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The color scale with white after red mimics geography maps, where this looks quite natural (white being associated with mountain peak snow). It's a common color scale in environmental sciences. In R, it's available in terrain.colors().

"Maybe on average the ground level is collapsing?"
In the long term yes, and then it's called subsidence. I think that's what the second map displays.

"shouldn't the sinusoidal curve [in the first map] drift downward over time?"
Yes. And it shouldn't be that smooth in the first place, as you already pointed out.

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