# Earthquake Light Model

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Hello everybody!

Earthquake light is said to appear in the sky during some earthquakes
https://en.wikipedia.org/wiki/Earthquake_light
its mere existence is controversial and poorly explained. Several explanations have been proposed, I'm pleased with none, so I just feel the need to add my own piece of mess to the ambient chaos.

Internet-era videos show short light reflected by clouds for which narrow sources can be seen on the ground. Electric sparks explain these neatly, prompting some people to reduce all observations to mundane causes. Though, earthquake light has been reported centuries ago and also over the Ocean, a big difficulty for triboelectric, ionic and mundane explanations.

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My attempt relies on vertical ground or Ocean movements transmitted to the atmosphere which propagates them upwards. As an example, I take peak 0.5m/s vertical speed and 2Hz sine, or peak 0.64g and 40mm. The wavelength is 750m in the Ocean, whose lower impedance can nearly double the amplitude, and 170m in the lower atmosphere. Supposing a plane acoustic wave (inaccurate but simpler), the impedance is 400ohm near the ground, this wave's peak pressure 200Pa and power density 100W/m2, and a 5s burst carries 250J/m2. If the tectonic plate moved vertically over 20km*20km, the peak acoustic power is pleasant 40GW and the burst energy 100GJ.

As its density decreases very little over one wavelength height, the atmosphere transmits the power perfectly to the altitude through the dropping density and acoustic impedance. I see only turbulence that could hamper this transfer.

We can take a constant sound wavelength, as the velocity depends only on sqrt(T) and on the mean molar mass. From 340m/s, it drops to 280m/s in the stratosphere, then increases to 320m/s, drops to 250m/s at the mesopause and increases again. Data is from pages 9/54 and 30/54 of
"Atmospheric Composition and Vertical Structure" by Thomas W. Schlatter

At 86km altitude, the density is 7mg/m3, the temperature 187K, and the acoustic impedance /4702. For our wave,

• The sound pressure is /470 or 0.4Pa, about the atmospheric pressure
• The displacement speed is *470 or 235m/s, about the sound velocity there.

so the acoustic wave becomes a Mach wave, with strong and steep changes of temperature and pressure that propagate faster than sound.

I won't try to estimate the Mach's wavefront thickness nor the propagation losses, sorry. Someone else shall do it.

Admitting that the wave energy is kept, over arbitrary 500m wavelength now, thinner air at even higher altitude spreads this energy on less mass.

Around 120km altitude, the density is 22µg/m3. The (arbitrarily) 3* longer wave spreads the energy on little air mass: 50J/m2/wavelength over 11mg/m2/wavelength. A sine distribution would give a peak of 9MJ/kg or over 4000K, and the Mach wavefront is even hotter, letting the air radiate light efficiently.

At these 120km at rest, the molecular mean free path is 1.2m, so a sinewave of lambda/2pi=81m is still propagated, but at 150km the mean free path is 33m so the 2Hz sinewave stops approximately there, a shockwave supposedly too. It takes some 27km to multiply the mean free path by 2.7, and the wave energy must be lost over such a distance; if this occurs at 150km, the burst's 250J/m2 spread over 56mg/m2, and the losses heat the air to 4000K too, so it radiates light. Though, I expect the previous process to have already attenuated the wave.

This latter dissipation happens at an altitude where our atmosphere is warmer and occurs for all causes on the ground, including Ocean waves and wind turbulence. It must happen also at our Sun's chromosphere, maybe corona.

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According to my model :

• Stronger earthquakes produce light more likely, vertical movements are needed, and the Ocean is no drawback;
• Direct line of sight is possible up to 1200km (400km were observed);
• Up to 40GW per front are available to produce light. At 100km it's as much as 40kW at 100m: room for inefficient conversion and for a hemispherical pressure wave, rather than plane;
• The light must appear over the strongest vertical movement and some 5min later. It must be broad (but refraction applies).

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The air movement at 1km/s in the 40µT geomagnetic field induces only 40mV/m, very little for a gas discharge. Bad alternative explanation to my eyes.

The 4MJ/kg heat deposited at 150km would suffice to propel this air to hundreds of km height. Transferring the 0.1Hz movement to higher, thinner air amplifies the speed (and the temperature). As some air reaches the lower Van Allen belt, it must glow like any Polar light. Though, this light would last for about 5min.

Marc Schaefer, aka Enthalpy