Saturday, February 14, 2009

Followups on the History of our Planet

Mike said:
Again, the Earth was already pretty geologically active prior to this impact, but definitely way moreso afterwards.
Ben wrote:
I'd like to know more here. How exactly was Earth "more geologically active" after Theia collided and merged?
Oh, I just mean that the crust probably cooled and solidified sometime between when it formed 4.6 billion years ago, and the impact 3.9 billion years ago. Just from a pure energy calculation, you can guess it almost certainly remelted after the impact.

It's even quite possible that primitive life could've arisen in that 700 million year window (since it only took a couple hundred million years after the impact to do so), but would certainly have been obliterated once there was nothing but hot lava to stand on.



Mike said:
Whoa, super fast-forward! We just skipped *most* of the history of Earth. The Giant impact happened about 3.9 billion years ago...Pangaea formed only 250 million years ago.
Ben then asked:
Anything interesting happen during those 3.9 billion years there?
Well, the whole Precambrian era was not the most exciting time-period, kinda like how in a Western Civ class they'll skip straight from "End of the Roman Empire" to "The Renaissance".

Mostly it was just a bunch of blue-green algae floating around the primitive oceans (think: primordial goo), spending a couple billion years turning the CO2-rich atmosphere into the oxygen-rich atmosphere we enjoy today. In fact, that was a prerequisite for multi-cellular life to arise.

One event that is notable, though, is the Cryogenian period, some 800 million years ago. This is still a subject of heavy debate, but it looks probable that for some time the entire Earth was completely covered in glaciers, leading to the term "Snowball Earth". There's definitely evidence based on banded iron deposits that the ocean was completely sealed off from the atmosphere...the most probable explanation is that a global ice sheet separated the two.




Mike said:
Imagine you put small plates of styrofoam on top of some boiling water...at certain times they'll all lump together as they're pushed by the convective flow. As they drift around as a single mass, they might pass over a convective plume...when this happens, they'll get pushed apart again, and the cycle repeats.
Ben asked:
Wow, that is an *awesome* explanation.

But why is it so slow? I mean, is the molten magma convection really
so slow as to take *millions* of years to travel? And if it's
happening at such an insanely slow speed, is it really the same
convection-phenomenon we see in boiling water? The same differential
equations?
Well, first let's understand how convection in normal fluids works.

Imagine we have a "parcel" of air at sea level and at the ambient temperature there. Due to some random perturbation, it rises slightly. Now, the atmospheric pressure at that greater height is less, so our parcel will expand and cool in the process.

Since it's colder, we'd expect it to fall back to the surface...but remember that temperature decreases with height, too. So, we ask the question, "Is our cooled parcel of air still warmer than the surrounding air?"

The answer ends up depending sensitively on the temperature gradient with height. If the gradient is steep - i.e. temperature drops quickly with height - then our parcel will be warmer than the surrounding medium. This means it's buoyant, and continues rising...so convection sets in. In the gradient is shallow - i.e. temperature drops slowly with height - then our parcel is colder than the surrounding medium and just falls back to its original position and our atmosphere is stably stratified.

It turns out that the critical threshold gradient separating the two answers, known as the "adiabatic lapse rate", goes as:
dT/dz = -g/Cp
where T is the temperature, z is height, g is gravitational acceleration, and Cp is the specific heat. In plain English, that means to maintain convection you have to have a big enough temperature difference between hot-at-the-bottom and cold-at-the-top, modulated by the local gravity and how much heat the convective medium can hold.

So to get back to your question, yes, this differential equation governs convection *everywhere*...in your lava lamp, in the water on the stove, in the atmosphere, and even in the magma in the mantle.

Now, I've been a little disingenuous in describing the mantle as a molten liquid. Technically, it's what's known as a "rheid". For short term-phenomena, a rheid can pretty much be thought of as a solid...it will even permit transverse seismic S-waves to pass through it (a wave mode that will not pass through liquid). Over the long-term, though, it will flow as an extremely viscous, plastic material when put under strain. We're talking *really, really* viscous here...if water has a viscosity of 1 and honey has a viscosity of a few thousand, rheids in the mantle are on the order of a few billion.

It's this viscosity that slows the process down. Think of it like this: if you drop a rock in air, it'll fall much faster than a rock dropping through water, which will fall much faster than a rock dropping through yogurt. Gravity is still acting the same way in all three cases, but the damping term increases in each case. Similarly, the buoyant acceleration of convection is still just as strong for magma as it is for any other convective process...but the extreme viscosity acts as such a strong damping term that the terminal velocity is very, very slow. A single convective overturn in the mantle is on the order of a million years.

Mike.

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