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The phrase "approach the surface" is correct and usable in written English.
It can be used in contexts related to physical movement towards a surface, such as in scientific, technical, or metaphorical discussions.
Example: "As the submarine began to approach the surface, the crew prepared for their ascent."
Alternatives: "move towards the surface" or "get closer to the surface."
Exact(27)
Others live deeper and do not approach the surface.
Gravity anomalies are low over thick sedimentary layers and high when denser rocks approach the surface.
As diapirs first rise through the planet's interior and approach the surface, they can lift the rocks above them, fracturing the surface in a radial pattern.
Some lantern fish live in the depths to 300 metres (about 1,000 feet) by day, but at night they may approach the surface.
Their energy is spent in crossing that great submerged highland east of Cape Cod known as Georges Bank, the crests of whose highest hills approach the surface at the Cultivator Shoals.
This is good news, because a much faster rotation could have made it harder to approach the surface, says mission manager Makoto Yoshikawa of JAXA's Institute of Space and Astronautical Science in Sagamihara.
Similar(33)
In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D.
The pressure drops as the boiling water approaches the surface, causing it to flash into steam.
"But as the diver approaches the surface, the decreasing water pressure causes a drop in pressure of the oxygen in the brain.
Images taken by the spacecraft as it approached the surface showed one large crater, 500 feet wide, and a smattering of small ones.
All arteries have a pulse, but it is most easily felt at points where the vessel approaches the surface of the body.
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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