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"progressive deepening" is correct and usable in written English.
It is usually used to describe a process of becoming increasingly more involved or detailed. For example, "The training program was designed to promote progressive deepening of the participants' knowledge and skills."
Exact(4)
The conventional interpretation of the Jurassic Lower Cretaceous succession in the Porcupine Basin suggests an extensional setting with progressive deepening of the basin.
We modelled a more complex initial geometry closer that observed in the field by simulating the northward progressive deepening of a potential décollement (the Gault clay).
Atrophic withering, fine wrinkling and progressive deepening of facial creases ensue.
Clinically, the disease is monitored by examining ONH morphology for signs of glaucomatous optic neuropathy, which if untreated will be recognised as a progressive deepening and enlarging of the cup and thinning of the neuroretinal rim.
Similar(56)
The change in both factors is related to the landscape evolution, mainly with the development and progressive enlargement and deepening of the nearby doline.
And as the federal Conservative government, increasingly indifferent to Quebec, shifts economic and political power westward to Alberta, such progressive yearnings could deepen.
Soil development is hypothesised to be often non-linear with time and characterised by stages of progressive and regressive evolution caused by upbuilding (formation, profile deepening) and erosion (profile shallowing).
There was consensus among the progressives on the panel – which was hosted by Guardian Australia's Lenore Taylor, and featured Katharine Murphy – that inequality was deepening in Australia.
The recession is deepening.
Deepening rifts Too optimistic?
Instead the gulf is deepening.
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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