Earth, cut in half.

February 23, 2011 4:30 PM

Is anyone aware of an image that's been generated depicting the whole circle of the earth in section view, showing the topography of the relevant land masses and sea floors?

It occurs to me that I've never, as far as I can remember, seen such a thing. Of course there are many small-scale images like this, but I'd like to find one that shows the entire circle of the earth in section view, if it exists. My google searches aren't turning up anything; surely someone's created such a thing before? All I can find are a number of "section cuts" of the earth which are really cutaways of a quadrant of the sphere, showing the geologic layers. I'm not particularly interested in the geology inside the earth, but rather the topography of the surface and it's scale relative to the earth's volume. I realize the detail of the surface is quite minute compared to the earth's size, which is part of why I find the idea of such an image so intriguing. That said, I expect it would probably have to be quite high-resolution to show anything meaningful; perhaps unfeasibly high? Still, it seems like something some topography nerd or another would have tried to tackle, even if it has to be executed in many sections...

Failing the whole earth, a similar visualization of a particular ocean/land-mass section would also be interesting.

While I doubt I would have the time to tackle such a problem anytime soon, I would also be interested in suggestions for generating such a whole-earth image from available datasets if one doesn't yet exist.

posted by brightghost to science & nature (15 answers total)

I don't know where you would find topographic vector data for free, but you might import that into Google Earth Pro.
posted by Blazecock Pileon at 5:08 PM on February 23, 2011

You made me curious so I did some calculations. I could be getting my arithmetic wrong, so worth doublechecking, but -

The radius of the earth is around 6370 km.
(The earth is not perfectly round, it's shaped like a slightly squashed ball, a bit fatter at the equator. Thus you get different radius measurements depending where you measure. The radius at the equator is 6378 km. The radius at the poles is 6356. NASA gives the "volumetric radius" as 6371, so let's use 6370 as a nice round number.)
Let's round off and say the diameter is around 12600 km.

Mt Everest is 8.8 km above sea level.
Challenger Deep in the Mariana Trench is 10.9 km below sea level.
So all of the variation in surface topography will be within those 20 km.

For your ideal image, I imagine you'd want to see the topography at some reasonable scale; maybe you'd want Everest to be 1 inch tall and the Mariana Trench to be a little over 1 inch deep. 2 inches maps to 20km.
We'll divide the diameter (about 12600) by 10=1260. 12600 km maps to 1260 inches = 105 feet.

To have Everest be 1 inch high, the diameter of earth in such a diagram will be 105 feet.
posted by LobsterMitten at 5:33 PM on February 23, 2011 [5 favorites]

i believe the problem is mostly a scale thing...the image you're desiring would basically be no different than a circle. the height of mount everest is ~5.5 miles (above sea level), while the mariana trench is only about ~6.8 miles deep (below sea level), for a total level variance of ~12 miles out of ~8000 (diameter of the earth) or about .15 percent...i saw a picture of earth's orbit around the sun (eccentricity= ~3 percent) and nobody in the class could tell the difference between that ellipse and a circle...it's really not all that different from a sphere, and any topographic globes or sectional illustrations you've seen are (for the most part) grossly exaggerated in scale for the benefit of clarity...
posted by sexyrobot at 5:43 PM on February 23, 2011

One fact that you often hear bandied about is that the Earth is smoother than a billiard ball. Phil Plait did the math to check this, and I trust him. If your cutaway picture of the Earth was to fit nicely in a browser window it would have to be around 800 pixels in diameter; at this scale the distance from the top of Mount Everest to the deepest part of the ocean will be about 1.2 pixels (according to my calculations).
Just draw a nice round circle with a 1px border in any drawing application and you're basically close enough! I think the insignificance of surface topology on a whole-Earth scale makes it very unlikely that the image you seek exists.
On preview, what everyone else says.
posted by nowonmai at 5:46 PM on February 23, 2011 [1 favorite]

(or what lobstermitten said)
posted by sexyrobot at 5:47 PM on February 23, 2011

To follow on to lobstermitten, you can get the diagram down to about 4ft if you're willing to have a 1mm Everest.
posted by rhizome at 6:31 PM on February 23, 2011

Also, note that the Earth is an oblate spheroid, ~43 km wider in diameter at the equator than at the poles, which is even larger than the total range of topography.
posted by theodolite at 7:02 PM on February 23, 2011

Yes, I did some mental math while typing this up and arrived at a similar conclusion to you all, though clearly I underestimated the uniformity a bit. It's not of course going to be anything interesting at computer-screen-scale, but a very large image that one could zoom in on would still, I think, be an interesting artifact. And per LobsterMitten's calculations, I think a section of such an image at, say, 50 foot diameter with a half-inch Everest could make an interesting wall-scale installation. Of course it would depend on determining a sufficiently-interesting section plane with identifiable details.

So I guess my question now is if anyone has advice on manipulating GIS data of this sort. I've come across the USGS' GTOPO30 data set, which provides elevation data of the earth at a 1km scale, which seems like it could yield some interesting images. It's available in the form of .bil binary raster files with .hdr and .blw companion files; any recommendations of software for manipulating this sort of data? The goal being plotting a line across the data field and transforming it into a 2d vector profile.
posted by brightghost at 7:06 PM on February 23, 2011

Most of the GIS applications for generating cross-sections create them as a "graph" and don't seem to build in the ability to wrap these around a circular cross section. That said, ArcGIS is the industry standard for GIS. The GTOPO30 data is available as part of the ESRI data and maps that comes with ArcGIS. Thereare also some inport scripts available.
posted by buttercup at 8:09 PM on February 23, 2011

buttercup, if I could generate the profiles as bitmaps or (preferably) vectors the curvature could be easily handled in post-processing. Do you know if the free 'ArcGIS Explorer' program would let me extract the data I need from this set, or would it require one of the paid versions? I don't have access to a computer running Windows, and as I've managed to avoid it thus far I'm reluctant to install Silverlight to see if their web application does what I need.
posted by brightghost at 8:35 PM on February 23, 2011

Close to what you want. although not exactly:
Cross-section of one narrow radius of earth with Everest and Mariana Trench to scale (though not in correct geographic position of course)

Cross-section of water depth of Atlantic Ocean, east-west across the Mid-Atlantic Ridge

Linked from a previous post on the blue, which has various interesting things including this comment about how the earth is about as smooth, proportionally, as a ball bearing.

(I realize you've moved on to make the image yourself; just posting these here out of interest.)
posted by LobsterMitten at 11:48 PM on February 23, 2011 [2 favorites]

National Geographic published a map with exactly this image way back in the 70's. I remember pulling it out of my Dad's copy of the magazine and just staring at it forever, pouring over all the under-sea details. It was the coolest thing.
posted by Thorzdad at 5:00 AM on February 24, 2011

My wife is an educator at a museum. She recently came across an analogy similar to those posted above: she uses a basketball and a sheet of paper. If the basketball is the earth, the crust is roughly proportional in thickness to the sheet of paper.
posted by hamandcheese at 11:48 AM on February 24, 2011

Thanks for those Lobstermitten, both interesting graphics. The Nat. Geo. lead sounds very interesting Thorzad, perhaps I will write them and see if anyone remembers such a thing. And thanks to everyone else for your helpful info, too.

In case it wasn't already clear, my interest here is purely my curiosity; I don't know when I'll have the time but I would like to see if I can make something out of the USGS data sometime soon. I'll surely report back here if anything comes of it.
posted by brightghost at 7:42 PM on February 24, 2011

Diversion: Ani DiFranco's "Everest" uses the ball bearing concept mentioned by LobsterMitten:

from the depth of the pacific
to the height of everest
and still the world is smoother
than a shiny ball-bearing

posted by kristi at 9:45 AM on February 25, 2011