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"the increased depth" is correct and usable in written English.
You can use it when you are discussing a change in the amount of something, for example: "The increased depth of the lake allowed us to explore further."
Exact(28)
The increased depth of fine sediment in these areas also favored vegetative encroachment.
The increased depth to paralithic contact, chemical denudation and mineral transformation are likely functions of greater water availability and increased primary productivity.
Through on-line plasma emission acquisition and analysis, we obtain the positive association between the increased depth and the optical signal output.
In the present study, the increased depth sensitivity of hard X-ray photoelectron spectroscopy (HAXPES) as compared to conventional X-ray photoelectron spectroscopy (XPS) is used to study electrochemical changes at such a buried carbon/SEI.
Tiplady described her role in the episode as not being "just the cute Jordan Black with easy scenes and lots of giggling", and added that the increased depth her character was given served to heighten her interest in acting.
The increased depth of the 454 data sets can cause CAP3 and other assembly programs to run out of memory.
Similar(32)
Open image in new window Fig. 4 a Spatial resolution of PET deteriorates towards the edge of the FOV because of the increased depth-of-interaction effects (b).
It was a sign of the increasing depth and maturity of the medium.
Another view was that it was due to the increasing depth and sophistication of financial markets.
The increasing depth of plants' roots led to more washing of nutrients into rivers and seas by rain.
For all the sequence encoding schemes, the prediction accuracies decrease with the increasing depth levels.
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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