The Floor Was the Frame
Somewhere above Budalen in central Norway, about two thousand years after anyone last worked it, there is a bloomery. Five furnaces lined with stone, in a row on a terrace above a stream, and slag heaps fanning downhill from them. Iron ore was roasted there and smelted in charcoal. The clay walls got hot enough that the iron in them, when it cooled, froze in the direction of the Earth’s field at that moment and has pointed that way ever since.
That is why you can find a kiln with a magnetometer. The fired clay is a weak permanent magnet sitting in unfired soil, and a sensor carried over it at knee height sees a bump of a few hundred nanotesla. The Earth’s own field is about fifty thousand.
A new paper asks what happens if you carry the sensor on a drone instead. Drones are cheap and fast and they don’t trip over roots. They also fly higher than knees, and the question is how much higher you can go before the kiln is gone.
The authors built a synthetic kiln to find out. A disk of fired clay two metres across, buried just under the turf, magnetized along a field that dips seventy degrees. They computed its field at ground level, added a gentle slope and some soil noise, and then did the standard thing to lift the map into the air. It’s called upward continuation, and it is lovely. Take the map apart into waves. Short waves are sharp detail, long waves are broad swells. Going up by h metres damps every wave by a factor that depends on its wavelength: the short ones die fast, the long ones barely notice. Put the waves back together and you have the map as it would look from h metres up.
Their table shows the kiln at 323 nanotesla from 20 centimetres, 36 at two metres, 10 at four. Then it stops. At ten metres, 4.8. At fifteen metres, 4.8. The paper says the floor is the slope and the soil noise, what’s left when the kiln has faded into the background.
I rebuilt it from the text, and then ran their own script, which they published. Both match the table to the tenth. Then I turned the slope off and the soil off and the noise off. The floor stayed at 4.8.
It wasn’t the ground.
The damping factor has a blind spot, and it’s the longest wave of all. That wave has no wiggle. It’s just the average over the whole map, and the filter leaves it exactly alone. Go high enough and every other wave has died, so all that’s left is the average. And the average of their map is not zero. The field of a buried magnet averages to zero over an infinite plane, but they drew a square ten metres on a side around it, and inside that square it averages 4.75. So from fifteen metres up the kiln shows as a flat 4.8 everywhere. The number comes from where they put the edges of the map.
Worked out directly, one dipole at a time with no map, the kiln from fifteen metres is 0.23 nanotesla. From ten, 0.71.
None of this helps the drone. Mostly it does the opposite: the true decay is faster, so the paper’s advice to fly low gets a little stronger. At four metres their three percent is really two and a half. The part I liked best went the other way. Their real data from Budalen came from a gradiometer, which measures how fast the field changes with height, and that falls off faster than the field does. Compare like with like and the real site holds up better at altitude than one kiln would, three to five times better at four metres. Five furnaces and their slag, seen from above, blur into one broad hill that you can still find. They call it a magnetic plume and suggest flying high to find the site and low to read it. The numbers back them up, more than their own comparison showed.
I told them on their GitHub. It’s a small thing and I hope it reads as small.
I keep thinking about the 4.8. From ground level the frame doesn’t matter at all. There the kiln is everything, hundreds of nanotesla, and the edge of the map is somewhere off in the grass. You only meet the frame from high up, once the thing you came to see has thinned out below what the frame contributes on its own. At that height you’re reading the frame you drew. The instrument is working fine. It’s measuring you.
The furnace at Budalen doesn’t know how wide anyone’s map is. Its clay still points the way the field pointed the night it cooled, two thousand years back, which is more than any number in a table can say about itself.
