It's called "The Stereoptical Process". From the Wikipedia entry for Max Fleischer:
"These color cartoons were often augmented with Fleischer's patented three-dimensional effects promoted as "The Stereoptical Process", a precursor to Disney's Multiplane. This technique used 3-D model sets replacing flat pan backgrounds, with the animation cels photographed in front. This technique was used to the greatest degree in the two-reel Popeye Features Popeye the Sailor Meets Sindbad the Sailor (1936) and Popeye the Sailor Meets Ali Baba's Forty Thieves (1937)."
The patent for the Stereoptical Process:
used the setback process:
"The setback rig consists of a forced-perspective, miniature set mounted on a turntable, serving as background to the cel art held in a vertical glass platen, and a horizontal animation camera. The turntable is rotated incrementally behind the cels, creating the effect of a “tracking shot” — the 2D animated character, in a side-view walk cycle, traverses a realistically proportioned 3D environment which moves perspectivally across the background."
Also:
This is from Popeye the Sailor Meets Sinbad the Sailor. The film was ready in 1936 so this is probably from 1935. The company, Fleischer Studios, was the main rival of Disney at the time, but due to some bad decisions was bankrupt by 1942. I don't really know where OP got the "1950s" from. I don't think this system was used by then anymore -- I don't know why: I don't think it was any more expensive than the more popular method of doing quality animation. Of course, by 1950s animation was started to be done on the cheap and Hanna-Barbera was ready to step on the stage.
That cartoon filming system allowed putting 3D-objects on the background and foreground of the animation. It was extremely delightful system and allowed visual tricks like no other system. The end-results looked more "eye-popping" than most early Pixar-films.
Both Disney and Fleischer published these "making of"-films (fron which this gif is taken). Surprisingly, Fleischer was more advanced both technologically and socially - I remember that Fleischer had female artists while Disney only had them as colourists and called them on the screen with incredibly diminishive ways.
There's a Reddit discussion about that technique.
Here's a quick animation about "How cartoons were made in the 1950's"
A Youtube video: Popular Science | 35mm | Fleischer Studios Behind The Scenes | 1938 | Max Fleischer Popeye Cartoon
At 3:30 you can see the mountain being rotated on the wheel.
See how it looked on screen!
At 4:18
Coincidentally, its the Fleischer Studio channel
More links:
Popeye animation:
X post:
https://twitter.com/CinemaVsDave/status/1131970188411383810
https://floobynooby.blogspot.com/2015/09/the-innovations-of-fleischer-studios.html
https://www.fleischerstudios.com/ray3.html
https://www.classicmoviehub.com/blog/max-fleischer-universe-master-illustrators-at-work/
Popeye the Sailor: