run.
The depth of cure test revealed significant difference among the photoactivation methods for C3 denying the hypothesis that photoactivation methods do not affect the depth of cure.
Asthenospheric upwelling can affect the depth and dip angle of the slab by changing the thermal state or mantle flow beneath the volcanic front.
Similar(37)
The rates of decrease and increase of the radiation flux affect the depths of the "wells" and were found to be rapid and shallow for the "Harmattan Well", and gentle and deep for the "Rain Well".
The conductivity σ also affects the depth of penetration, which is commonly represented by the skin depth, Sd.
The velocity anomalies related to salt such as pull-up event could have affected the depth estimations.
The glucan solution (3%, v/w) has opalescent, bluish-white colour and the concentration affected the depth of colour.
The model we presented to account for this observation identified two channels through which the variation in the informal sector size affects the depth of the financial sector.
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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