Thursday, February 01, 2018

A Meteor in Michigan: Some Seismicity and Some Geometry

On January 16, a little after 8:08pm local time, a bright flash lighted the sky, and by some, even a bang was heard.  An object, a meteor, that earlier had entered our atmosphere became so heated by air friction that it exploded.  Some have reported surface recovery of small fragments of the object near the explosion.

Have a look at videos of the object and its explosion flash here: (from MLive).

The explosion was recorded by several seismic stations in the region, with the AAM station of Ann Arbor showing a remarkably clean signal (below). The USGS calculated the magnitude as M2 based on groundshaking, but the source is very different from earthquake-generating fault motion in the solid Earth. Let’s use some basic geometry to learn a bit more about the event.

Observations place the flash about 30km north from the Ann Arbor-AAM seismic station.  The energy of the flash reached the AAM station at 8:10:15pm local time, meaning that ~100 seconds had passed since the reported 8:08:33pm time of the flash [best time estimate from posted videos].   This allows us to test whether the energy passed through the atmosphere or the solid Earth, or a combination.  Compressive (P) waves travel about 340m/sec in the lower atmosphere, while P ground waves travel ~5000m/sec in the rocks of Michigan.

Air waves
If the energy source is an explosion in air, than 100sec x 340m/sec gives a distance to the explosion of 34km.  With a horizontal distance of 30km, trigonometry gives an elevation for the explosion of ~16km above the surface.  The slow speed of the object indicates that it was already deep into our atmosphere, so this elevation seems reasonable.

Ground waves
If the energy is from impact of the object, then ~50km distance of the projected impact point to the AAM station at solid Earth wave speeds, means that the energy would have reached the station in ~10 seconds.  This short time neither matches the timing of events, nor observation of scattered meteorite pieces before the projected impact point.

Air and ground waves
If the energy was transferred by waves traveling from the surface location to the AAM station, the travel time would have been 30,000m ÷ 5000m/s, is 6 seconds.  Thus the soundwave in the atmosphere would have traveled ~95 seconds from explosion to surface, meaning an elevation of 95sec x 340m/sec, is 32 km.  Twice that of the sound waves through air only scenario above, and a little high.

Looking at the lower WNW trajectory of the meteor, the angle was estimated at 30o from the projected surface intersection of its path, which is about 30 km from the explosion.  Using trigonometry, this means that the explosion occurred at an elevation of ~17km.  This estimate matches the first, air-only calculation of elevation very well, but not the calculation involving solid Earth groundwaves.

We learn from the Ann Arbor seismic record and reported timing of events that regional shaking associated with the exploding MI meteor is from the pressure of sound waves passing through air.  This pressure was enough to shake buildings and be heard locally, and move the ground surface over several 10s of km.  The exploding object did not significantly pass groundwaves through solid Earth, nor was physical impact of the object a source of energy.  Given the USGS M2 equivalence of groundshaking, we also can try to estimate the surface expression of the explosion at ~16km elevation.  Whereas an M2 earthquake is equivalent to exploding several tens of kg of TNT in solid material, a real calculation of the explosive power at elevation in the atmosphere is beyond my abilities.

So, a seismic station, citizen observations and basic trigonometry illuminate some details of a January 16 exploding meteor over Michigan that mesmerized local scientists and the public alike.

Thanks to my office colleagues Eric Hetland, Yihe Huang and Jeroen Ritsema for fun conversations.

Follow Ben van der Pluijm on Twitter: @vdpluijm

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