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The phrase "a depth of over" is correct and usable in written English.
It can be used when describing measurements, particularly in contexts related to water, geology, or any situation where depth is relevant.
Example: "The lake has a depth of over 50 meters, making it one of the deepest in the region."
Alternatives: "a depth exceeding" or "a depth greater than".
Exact(15)
Descending by Mir submersible to a depth of over 4km, a Russian-led expedition planted a titanium Russian flag beneath the North Pole (pictured).
"With our relief well efforts, we've drilled to a depth of approximately 5,400 measured feet (we have to drill to a depth of over 8,000 feet), and remain on schedule to complete this process between late February and late March".
The mines reach a depth of over 500 m, where thick lignite seams are mined (Figure 3).
Sitaro is an archipelago of volcanic oceanic islands that arise from the sea floor at a depth of over 1,000 m within the Sangihe arc (Shekelle et al. 2008).
The mine was subject to deep mining condition with a depth of over 735 m. Figure 10 shows the modelled vertical strata de-stressing in and about the LW panel.
The squid Brachioteuthis may ascend from a depth of over 1,000 meters to less than 200 meters each day at dawn, which adds to the thrill of their commute a pressure shift from 1,500 pounds per square inch to 300, a differential equivalent to 80 atmospheres.
Similar(45)
Initial U.S.G.S. data suggested that the earthquake was quite shallow, at a depth of just over half a mile below the surface.
In a similar vein, an Austrian group called Gelatin has built the Eighth Wonder of the World, a hole filled with water into which people are invited to dive to discover, at a depth of just over 11 feet, the wonder in question.
The water pooled to a depth of 45 meters over an area about 850 kilometers across.
Measured at a depth of 4 cm over a period from July, 25th 2014 to July, 25th 2015*.
Correction: This article originally stated the amount of water consumed by humans each year, 9.087 cubic kilometers, would flood the state of California to a depth of a little over 2 centimeters.
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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