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Warren Platts
2008-Jan-19, 06:11 AM
The intrinsic power (or luminosity) of a planet is its emitted power less the power absorbed from its sun. I'm having a heck of a time trying to figure out the Earth's intrinsic power. A Google search of Earth's intrinsic power mainly links to magic sites. A Google search of Earth's energy budget reveals scads of flow charts like the attached that show how the Earth emits just as much radiation as it absorbs from the Sun (342 watts per meter). But this can't possibly be the case--that the intrinsic power of the Earth is zero; unless, of course, plate tectonics and volcanos are ultimately solar powered! :mad:

The situation is rather ironic considering: (1) all the anxiety associated with future climate change; and (2) that the intrinsic power of other planets like Jupiter is routinely calculated. For example, my Jupiter book (http://www.amazon.com/Jupiter-Satellites-Magnetosphere-Cambridge-Planetary/dp/0521035457/ref=pd_bbs_2/102-3684155-1555343?ie=UTF8&s=books&qid=1200722767&sr=8-2) (Tab. 3.3) states that Jupiter absorbs 5.014 x 1024 ergs per second, whereas Jupiter emits 8.365 x 1024 ergs per second, leaving an intrinsic power of 3.350 x 1024 ergs per second.

Any ideas?

antoniseb
2008-Jan-19, 06:23 AM
... Earth's energy budget reveals scads of flow charts like the attached that show how the Earth emits just as much radiation as it absorbs from the Sun (342 watts per meter). ...

I agree that there must be some loss of interior thermal energy, as well as some minor losses in other ways, such as the increase in the Moon's orbit and the interior magnetic field accelerating particles and compass needles.

But I wouldn't be surprised to find that this value is small compared to the energy it gets from the Sun, and therefore a little hard to measure directly.

I am now curious to know the answer, and look forward to seeing someone knowledgeable on the subject post here.

Ronald Brak
2008-Jan-19, 06:55 AM
About 4 watts per square meter, so not much. Much less than what the earth receives from the sun, about 1%.

Warren Platts
2008-Jan-19, 12:42 PM
About 4 watts per square meter, so not much.

Thanks Ronald, but do you have a reference for that figure? 4 W m-2 may not sound like much, but according to Hansen et al. (2005, 1432) (http://pubs.giss.nasa.gov/docs/2005/2005_Hansen_etal_1.pdf), only 0.85 W m-2 is driving global warming. (Yes, there's much uncertainty built into the 0.85 figure, probably even more than the ± 0.15 W m-2 given by Hansen et al.--see discussion in Lubos Motl's blog (http://motls.blogspot.com/2005/04/earths-energy-balance.html)for an admittedly biased discussion of these figures.) So if 4 W m-2 is not being taken into account, I could see how that might affect a 0.85 W m-2 estimate for our net energy absorption.


Much less than what the earth receives from the sun, about 1%.Of the energy the Earth receives from the Sun, only 235 watts per meter is actually absorbed. The rest is reflected back into space at visible and UV wavelengths. So at 4 watts per square meter, that's more like 2%--small but maybe not negliglible for our purposes here on the ground.

antoniseb
2008-Jan-19, 12:49 PM
...So if 4 W m-2 is not being taken into account, I could see how that might affect a 0.85 W m-2 estimate for our net energy absorption...

That's an interesting thought. This figure is a constant in any issue of balance of global temperature. It's use may be important, but it isn't a factor being affected by people activities yet.

Ronald Brak
2008-Jan-19, 01:03 PM
About 4 watts per square meter, so not much. Much less than what the earth receives from the sun, about 1%.

Sorry, that figure was off the top of my head and is totally wrong. Apparently it's actually about 0.075watts per square meter.


Of the energy the Earth receives from the Sun, only 235 watts per meter is actually absorbed.

For a square meter of earth at the equator at noon I think it would be about 630 watts, if that square meter had the earth's average albedo. We start at with 1366 watts at the top of the atmosphere, about 366 watts are absorbed by clear skies and an average of about 37% is reflected by the earth's albedo, so roughly 630 watts.

When you consider that it's not always noon or clear skies and that the earth is an average of 287 degrees above absolute zero, it's not hard to see how 0.85 watts can make a significant difference in temperature.

Warren Platts
2008-Jan-19, 05:46 PM
Sorry, that figure was off the top of my head and is totally wrong. Apparently it's actually about 0.075watts per square meter.
I don't doubt you, but I'd like to know how they figured that out. It's rather precise (2 sigificant figures), so I'm just curious how that number was arrived at. Actually it seems kind of small. Consider for example that total human industrial energy consumption = 1.5 x 1013 W and that the total land area of the Earth is 1.5 x 1014 m2. Since humans live mostly on land, that works out to 0.1 W m-2. Averaged over the whole Earth, that's still 0.03 W m-2--about half of your 0.075 W m-2 figure. In other words, the raw heat energy released by human burning of fossil fuels and uranium is about half of that which is required to power plate tectonics and all the volcanos, earthquakes, and tsunamis that happen--which is pretty striking if true.

Actually, one commentator at the Lubos Motl blog states the following:


They have forgotten many important factors, for example there are heat generated by the natural decay of some radioactive elements in the crust of the earth, like U238 and U235. There are 4 ppm of U238, and approximately 1/137 of U235. So that's a huge amount generating a few 10 watts per square meter.


And there's also tidal friction to be taken into account as well that would have to be added to the Earth's intrinsic power.

So really, there are at least three terms that have to be added to come up with Earth's intrinsic power:

heat released by radioactive decay
tidal friction
heat energy released by human activities
primordial heat left over from the origin and gravitational contraction of the planet


For a square meter of earth at the equator at noon I think it would be about 630 watts, if that square meter had the earth's average albedo. We start at with 1366 watts at the top of the atmosphere, about 366 watts are absorbed by clear skies and an average of about 37% is reflected by the earth's albedo, so roughly 630 watts.
The 235 watts per square meter figure is arrived at as follows:

mean Earth radius = 6,371,000 m;
cross section of Earth = 1.28 x 1014 m2
solar "constant" = 1,366 W m-2
total solar energy intercepted by Earth = 1.74 x 1017 W
total surface area of earth (4 x cross-section) = 5.1 x 1014 m2
average solar energy per meter on Earth = 342 W m-2
albedo = 0.312
total absorbed energy = 235 W m-2

Ronald Brak
2008-Jan-19, 06:01 PM
This page might help:

http://geophysics.ou.edu/geomechanics/notes/heatflow/global_heat_flow.htm

Warren Platts
2008-Jan-19, 09:55 PM
I found this enigmatic quote:


Nature.com (subscription),Earth's heat output is estimated to be around 44 terawatts, about twice that expected from radioactive decay.
(A terawatt is 1012 Watts.) It links to Nature.com obviously, but I don't have the password, and I'm not about to pay the $30 without being able to read the article first! :D

But hey, Nature rarely prints stuff that isn't true, so lets just go with the 4.4 x 1013 watts. It's interesting that they say it's twice that which is expected from radiation. Well, then probably a good portion of the rest can be explained as the result of raw heat generated by fossil fuel and concentrated uranium burning by humans! :neutral:

Warren Platts
2008-Jan-20, 10:46 AM
So if Earth's intrinsic power is 44 terawatts (4.4 x 1020 erg s-1 compared to Jupiter's intrinsic power of 3.35 x 1024 erg s-1), then going back to the equation:


22 terawatts from radioactive decay
15 terawatts from human industrial activities according to British Petroleum
4 terawatts of tidal energy
3 terawatts unaccounted for

Of the 3 terawatts unaccounted for, one of those can be accounted for by just human body heat! 100 Watts X 10 billion people = 1 terawatt! Throw in domestic animals, waste heat from nuclear power plants, unprecedented transfers of nitrogen from the atmosphere straight into soil that gets translated into preternatural vegetational fermentation, and it's easy to see where the other 2 terawatts come from.

I think it was Vernadski in the 1940's who said that humans were a geological force. :D

I think we pretty much count as a Type I civilization at this point. . . . :dance:

Congratulations to all! :neutral:

kzb
2008-Jan-21, 01:19 PM
My guess is the Nature articlefigure of 44TW is not including human activity. Like you I'm not paying the subscription.

I've not got time just now, but there are things on Wikipedia concerned with this, and it has cropped up before here on other threads.

The bulk of the Earth's heat production is from decay of primordial radionuclides. There is also significant heating from tidal energy, and there is a layer within the earth which is expanding outwards about 1cm/yr as it crystallises, releasing latent heat. However I would say this latter is simply stored gravitational potential energy from when the Earth was formed.

AndreasJ
2008-Jan-21, 03:44 PM
Of the 3 terawatts unaccounted for, one of those can be accounted for by just human body heat! 100 Watts X 10 billion people = 1 terawatt!
Since human body heat largely comes from photosynthesis (by way of McDonald's) isn't this solar rather than intrinsic energy?

ExpErdMann
2008-Jan-21, 03:50 PM
My guess is the Nature articlefigure of 44TW is not including human activity. Like you I'm not paying the subscription.

Maybe you can see this article about the geoneutrinos (http://www.nature.com/nphys/journal/vaop/nprelaunch/full/nphys013.html). You're correct. Human activity is not part of the story.


The bulk of the Earth's heat production is from decay of primordial radionuclides. There are only estimates of this contribution, based on what quantities of these elements reside inside the earth.

There is also significant heating from tidal energy, and there is a layer within the earth which is expanding outwards about 1cm/yr as it crystallises, releasing latent heat. However I would say this latter is simply stored gravitational potential energy from when the Earth was formed.
Most scientists would not support the latter idea, only some of the expanding earth supporters possibly (the fast expansion camp). I am an expanding earther myself (slow expansion) and I think Earth's internal heating could be linked to this expansion, but that is my own ATM view.

kzb
2008-Jan-21, 06:39 PM
Sorry I got the expansion rate a thousand times too fast ! The link below gives 1cm/1000 year, not 1cm/y as I put.

Would you say this is a fairly mainstream view?

http://www.physorg.com/news62952904.html

Quote:
<<Then there's latent heat, Marone says. This type arises from the core's expanding as the Earth cools from the inside out. Just as freezing water turns to ice, that liquid metal is turning solid—and adding volume in the process. "The inner core is becoming larger by about a centimeter every thousand years," Marone says. The heat released by this expansion is seeping into the mantle.

For all this, however, Marone says, the vast majority of the heat in Earth's interior—up to 90 percent—is fueled by the decaying of radioactive isotopes like Potassium 40, Uranium 238, 235, and Thorium 232 contained within the mantle. These isotopes radiate heat as they shed excess energy and move toward stability. "The amount of heat caused by this radiation is almost the same as the total heat measured emanating from the Earth." >>

Warren Platts
2008-Jan-21, 06:52 PM
My guess is the Nature article figure of 44TW is not including human activity. Like you I'm not paying the subscription.
Well I'm mainly interested in an order of magnitude estimate--I mean how can one measure the intrinsic power of the Earth? You can't just stick in one temperature probe and then integrate over the whole Earth's surface. So if human activities aren't being taken into account for the 44 TW figure, then humans are only putting out 1/3 of the total intrinsic power of the Earth, rather than 1/2. :clap:

That's still pretty freaking amazing. . . .


Since human body heat largely comes from photosynthesis (by way of McDonald's) isn't this solar rather than intrinsic energy?
I think it was Paul MacCready who recently calculated that humans and their vertebrate commensals compose something like 98% of the Earth's total vertebrate biomass.

According to Wikimedia (http://en.wikipedia.org/wiki/Biomass_(ecology)), "Humans comprise about 250 million tons (0.33%) of the Earth's biomass, domesticated animals about 700 million (1.0%)." So there's at least 3 TW right there. Should it be counted as reemited solar energy? Mostly, I guess. On the other hand, humans are contributing supermassive amounts of nitrogen and phosphorus into the biosphere that weren't there before. In other words, more plant biomass is being produce now than ever. The energy in such plant biomass is eventually released as heat. Probably, a brown and stubbly field reflects more sunlight back into space than does a lush, irrigated corn field. So how do you classify solar inputs that are higher than the prehistorical level?

kzb
2008-Jan-21, 06:54 PM
ExpErdMann wrote:
<<Maybe you can see this article about the geoneutrinos>>

Hmmm... I'd like to know how they arrived at the net figure !? 152 events observed, only 20-25 after background subtraction... that means the background is 152-25= 127 on the most generous assumption.

Does anyone else have any comments on the Poisson statistics of this ?

By my reckoning, the net count is not even significantly above zero at the 95% confidence level.

The 95% cofidence range on the net count is 25 +/-34 !

ExpErdMann
2008-Jan-21, 07:22 PM
I'm no statistician, but I was pretty skeptical on this point too. It was somehow good enough to get into Nature though.

kzb
2008-Jan-22, 01:34 PM
In my way of seeing things, the "intrinsic power" of the earth would not include biomass power. I see the intrinsic power as very much that which comes from WITHIN the planet, especially as t

Biomass runs off solar energy, except for the small amount of chemotrophs that live solely off chemicals released from the planet. No living thing actually creates any energy, it is simply diverting some energy for its own uses. The vast majority of this energy comes from sunlight trapped via photosythesis. That sunlight would hit the planet anyway.

Humans are just the same as any other animal. If we did not eat the food
produced by photosythesis, something else would, and the overall energy flow would be exactly the same. Our biomass simply REPLACES biomass of other creatures.

Now there's a bit of a complication here, in that we are the only animal to make significant use of fossil fuels. Fossil fuels are stored photosythetic energy from millions of years ago. Yes we are using them NOW, but I still would not include them in the "intrinsic power" of the planet. In any case, the other half of the equation is the oxygen necessary to combine with them to release energy, and that has been produced quite recently by photosynthesis.

Anyway, I'm pretty sure the fossil fuel combustion energy output (as opposed to the greenhouse effect that is thought to be a consequence of CO2 production) is very small compared to the overall energy budget of the planet.

Michael Noonan
2008-Jan-22, 01:56 PM
Humans are just the same as any other animal. If we did not eat the food
produced by photosythesis, something else would, and the overall energy flow would be exactly the same. Our biomass simply REPLACES biomass of other creatures.


Just like algae replaces the biodiversity of coral reefs.

kzb
2008-Jan-22, 06:42 PM
Michael Noonan wrote:
<<Just like algae replaces the biodiversity of coral reefs>>

Algae is a photosynthetic plant, whereas coral is an animal, as are the creatures that live in and around it. The algae is trapping energy for the biosphere from the sun, whereas the coral is using it up. So don't be down on it, the algae could well be increasing biodiversity elsewhere, in a less obvious and appealing fashion.

ExpErdMann
2008-Jan-22, 08:52 PM
Sorry I got the expansion rate a thousand times too fast ! The link below gives 1cm/1000 year, not 1cm/y as I put.

Would you say this is a fairly mainstream view?

Yes, it sounds more mainstream now!


http://www.physorg.com/news62952904.html

Quote:
<<Then there's latent heat, Marone says. This type arises from the core's expanding as the Earth cools from the inside out. Just as freezing water turns to ice, that liquid metal is turning solid—and adding volume in the process. "The inner core is becoming larger by about a centimeter every thousand years," Marone says. The heat released by this expansion is seeping into the mantle.

For all this, however, Marone says, the vast majority of the heat in Earth's interior—up to 90 percent—is fueled by the decaying of radioactive isotopes like Potassium 40, Uranium 238, 235, and Thorium 232 contained within the mantle. These isotopes radiate heat as they shed excess energy and move toward stability. "The amount of heat caused by this radiation is almost the same as the total heat measured emanating from the Earth." >>

I think here Marone is on shakier ground. He's merely assuming that there are concentrations of these isotopes in the mantle which can generate the observed heat. I think the mainstream idea here is (or at least was) that these isotopes are actually concentrated mostly in the crust. And the observed quantities in the crust are only able to generate about 1/2 the observed heat. In that case, the other roughly 1/2 of the observed heat emission is unexplained. Note that there is a similar problem in explaining Jupiter's and Saturn's emissions and in those instances the radioactivity argument cannot be used.

Warren Platts
2008-Jan-23, 03:11 AM
Yes, it sounds more mainstream now!


I think here Marone is on shakier ground. He's merely assuming that there are concentrations of these isotopes in the mantle which can generate the observed heat. I think the mainstream idea here is (or at least was) that these isotopes are actually concentrated mostly in the crust. And the observed quantities in the crust are only able to generate about 1/2 the observed heat. In that case, the other roughly 1/2 of the observed heat emission is unexplained. Note that there is a similar problem in explaining Jupiter's and Saturn's emissions and in those instances the radioactivity argument cannot be used.

The problem with Jupiter is not that it's too hot. It's too cold! :p

Warren Platts
2008-Jan-23, 03:28 AM
In my way of seeing things, the "intrinsic power" of the earth would not include biomass power. I see the intrinsic power as very much that which comes from WITHIN the planet, especially as t

I agree that the 1 terawatt of body heat produced by humans should not be counted against the intrinsic power calculus. Strickly speaking, the intrinsic power of any planet is just the net difference between the solar input and the planetary output.

The human nitrogen factor is huge. There is no denying that.

What that does to the intrinsic power, I don't know.

So let's leave out the 1 terawatt body heat factor.

That still leaves 15 terawatts from fossil fuels and uranium.

ExpErdMann
2008-Jan-23, 03:38 PM
The problem with Jupiter is not that it's too hot. It's too cold! :p
No, it's too hot. Here (http://arxiv.org/PS_cache/physics/pdf/0112/0112018v1.pdf) is a paper which gives one of many possible explanations for the excess heat emission. See paragraph 1.

Warren Platts
2008-Jan-23, 06:55 PM
No, it's too hot. Here (http://arxiv.org/PS_cache/physics/pdf/0112/0112018v1.pdf) is a paper which gives one of many possible explanations for the excess heat emission. See paragraph 1.

Sir, you are exactly right about that. I meant to write that Jupiter is too hot, as you say. :doh:

Warren Platts
2008-Jan-23, 07:05 PM
In my way of seeing things, the "intrinsic power" of the earth would not include biomass power. I see the intrinsic power as very much that which comes from WITHIN the planet, especially as t

Biomass runs off solar energy, except for the small amount of chemotrophs that live solely off chemicals released from the planet. No living thing actually creates any energy, it is simply diverting some energy for its own uses. The vast majority of this energy comes from sunlight trapped via photosythesis. That sunlight would hit the planet anyway.
I agree. However, the definition of intrinsic power is the power emitted less the power intercepted from the Sun. I think we have to count fossil fuel heat because it's real.


Humans are just the same as any other animal. If we did not eat the food produced by photosythesis, something else would, and the overall energy flow would be exactly the same. Our biomass simply REPLACES biomass of other creatures.Now that's not true at all. We are sucking N2 out of the atmosphere to make ammonia. We are turning deserts into blossoming corn fields. We are making way more biomass than there was before us.


Now there's a bit of a complication here, in that we are the only animal to make significant use of fossil fuels. Fossil fuels are stored photosythetic energy from millions of years ago. Yes we are using them NOW, but I still would not include them in the "intrinsic power" of the planet. In any case, the other half of the equation is the oxygen necessary to combine with them to release energy, and that has been produced quite recently by photosynthesis.It has to count as intrinsic power because of our definition of 'intrinsic power'.


Anyway, I'm pretty sure the fossil fuel combustion energy output (as opposed to the greenhouse effect that is thought to be a consequence of CO2 production) is very small compared to the overall energy budget of the planet.
This is the surprising and strikingly freaky weird result of the present investigation: that the heat we put out rivals the heat put out by all the volcanoes and earthquakes and lava flows out there. :neutral:

cmsavage
2008-Jan-23, 10:03 PM
ExpErdMann wrote:
Hmmm... I'd like to know how they arrived at the net figure !? 152 events observed, only 20-25 after background subtraction... that means the background is 152-25= 127 on the most generous assumption.
. . . .
The 95% cofidence range on the net count is 25 +/-34 !
They did expect 127 +/- 13 background events, but the background neutrinos did not have the same energy spectrum as the signal, so it is not a simple Poisson subtraction. Confidence intervals for Poisson statistics do not correspond to the +/-(2)sigma (for 95%) number of events anyways; you generally only do that for Gaussian statistics. The paper gives a 90% confidence level interval of 4.5 to 54.2 events (using a maximum likelihood analysis, if you know what that is). They also gave a 99% confidence upper limit of 60 TW from U238 and TH232 decay.

kzb
2008-Jan-24, 01:17 PM
Hi cmsavage, it's quite customary in radiometrics to use Gaussian statistics to model the Poisson distribution. The fit is not that good at "small" number of events, but gets better as the numbers go up. Depending on which textbook you read, different authors recommend anywhere from 20 to 100 events as the lower limit for use of the Gaussian statistics. It's a special kind of Gaussian distribution, as the standard deviation is the square root of the mean.

In simple radiometrics, the SD of the net count in this case would be

SD net count = SQRT(gross count+background count)

However, it's clear from what you say the uncertainty evaluation in the paper is not simple, and any small difference between Poisson and Gaussian statistics is the least of our worries here.

I would say, if the background events are distinguishable events, then they are not really background at all. Why take them into account? Or is it that some are distinguishable and some are not?

ExpErdMann
2008-Jan-24, 03:45 PM
Here is a part of the abstract from the 2005 Nature study:


Assuming a Th/U mass concentration ratio of 3.9, the 90 per cent confidence interval for the total number of geoneutrinos detected is 4.5 to 54.2. This result is consistent with the central value of 19 predicted by geophysical models. Although our present data have limited statistical power, they nevertheless provide by direct means an upper limit (60 TW) for the radiogenic power of U and Th in the Earth, a quantity that is currently poorly constrained.

The upper limit of 60 TW corresponds to the 54.2 figure, but the lower count of 4.5 would correspond to a value far lower than what the geophysical models predict for radiogenic decay (which they say is 19 TW). Their study just puts a huge bracket around the 19 TW value. They're essentially saying that their results can be considered consistent with radiogenic decay explaining all the Earth's heat emission. But they are also consistent with decay causing less than what the geophysical models predict.

In the article, they say that the most significant background events are due to cosmic rays, but that breakdown of nuclear fission products is also a contributor.

Warren Platts
2008-Jan-24, 06:35 PM
Here is a part of the abstract from the 2005 Nature study:



The upper limit of 60 TW corresponds to the 54.2 figure, but the lower count of 4.5 would correspond to a value far lower than what the geophysical models predict for radiogenic decay (which they say is 19 TW). Their study just puts a huge bracket around the 19 TW value. They're essentially saying that their results can be considered consistent with radiogenic decay explaining all the Earth's heat emission. But they are also consistent with decay causing less than what the geophysical models predict.

In the article, they say that the most significant background events are due to cosmic rays, but that breakdown of nuclear fission products is also a contributor.

You have to admit that it's pretty amazing that fossil fuel we're burning adds up to a significant fraction of the Earth's heat emission.

ExpErdMann
2008-Jan-24, 07:26 PM
Okay, it's interesting! Here's a Wikipedia graph (http://en.wikipedia.org/wiki/Image:World_Energy_consumption.png) which breaks it down a bit.

kzb
2008-Jan-25, 04:21 PM
<<We are sucking N2 out of the atmosphere to make ammonia. We are turning deserts into blossoming corn fields. We are making way more biomass than there was before us. >>

If this is really true (and actually I thought deserts were advancing), the fact is the biomass does not create energy. It runs off sunlight which would hit the Earth anyway, whether it was there or not.

<<This is the surprising and strikingly freaky weird result of the present investigation: that the heat we put out rivals the heat put out by all the volcanoes and earthquakes and lava flows out there. >>

If true, ie that anthropogenic heat production from nuclear and fossil fuels rivals the heat escaping from within the planet, it still is a small fraction of the energy budget of the planet. I'm sure solar energy input is far greater than either, and relatively small changes in albedo and greenhouse effect would swamp either.

cmsavage
2008-Jan-25, 05:00 PM
Hi cmsavage, it's quite customary in radiometrics to use Gaussian statistics to model the Poisson distribution. The fit is not that good at "small" number of events, but gets better as the numbers go up. Depending on which textbook you read, different authors recommend anywhere from 20 to 100 events as the lower limit for use of the Gaussian statistics. It's a special kind of Gaussian distribution, as the standard deviation is the square root of the mean.
A Poisson distribution can be approximated by a Gaussian for large numbers of events, but when you do subtractions, you have to be careful because you can come back down to small numbers again. In any case, if you are talking about an error in the number of events that is close (or larger) than the expected number of events, like the 25 +/- 34 (2 sigma) number you gave, then the approximation is no longer appropriate. You cannot have a negative number of events, so if your approximations are allowing for that, then they are no longer valid. Saying the background is 127 +/- 13 with an approximately gaussian distribution is fine, but 25 +/- 17 is not.

I made a mistake in mentioning "Confidence intervals for Poisson statistics do not correspond to the +/-(2)sigma (for 95%) number of events" since that 25 is not Poisson distributed. However, that statement still applies for many different distributions (not just Poisson), including the correct distribution for that 25 events number.


I would say, if the background events are distinguishable events, then they are not really background at all. Why take them into account? Or is it that some are distinguishable and some are not?
Individual events are not distinguishable, but populations can be on a statistical level. Say some experiment is looking at neutrinos scatters in the energy range 1-10 MeV. Suppose the background events are evenly distributed in that range, but that the signal event rate is expected to be proportional to the energy (that is, more likely to give higher energy scatters). If you observe a 7 MeV event, you cannot be sure if it is a background or signal event. If you observe events at 2.3, 3.2, 5.1, 6.6, 6.8, 7.9, 8.2, 8.7, 9.0, and 9.6 MeV, you cannot determine if each individual event is signal or background, but it is quite apparent that many of those events are likely signal events since they predominantly occur at higher energies.

That is essentially what is happening here. Individual events are not distinguishable, so you cannot remove the background. But the signal is distinguishable on a statistical level for many events.

Warren Platts
2008-Jan-26, 12:46 AM
If this is really true (and actually I thought deserts were advancing), the fact is the biomass does not create energy. It runs off sunlight which would hit the Earth anyway, whether it was there or not.OK fine. Let's take the human body heat off the table.



If true, ie that anthropogenic heat production from nuclear and fossil fuels rivals the heat escaping from within the planet, it still is a small fraction of the energy budget of the planet. I'm sure solar energy input is far greater than either, and relatively small changes in albedo and greenhouse effect would swamp either.
The Hansen et al. (2005) paper says we are absorbing 0.85 watts per square meter more than we emitting, and that's what's driving global warming. There are 150,000,000,000,000 square meters on the Earth; that adds up to 127 terawatts that we are absorbing. So the human heat factor (15 terawatts) is small in comparison.

But the total intrinsic power is on the order of 60 terawatts, apparently. It's foolish to leave this out of models that attempt to describe the heat budget of the Earth. Just one man's opinion. :neutral:

kzb
2008-Jan-28, 06:31 PM
Hi Warren Platts, according to Wikipedia, solar input is 174,000TW:

http://en.wikipedia.org/wiki/World_energy_resources_and_consumption#Nuclear_pow er

<<But the total intrinsic power is on the order of 60 terawatts, apparently>>

That is the UPPER LIMIT as derived by the geoneutrino experiment and clever statistics. The best estimate is far less than that, 19TW.

Our power consumption (which in the Wiki article I think does not include our own metabolism), is 15TW of which 92.5% is fossil fuel + nuclear, ie 14TW from non-solar powered sources.

So that 14TW power consumption is 0.008% of the solar input, and the best estimate "intrinsic power" input is 0.011% of solar.

<<It's foolish to leave this out of models that attempt to describe the heat budget of the Earth.>>

I see what you're getting at, the 19TW of intrinsic power is quite significant in comparison to the 127TW that is going into the global warming model. However, it's probably reasonable to leave it out if it is assumed to be a constant over the time scales under consideration. It's only about 0.01% of the energy budget, so even if it does vary slightly it's not going to change anything?

(BTW, in the Wikipedia article above, it's not clear on a cursory read if the power consumption is net or gross. For example nuclear is 6% of energy consumption, but that presumably is as electricity. It takes about another 200% of heat to produce that electricity ? The same argument would hold for fossil-fuel electricity also.)

ExpErdMann
2008-Jan-28, 06:45 PM
(BTW, in the Wikipedia article above, it's not clear on a cursory read if the power consumption is net or gross. For example nuclear is 6% of energy consumption, but that presumably is as electricity. It takes about another 200% of heat to produce that electricity ? The same argument would hold for fossil-fuel electricity also.)

Good point, kzb. In that case the energy we are releasing could be more than what is being radiated from within. I wonder if we chanelled all that energy to specific points if we could stop these crazy continents from moving all over like they do.

Warren Platts
2008-Jan-29, 05:10 AM
Hi Warren Platts, according to Wikipedia, solar input is 174,000TW:
That agrees with my calculations: (http://www.bautforum.com/1155699-post7.html)


mean Earth radius = 6,371,000 m;
cross section of Earth = 1.28 x 1014 m2
solar "constant" = 1,366 W m-2
total solar energy intercepted by Earth = 1.74 x 1017 W




<<But the total intrinsic power is on the order of 60 terawatts, apparently>>

That is the UPPER LIMIT as derived by the geoneutrino experiment and clever statistics. The best estimate is far less than that, 19TW.
See, this is what I find so counterintuitive. If you're right, the intrinsic power barely exceeds human energy consumption. And actually, if you figure in solar powered human and human commensal biological activity, human power is greater than the intrinsic power. It just seems to me that something's got to be wrong somewhere. I mean all these continents moving around on less energy than it takes our cars to drive around? But hey, what do I know? (Not much :neutral:) Well, I guess it must be because our cars move faster, and so it's that kinetic v2 energy thing.


So that 14TW power consumption is 0.008% of the solar input, and the best estimate "intrinsic power" input is 0.011% of solar.So Jupiter has it going on! :D



(BTW, in the Wikipedia article above, it's not clear on a cursory read if the power consumption is net or gross. For example nuclear is 6% of energy consumption, but that presumably is as electricity. It takes about another 200% of heat to produce that electricity ? The same argument would hold for fossil-fuel electricity also.)
I don't know, but I would guess they take the BTUs of the raw fossil fuel fuel burned, but probably not the uranium.

kzb
2008-Jan-29, 01:03 PM
Warren Platts wrote:
<<See, this is what I find so counterintuitive. If you're right, the intrinsic power barely exceeds human energy consumption>>

Going by the figures we are given, it does look as though they are comparable quantities -in fact taking into account the uncertainties human power might even exceed the intrinsic power.

However, if you were taking measurements of the Earth from a distant planet, I still think you would be on a hiding to nothing trying to derive the intrinsic power of Earth, whether or not human power is included in that. It is so small compared to the solar input and the radiated energy figures.

When calculating the energy balance, you are subtracting similar numbers, both with attached uncertainties. The uncertainty on the net figure would be relatively large, and undoubtedly swamp the 0.019% sum of intrinsic and human power.

Anyway, I've had another thought, and that is the energy radiated (and used for moving continents etc) by the planet from internal sources might be greater than it is currently producing. This would mean the Earth is slowly cooling internally, ie it is using up stored energy. In this way, the observed intrinsic power could be significantly greater than the estimated current radiogenic and tidal energy production.

kzb
2008-Jan-29, 06:51 PM
Thanks for your comments cmsavage:
<<A Poisson distribution can be approximated by a Gaussian for large numbers of events, but when you do subtractions, you have to be careful because you can come back down to small numbers again.>>

But what about the Central Limit Theorem? This says that combinations of non-Normal distributions tend towards the Normal.

I have actually seen an intereting computer demonstration of combinations of rectangular distributions, such as you would get throwing a die or dice. Two dice give a triangular distribution, three dice give something beginning to look like a Normal distribution, and four dice give something that is almost impossible to tell by eye any different to a Normal distribution.

I must confess I do not know the distribution resulting from two Poisson distributions. However the message on the course I was on was the Central Limit Theorem tends to apply when combining uncertainties.

<<In any case, if you are talking about an error in the number of events that is close (or larger) than the expected number of events, like the 25 +/- 34 (2 sigma) number you gave, then the approximation is no longer appropriate. You cannot have a negative number of events,>>

Yes but I can OBSERVE a negative net number of events. If I find a background count of 127, I can later observe a gross count of say, 120. That could happen on statistical grounds, and my net count is -7.

<<...so if your approximations are allowing for that, then they are no longer valid. Saying the background is 127 +/- 13 with an approximately gaussian distribution is fine, but 25 +/- 17 is not.>>

I know it's an approximation, but probably what this is telling me, with justification, is that my net count is not significantly above zero at the chosen confidence level.

Anyway, it looks like they have what is effectively spectral data. Some of the background is not true background in this sense.

cmsavage
2008-Jan-30, 04:19 PM
But what about the Central Limit Theorem? This says that combinations of non-Normal distributions tend towards the Normal.
The Central Limit Theorem applies to sums of quantities, where each of those quantities are independent but have identical probability distributions. The problem here is that the background and total number of events are not summed, do not have identical distributions, and are not independent. The Central Limit Theorem is also the limit where the number of quantities being summed becomes large; the two quantities here do not really qualify.


I must confess I do not know the distribution resulting from two Poisson distributions.
When taking two independent sources of events that are Poisson distributed with averages u1 and u2, like the number of background and signal events, then the total number of events is Poisson distributed with average u1+u2. However, the analysis here is not taking two independent sources. It takes the total number of events and background events, which are not independent quantities, and tries to reconstruct the number of signal events. There is no "nice" distribution for that case: it is not Normal, Poisson, or any of the other basic distributions.

If the background and total number of events were large and very different, so that the number of signal events must be large, then a Normal distribution might make a good approximation. But that is not the case here: the number of signal events is clearly small.


Yes but I can OBSERVE a negative net number of events. If I find a background count of 127, I can later observe a gross count of say, 120. That could happen on statistical grounds, and my net count is -7.
No, you cannot OBSERVE a negative number of events. The -7 you gave is the number of events over the average, but is not the actual number of signal events. You can observe less than expected, but the number of actual background, signal, and total events will always be positive or zero in any particular observation. The experimental analysis was trying to place limits on the actual number of signal events they observed and, from that, place limits on the average expected number of signal events. Any analysis that includes a negative number of actual events is no longer applicable to the actual situation.

I think the biggest problem here is that the two known quantities, the total number of events and the expected background rate, are not independent quantities. Even though, in any given observation, the total number of events may be below the expected number of background events, the total number of events will always equal or exceed the background events in that observation. A lot of the basic statistical theorems (such as the Central Limit Theorem) apply only to independent quantities and cannot be applied here. If we instead knew the expected signal and background rates (the true independent quantities) and wanted to estimate the total rate, then things would be a lot easier.

I routinely analyze results from experiments with a small number of events (with or without background), so I am quite familiar with the statistics used here. My life would be a lot easier if I didn't have to deal with all these statistical issues. :)

Warren Platts
2008-Feb-01, 12:40 PM
See, this is what I find so counterintuitive. If you're right, the intrinsic power barely exceeds human energy consumption. And actually, if you figure in solar powered human and human commensal biological activity, human power is greater than the intrinsic power. It just seems to me that something's got to be wrong somewhere. I mean all these continents moving around on less energy than it takes our cars to drive around? But hey, what do I know? (Not much :neutral:) Well, I guess it must be because our cars move faster, and so it's that kinetic v2 energy thing.

Consider work performed the following earthquakes: (http://en.wikipedia.org/wiki/2004_tsunami#Energy_released_by_the_earthquake)


1964 Alaskan: 2.5 x 1030 ergs
1960 Chilean: 7.5 x 1029 ergs
2004 Indonesian: 4.0 x 1029 ergs
Total = 3.65 x 1030 ergs (3.65 x 1023 Joules)


averaging over 50 years yeilds 232 terrawatts required to cause those three earthquakes. Since this figure does not include other tectonic activities, the total power required for plate tectonics must be much higher, and thus much larger than human industrial power consumption, but still only on the order of ~1% of the solar power absorbed by the Earth (~120,000 terawatts).

What gives?

If we take the data from the geoneutrino experiment at face value (~19 terrawatts), then where is the extra energy coming from?

Could it be that plate tectonics is solar powered??? :confused:

Warren Platts
2008-Feb-01, 05:47 PM
Could it be that plate tectonics is solar powered??? :confused:

Well, it might work this way: the intrinsic power is the radiometric heat plus primordial heat left over from when the Earth was a molten ball of lava. Early calculations of the Earth's age (http://en.wikipedia.org/wiki/Age_of_the_Earth#Early_calculations:_physicists.2C _geologists_and_biologists) by Lord Kelvin suggested the Earth's age was between 24 and 400 million years, but of course his calculations did not take into account radioactive decay. With the eventual discovery of radioactive decay and radiometric dating, Kelvin's calculations were forgotten--except for the supposed fact that the Earth had spent its bank account of primordial heat long ago, thus apparently implying that the only source of heat driving plate tectonics nowadays is radioactive decay.

But as a pointed out above, the best estimate of the power by the geoneutrino experiment is 19 TW, with an upper limit of 60 TW.

Yet simple back of the envelope calculations of the energy released by earthquakes suggests that it takes a lot more than 60 TW to drive plate tectonics. Therefore, the intrinsic power of the Earth must be much higher than 60 TW.

But solar power can't be the heat source because temperature increases as we drill down from the surface.

So, the only other heat source is primordial heat. Here solar power might play an indirect role, however. By heating the surface, the Sun slows down Earth's cooling rate, allowing much primordial heat still down there.

My hunch is that Lord Kelvin didn't take into account the heating of the surface of the Earth, and perhaps the insulating effect of the atmosphere (the greenhouse effect) that could radically slow down the cooling of the Earth's interior. But not having read Kelvin's work on the subject I can't say for sure. Perhaps someone reading this post knows whether Kelvin took solar power into account in his calculations.

Hornblower
2008-Feb-01, 09:32 PM
Since when is the rate at which heat escapes from the interior of our planet indicative of the amount of energy available for the cause of plate tectonics?

Warren appears to be misinterpreting the relatively low level of heat flow upward and out through the surface as a shortage of energy for driving plate tectonics. I interpret it as retention of internal heat by a good insulator.

Planet Earth's innards are very hot, because of the original heat of the planet's formation, replenishment from radioactive decay, and the slow rate at which heat escapes through the surface. It is plenty hot down there to keep part of the iron core molten, and the overlying mantle molten or at least soft enough to flow under pressure. This fluidity, along with whatever nonuniformity of temperature and density distribution there might be, makes convection possible. Convection is a gravity-driven movement enabled by deformability and uneven density. My educated belief is that convection is causing the mantle to flow and drag the continents with it. If any geophysicists out there disagree with me, please speak up.

Warren Platts
2008-Feb-02, 05:05 AM
Warren appears to be misinterpreting the relatively low level of heat flow upward and out through the surface as a shortage of energy for driving plate tectonics. I interpret it as retention of internal heat by a good insulator.

Not quite. And I agree that the surface and atmosphere are good insulators. I'm saying that radioactive decay does not provide enough energy to drive plate tectonics. We don't know what the heat flow through the surface is. I'm saying that it's probably much higher than the geoneutrino experiments say it is; that is, the Earth is a giant heat engine, and that primordial heat energy is lost to space, and that helps to drive plate tectonics. Hot mantle material rises in the rift zones, and cool crust gets subducted; that's what drives the convection. The Earth isn't a perpetual motion machine. It has to pay for plate tectonics with energy. Radioactive decay isn't enough. The only other plausible source of energy is primordial heat. Therefore, the intrinsic power of the Earth must be much higher than 60 TW; yet the intrinsic power is still low enough (on the order of 1%) so as to not be obvious to infrared surveys conducted by satellites.

Warren Platts
2008-Feb-03, 03:05 AM
I've done some more thinking--always a dangerous thing, no doubt. The NASA Hansen et al. paper can't account for 0.85 watts per square meter; that is, solar income outweighs the infrared expenditures that they can account for by 0.85 watts per square meter.


Since the total surface area of Earth is 5.1 x 1014 m2, that's 433.6 terrawatts. Yet the energy required to fund the last big three earthquakes was ~230 terrawatts. Assuming that the big three have only accounted for half the seismic activity on Earth over the last fifty years, then that's ~460 terrawatts--just about the right amount to make up the difference.

:think:

kzb
2008-Feb-04, 06:40 PM
Warren Platts -Earthquakes are usually the the sudden release of pent-up strain, built up over many years. Possibly the 50-year period in question is atypical? If lots of strain builds up, perhaps the first big earthquake sets others off in a cascade. In fact I think I saw a TV programme on this a few years back.

There is another kind of earthquake caused by explosive crystallisation. This again is sudden release of stored energy, so the power may be much more than average.

ExpErdMann
2008-Feb-04, 07:11 PM
I've done some more thinking--always a dangerous thing, no doubt. The NASA Hansen et al. paper can't account for 0.85 watts per square meter; that is, solar income outweighs the infrared expenditures that they can account for by 0.85 watts per square meter.


Since the total surface area of Earth is 5.1 x 1014 m2, that's 433.6 terrawatts. Yet the energy required to fund the last big three earthquakes was ~230 terrawatts. Assuming that the big three have only accounted for half the seismic activity on Earth over the last fifty years, then that's ~460 terrawatts--just about the right amount to make up the difference.

:think:

I don't think you can have it right here. Terrawatts is a measure of the energy output per unit time. You should be using joules or ergs for the total earthquake energy.

Warren Platts
2008-Feb-05, 03:12 AM
Warren Platts -Earthquakes are usually the the sudden release of pent-up strain, built up over many years. Possibly the 50-year period in question is atypical? If lots of strain builds up, perhaps the first big earthquake sets others off in a cascade. In fact I think I saw a TV programme on this a few years back.

There is another kind of earthquake caused by explosive crystallisation. This again is sudden release of stored energy, so the power may be much more than average.

Well, worldwide seismograph networks have only been in existence for the last 50 years or so. And there were some doosies back in the pre-seismograph era (e.g. Krakatoa, Lisbon, San Francisco, New Madrid Missouri). So I'm not prepared to suggest that the last 50 years have been atypical as far as earthquakes are concerned.


I don't think you can have it right here. Terrawatts is a measure of the energy output per unit time. You should be using joules or ergs for the total earthquake energy.
From post #41, I summed the total energy released from the three biggest earthquakes: 3.65 x 1023 Joules. There are approximately 3.14 x 107 seconds per year. So, averaging over 50 years:



3.65 x 1023 Joules


______________________________


50 x 3.14 x 107 seconds



= 2.32 x 1014 Joules per second


= 232 terawatts


Of course the energy is released very suddenly. But it takes a lot of power to build up that strain over time. It's like a flea getting ready to jump.

The main point is that radioactive decay, as measured by the geonuetrino experiments (even if we go for the upper limit of 60 terawatts) does not even come close to accounting for the power required for plate tectonics.

So, either the geoneutrino experiments are fundamentally flawed, or else there is another power source that needs to be included in intrinsic power calculations.

kzb
2008-Feb-05, 01:06 PM
Warren Platts, I've checked your calculation and I get much the same value as you (I get 231 terawatt). Ok how's this for an explanation. I can't quite get my head round it, but perhaps someone else can judge if this holds water or not:

The vast majority of the energy release from an earthquake is not spent on surface phenomena, but is dissipated within the body of the planet. Pent up strain energy is converted to other energy forms such as vibration, which is converted back to heat within the planet.

The vast majority of the energy is not therefore lost to space, but is converted back to heat energy within the planet, ready to power more earthquakes in the future. The average earthquake power can therefore exceed the steady-state "de novo" heat generation.

(As I said, I'm a bit unsure about this, there may be thermodynamic arguments against this picture ?)

ExpErdMann
2008-Feb-06, 05:59 PM
Warren Platts, I've checked your calculation and I get much the same value as you (I get 231 terawatt).

Yes, I was reading Warren's numbers incorrectly, sorry.


Ok how's this for an explanation. I can't quite get my head round it, but perhaps someone else can judge if this holds water or not:

The vast majority of the energy release from an earthquake is not spent on surface phenomena, but is dissipated within the body of the planet. Pent up strain energy is converted to other energy forms such as vibration, which is converted back to heat within the planet.

The vast majority of the energy is not therefore lost to space, but is converted back to heat energy within the planet, ready to power more earthquakes in the future. The average earthquake power can therefore exceed the steady-state "de novo" heat generation.

(As I said, I'm a bit unsure about this, there may be thermodynamic arguments against this picture ?)

This sounds like a perpetual motion machine you've built there. We have all this energy being released in these earthquakes. It has to be absorbed somewhere else or the Earth's interior would just get hotter and hotter. One possibility, and it's considered ATM in these here parts, is the energy goes into expanding the earth at a slow rate. What we would need is a large source of energy, greater than radioactivity allows, which can cause both the earthquakes and simultaneous expansion.

Hornblower
2008-Feb-06, 07:16 PM
In my earlier post I never argued that the observed plate tectonics activity is sustainable indefinitely.

For every joule of heat that leaves the mantle and escapes through the surface, there just might be many more flowing horizontally between primordial hot and cooler zones. Since very little is leaving through the surface, these zones eventually would equalize and the convection action should run down. That could take hundreds of millions or perhaps billions of years. For comparison I did a rough calculation on the cooling rate, using the heat loss generally agreed upon in this thread and the amount of heat still inside our planet, based on temperature and specific heat estimates. It would take several billion years for half of the present heat to escape.

We just might be observing a transient phenomenon with a time constant of some billions of years. Not a perpetual motion machine, but long lasting in terms of human lifetimes.

kzb
2008-Feb-07, 01:06 PM
<<This sounds like a perpetual motion machine you've built there.>>

This is what worried me !

However, I think you'd agree that very little of the total energy release from an earthquake gets radiated into space. Most of the energy ends up being converted back to heat within the body of the planet.

But I think you're right. The mechanical effects must depend on a temperature difference, and in this case that means a temperature gradient and heat flow out of the earth and into space.

I also think it would be a fair postulate that the efficiency of earthquake production, measured relative to the total energy flow, would be small. That means the total energy flow must be considerably in excess of 231TW.

So we are left either with with Hornblower's "out of equilibrium" argument, or the de-novo heat production is much greater than the accepted value ?

ExpErdMann
2008-Feb-08, 03:14 AM
<<This sounds like a perpetual motion machine you've built there.>>

This is what worried me !

However, I think you'd agree that very little of the total energy release from an earthquake gets radiated into space. Most of the energy ends up being converted back to heat within the body of the planet.

I'm not sure I can agree with that. For one thing, the mantle becomes hotter as you move down and so we would have the heat arising from the earthquake moving from a cooler zone to a hotter zone, if it moved downward. That only leaves lateral motion through the upper mantle and crust or leakage to space.


But I think you're right. The mechanical effects must depend on a temperature difference, and in this case that means a temperature gradient and heat flow out of the earth and into space.
The direction of heat flow is at least feasible then. I wonder if we're missing something about the fates of earhquake energy though.


I also think it would be a fair postulate that the efficiency of earthquake production, measured relative to the total energy flow, would be small. That means the total energy flow must be considerably in excess of 231TW.

I'm not sure where that other earthquake energy would be going, unless you're thinking about expansion.


So we are left either with with Hornblower's "out of equilibrium" argument, or the de-novo heat production is much greater than the accepted value ?

I'm not too keen on Hornblower's argument. From my reading (and your own post #14 related to Marone), geophysicists think the Earth's present internal energy is mostly due to radioactive heating. Now the geoneutrino experiments and other arguments place an upper limit on that of 60 TW (and it's most likely about 20 TW). From Warrens' calculation that's not enough to cause the earthquake energy released (about 230 TW). So, on balance, I'm inclined at this point to go with the de-novo heat production. (But I'm also somewhat biased here, as I have proposed an ATM mechanism for such energy production in the past.)

What I'm wondering is, what does geophysics say about the ultimate source of earthquake energy and why is it so much greater than what seems to be available?

Jerry
2008-Feb-08, 03:30 AM
As I mentioned on another thread, there is a satellite sitting in a warehouse in Maryland designed specifically to measure the net energy balance of the the Earth - current estimates are just that.

kzb
2008-Feb-08, 12:55 PM
ExpErdMann wrote:
<<I'm not sure I can agree with that. For one thing, the mantle becomes hotter as you move down and so we would have the heat arising from the earthquake moving from a cooler zone to a hotter zone, if it moved downward. That only leaves lateral motion through the upper mantle and crust or leakage to space.>>

I don't mean the HEAT, as such, is flowing from cold to hot. I mean the energy carried as vibration or movement. There's no thermodynamic reason why that cannot transfer energy from a cool zone to a hotter zone. I think it's because it is higher-grade energy.

As I understand it, it's seismic waves that have allowed the probing of the internal structure of the planet, at least some of the energy is propagated down into the deepest layers and core.

There are other places where some of the energy could end up. I believe there have been micro-changes in the rotation period and axis of rotation as a result of earthquakes. So that will have taken up some of the energy, and it won't appear (immediately) as heat.

Jerry, about the satellite, you make it sound a bit suspicious ! I wonder if this is one of those experiments designed to find what they want it to find...

Expansion-not so sure about this one.

Hornblower
2008-Feb-08, 01:25 PM
I stand by my gravitational out-of-equilibrium idea simply because I cannot think of anything better, even after all of this discussion. I think we are pretty much in agreement that a sustainable heat engine action would be characterized by more heat flow out of the mantle than what actually is observed.

As a rough analogy, consider a hydroelectric generating plant. If the Sun were to go away, there would be nothing to return water to the reservoir. That would not stop us from generating electric power for a while longer by drawing down the water that is in the reservoir, until it either is emptied or starts freezing up, whichever comes first.

Warren Platts
2008-Feb-08, 05:23 PM
As I mentioned on another thread, there is a satellite sitting in a warehouse in Maryland designed specifically to measure the net energy balance of the the Earth - current estimates are just that.
Considering all the hoopla over global warming, that is criminal.


In my earlier post I never argued that the observed plate tectonics activity is sustainable indefinitely.

For every joule of heat that leaves the mantle and escapes through the surface, there just might be many more flowing horizontally between primordial hot and cooler zones.
And downward. Most energy released from an earthquake is in the form of vibrations that travel throughout the earth. As these vibrations are damped, the big vibrations cause tiny vibrations of atoms and molecules--heat in other words. So within a matter of seconds, a large earthquake near the surface could cause a tiny bit of heating within the very core of the Earth itself.


Since very little is leaving through the surface, these zones eventually would equalize and the convection action should run down. That could take hundreds of millions or perhaps billions of years. For comparison I did a rough calculation on the cooling rate, using the heat loss generally agreed upon in this thread and the amount of heat still inside our planet, based on temperature and specific heat estimates. It would take several billion years for half of the present heat to escape.
I'd be curious how you did this exactly, and why it differs from Lord Kelvin's estimates.


We just might be observing a transient phenomenon with a time constant of some billions of years. Not a perpetual motion machine, but long lasting in terms of human lifetimes.No doubt!


I'm not too keen on Hornblower's argument. From my reading (and your own post #14 related to Marone), geophysicists think the Earth's present internal energy is mostly due to radioactive heating. Now the geoneutrino experiments and other arguments place an upper limit on that of 60 TW (and it's most likely about 20 TW). From Warrens' calculation that's not enough to cause the earthquake energy released (about 230 TW). So, on balance, I'm inclined at this point to go with the de-novo heat production. (But I'm also somewhat biased here, as I have proposed an ATM mechanism for such energy production in the past.)
Well, it might just be the case that the geoneutrino experiments are seriously and fundamentally flawed. How can you accurately measure something that barely exists and refuses to interact much with real matter?


What I'm wondering is, what does geophysics say about the ultimate source of earthquake energy and why is it so much greater than what seems to be available?Indeed, that is the question.

Hornblower
2008-Feb-08, 09:03 PM
*****
Originally Posted by Hornblower
Since very little is leaving through the surface, these zones eventually would equalize and the convection action should run down. That could take hundreds of millions or perhaps billions of years. For comparison I did a rough calculation on the cooling rate, using the heat loss generally agreed upon in this thread and the amount of heat still inside our planet, based on temperature and specific heat estimates. It would take several billion years for half of the present heat to escape.
*****
I'd be curious how you did this exactly, and why it differs from Lord Kelvin's estimates.



Not very exact, but here is my rough estimate.
Heat flow 4.4*10^13 j/s

Specific heat about 0.4j/(g*K); value for iron, roughly representative of interior of Earth

Mass about 6*10^27g

Temperature about 3,000K; much hotter toward center, cooler in mantle, should be pretty good ballpark average

Heat energy is roughly (specific heat)*mass*temperature.

Roughly 10^31 joules

Assuming an exponential cooldown, it should drop to 1/e times the present amount of heat in time T.

T = 10^31 j / (4.4*10^13 j/s) or roughly 2*10^17 s.

That is several billion years from now.

I could be off by an order of magnitude and it still would be a very long time.

This is not an estimate of the planet's age as done by Lord Kelvin. It is a projection of the future. It is intended to give a feel for how slowly a planet will cool from an initial molten state.

Warren Platts
2008-Feb-09, 03:11 PM
Not very exact, but here is my rough estimate.
Heat flow 4.4*10^13 j/s

Specific heat about 0.4j/(g*K); value for iron, roughly representative of interior of Earth

Mass about 6*10^27g

Temperature about 3,000K; much hotter toward center, cooler in mantle, should be pretty good ballpark average

Heat energy is roughly (specific heat)*mass*temperature.

Roughly 10^31 joules

Assuming an exponential cooldown, it should drop to 1/e times the present amount of heat in time T.

T = 10^31 j / (4.4*10^13 j/s) or roughly 2*10^17 s.

That is several billion years from now.

I could be off by an order of magnitude and it still would be a very long time.

This is not an estimate of the planet's age as done by Lord Kelvin. It is a projection of the future. It is intended to give a feel for how slowly a planet will cool from an initial molten state.

I salute you sir! Good job!

ExpErdMann
2008-Feb-09, 10:19 PM
And downward. Most energy released from an earthquake is in the form of vibrations that travel throughout the earth. As these vibrations are damped, the big vibrations cause tiny vibrations of atoms and molecules--heat in other words. So within a matter of seconds, a large earthquake near the surface could cause a tiny bit of heating within the very core of the Earth itself.
Okay, if the earthquake energy were being mostly rechanneled back into the lower mantle and core in this manner, then the energy would be available again to cause future earthquakes. The only thing slowing down this perpetual motion machine would be the small leakage of heat through the crust. You wouldn't need to come up with the 230 TW, just the 19-60 TW.


Well, it might just be the case that the geoneutrino experiments are seriously and fundamentally flawed. How can you accurately measure something that barely exists and refuses to interact much with real matter?
I can agree that the radioactivity number needs more pinning down than the geoneutrinos seem able to.

kzb
2008-Feb-11, 06:27 PM
ExpErdMann wrote:
<<Okay, if the earthquake energy were being mostly rechanneled back into the lower mantle and core in this manner, then the energy would be available again to cause future earthquakes>>

I still have my doubts about this concept, even though it was my own idea. Whilst it's true most of the earthquake energy is retained as heat, it's also true that earthquakes are a heat engine and depend on thermodynamics.

There must be a heat flow, temperature difference, sufficient to power the earthquakes over the long term, and that heat flow must be substantially larger than the mean long-term earthquake power. This is because a heat engine can never be 100% efficient (and in practice almost never more than a small fraction of this)

I think this follows from thermodynamic considerations or am I completely wrong?

ExpErdMann
2008-Feb-11, 07:22 PM
From this Wikipedia entry (http://en.wikipedia.org/wiki/Moment_magnitude_scale), it appears that only a tiny amount goes into seismic waves. Most goes into heat or fracturing/deforming rocks. This would argue against the idea that substantial energy can go back into the mantle and core. So we're back to needing a source for the 231 TW.

Jerry
2008-Feb-13, 02:45 AM
Jerry, about the satellite, you make it sound a bit suspicious ! I wonder if this is one of those experiments designed to find what they want it to find...

Expansion-not so sure about this one.

Not a great mystery or a great secret: One of Al Gore's pet projects that did not make it to the launch pad before the Bush administration took over. They simply pulled the funding for the launch vehicle. A classic head-in-the-sand approach to a very important scientific issue.

kzb
2008-Feb-15, 12:56 PM
ExpErdMann wrote
<<From this Wikipedia entry, it appears that only a tiny amount goes into seismic waves. Most goes into heat or fracturing/deforming rocks.>>

I don't think this affects my argument though. The point is that the energy is retained by the body of the planet and not radiated directly into space.

The energy going into fracturing/deforming rocks is a kind of stored potential energy. Over geological timescales this energy will eventually be recovered as heat.

As broken rocks are buried or subducted, the pressure and temperature rises and they are compressed back together. The chemical bonds are restored and heat is released.

I guess other forms of potential energy are created. If a plateau is raised by an earthquake, there is gravitational potential energy. If the motion of the whole planet is affected, there is stored energy there also.

But I find it doubtful that a planet can go on storing more and more potential energy indefinitely. Things will happen to restore equilibrium and convert it to heat.

ExpErdMann
2008-Feb-16, 05:12 PM
Consider work performed the following earthquakes: (http://en.wikipedia.org/wiki/2004_tsunami#Energy_released_by_the_earthquake)


1964 Alaskan: 2.5 x 1030 ergs
1960 Chilean: 7.5 x 1029 ergs
2004 Indonesian: 4.0 x 1029 ergs
Total = 3.65 x 1030 ergs (3.65 x 1023 Joules)


averaging over 50 years yeilds 232 terrawatts required to cause those three earthquakes. Since this figure does not include other tectonic activities, the total power required for plate tectonics must be much higher, and thus much larger than human industrial power consumption, but still only on the order of ~1% of the solar power absorbed by the Earth (~120,000 terawatts).

What gives?

If we take the data from the geoneutrino experiment at face value (~19 terrawatts), then where is the extra energy coming from?

Could it be that plate tectonics is solar powered??? :confused:

I've noticed a possible discrepancy between Warren's numbers for earthquake energy release above and the number in this article (http://www.britannica.com/eb/article-59571/earthquake).
There they give the annual energy release from earthquakes as 10^25 erg (10^18 J), which corresponds to a rate of only about .03 TW. I don't see any errors in Warren's calculations, but I think we should try to figure out this discrepancy before we try to account for Warren's higher rate. The online sources don't seem too helpful here.

Warren Platts
2008-Feb-17, 06:51 AM
I've noticed a possible discrepancy between Warren's numbers for earthquake energy release above and the number in this article (http://www.britannica.com/eb/article-59571/earthquake).
There they give the annual energy release from earthquakes as 10^25 erg (10^18 J), which corresponds to a rate of only about .03 TW. I don't see any errors in Warren's calculations, but I think we should try to figure out this discrepancy before we try to account for Warren's higher rate. The online sources don't seem too helpful here.
Yes, it's a mess out there. I shall nevertheless attempt to bring some order out of the chaos.

I shall refer to following references that are primarily from usgs.gov:


Broadband Source Parameters Computed at the NEIC (http://neic.usgs.gov/neis/nrg/bb_processing.html#energy)
Measuring the Size of an Earthquake (http://earthquake.usgs.gov/learning/topics/measure.php)
Magnitude 9.0 Sumatra-Andaman Islands Earthquake FAQ (http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav/faq.php)
Long period seismic moment of the 2004 Sumatra earthquake and implications for the slip process and tsunami generation; Stein and Okal, Northwestern University, Department of Geological Sciences (2005) (http://www.earth.northwestern.edu/people/seth/research/sumatra2.html)


There are several quantities that have to be distinguished and kept straight:


ES is the "radiated" energy
MO is the seismic moment expressed in energy
MW is the seismic moment magnitude and is a unitless number ranging from 0 to 10
ME is the energy magnitude and is also a unitless number ranging from 0 to 10


ES is commonly said to be "a measure of seismic potential for damage to anthropogenic structures" (ref. 1.). It is computed from measurements of broadband P-waves, also known as pressure waves. (Pressure waves are like sound waves that propagate through the Earth to be distinguished from S-waves that have an amplitude in directions perpendicular to the direction of propagation, rather like a double-dutch jump rope, and surface waves that are analogous to ocean waves. S-waves can only propagate through solid structures, whereas P-waves can also go through liquids--that's how we know we have a liquid core.)

Although MO looks like ME and MW, it is in fact a measure of energy, like ES. I guess the M stands for "moment", and the O stands for, well, the second letter of "moment" probably. It attempts to be a direct measure the work done by the earthquake. And what is an earthquake? It is what happens when two chunks of the Earth rub up against each other. So MO attempts to measure the area of the rupture, the friction between the plates and the distance the plates move to get an estimate of total work. It is analogous to a sanding block being rubbed against a piece of wood. You could hook up a spring scale to your sanding block and then use the scale to drag the sanding block; if you dragged the block exactly one foot, then whatever the scale said the force in pounds was would give you a precise estimate of the work you did in foot-pounds, that could be then converted into ergs or joules or megatons.

ME and MW are both evolutionary descendants of the old-fashioned Richter scale now only in use by the mass media. Both attempt to provide a classification system based on the relative strengths of earthquakes. The astronomical analogy is stellar magnitude, in which a unit difference between two stars indicates a factor of 2 or 10 or whatever difference in the luminosity of the stars.

Both ME and MW will tend to be similar for any given earthquake, but they need not be exactly the same. ME is mathematically related to ES according to the following formula (ref. 1., ref. 2.):



ME = (2/3)log10(ES) - 2.9

where ES is expressed in Joules.

MW, on the other hand, is mathematically related to MO according to this formula (ref. 2., ref. 4.):



MW = (2/3)log10(MO) - 10.7

where MO is expressed in ergs. One can solve for MO and derive the following equation:



MO = 101.5(Mw + 10.7)

If we go for the MW estimate of 9.3 for the 2004 Indonesian earthquake (ref. 4.)--as I think we should since it takes into account the superlong period seismic waves that the earlier USGS estimates ignored--that works to an even 1030 ergs--equivalent to 1023 J.

Now we can account for the discrepancy that worried ExpErdMann. He cites an Encyclopædia Britannica article, but it explicitly refers to ES and ignores the seismic moment, MO. Ref. 3 (scroll down about 5/8 down the page) lists the ES of 2 x 1018 J--a factor of 50,000 difference from the MO of 1023 J! Note that when you do the math, the ES of 2 x 1018 J listed in ref. 3. corresponds to a ME of 9.3--the same as the MW

Since most of the MO energy is absorbed within the Earth as heat, it is no wonder the Encyclopædia Britannica writes:


The total annual energy released in all earthquakes is about 1025 ergs, corresponding to a rate of work between 10 million and 100 million kilowatts. This is approximately one one-thousandth the annual amount of heat escaping from the Earth's interior. as if earthquakes have little to do with heat escaping from the Earth's interior! :lol:

I derived my figures from the Wikipedia article on the Indonesian earthquake (http://en.wikipedia.org/wiki/2004_Indian_Ocean_earthquake#Energy_released_by_th e_earthquake). But their figure of 4.0 x 1029 ergs corresponds to a MW of 9.035?!? So, I can see now that I have to revise my figures upwards. Furthermore, the USGS still thinks that the Alaskan earthquake was bigger than the Indonesian one (ref. 3.). However, back in the day, they didn't have the sophisticated seismographs that are available now--so it's likely that the magnitude of the Alaskan earthquake will be revised upwards in the future. So let's just call it a 9.4 MW so it will be more than the Indonesian earthquake, but less than the Chilean earthquake of 9.5 MW. So, according to my spreadsheet, these three generated seismic moments in decreasing order as follows:


9.5 --> 2 x 1023 J
9.4 --> 1.4 x 1023 J
9.3 --> 1.0 x 1023 J


If we can reasonably assume that these three earthquakes account for half of the total seismic moment of the last 100 years or so, and if there are pi x 109 seconds in 100 years, that's 2.8 x 1014 Watts or 280 TW. :neutral:

Warren Platts
2008-Feb-17, 04:37 PM
It is commonly said that most of an earthquake's energy is reabsorbed back into the Earth; so, a good way to think about ES and MO (see definitions in preceding post) is that the difference between the two is a measure of the proportion of released energy that is reabsorbed into the Earth. Thus the MO:ES ratio for the 2004 Indonesian earthquake is 50,000; only 0.002% was released at the surface to be available to wreck havoc.

Since earthquakes within subduction zones tend to occur much deeper than along seafloor spreading zones, I would guess that the MO:ES ratio for subduction zone earthquakes would be higher than that for seafloor spreading zones--but that's just a hypothesis of mine, I haven't checked it out.

Warren Platts
2008-Feb-17, 06:17 PM
I compiled a spreadsheet of every earthquake listed in the USGS Historic Worldwide Earthquakes (http://earthquake.usgs.gov/regional/world/historical.php) stretching from 1900 to 2007 and calculated the MO all of them and then summed to come up with a total seismic moment for the 107 years of 6.87 x 1023 Joules. This works out to a total average earthquake power of 2.04 x 1014 Watts; ~200 TW, basically. There is a strong "pull of the present" in the data, so this figure represents a lower bound. However, the data also show how the few big events truly dominate the picture.

What is the significance for the Earth's intrinsic power? Probably not much, I'm now thinking. When figuring a heat budget for the Earth's interior, the seismic moment energy released by earthquakes must be figured as a positive heat source, does it not? But most of this energy is not in fact radiated out into space eventually; rather, it is reuptaken in the crust in the form of strain. That is, the earthquake heat source and the crustal strain heat sink are a wash. Thus, the Earth earthquake system is pretty much a perpetual motion machine. It is only the radiative energy ES that actually radiates out into space. And that apparently is just a small fraction of the total heat loss of the planet. So, Kelvin was right. The primordial heat was lost long ago, and the radioactive decay power as detected by the geoneutrino experiments is more than enough to keep the whole system going. No need to invoke strange new mechanisms or expanding Earth theories.

Sorry about that Jerry and rtomes! :D

Of course, the radioactive decay is not itself nearly enough to power plate tectonics, mind you.

It's just that it turns out that most of the energy required for plate tectonics just comes from the earthquakes themselves. That is, the energy released by earthquakes gets recycled and becomes available to drive tectonics in the future. If it wasn't for the radioactive decay, however, the ES energy that is lost would eventually suck the planet dry, and plate tectonics would come to a grinding halt.

What is needed is a few good satellites that are specifically designed to measure the long-wave radiative heat loss of the Earth. I'm surprised we don't have them yet.

Anyway, here's the data I typed in in case you want to fool around with it:

MW MO (starting from most recent to earliest)

6.4 4.95E+18
6.6 9.89E+18
7.1 5.56E+19
6.7 1.40E+19
7.8 6.24E+20
7.4 1.57E+20
6.6 9.89E+18
6.5 7.00E+18
6.7 1.40E+19
6.8 1.97E+19
7.7 4.42E+20
6.5 7.00E+18
7.2 7.85E+19
5.4 1.57E+17
6.8 1.97E+19
6.8 1.97E+19
6.6 9.89E+18
7.4 1.57E+20
6.9 2.79E+19
7.4 1.57E+20
6.5 7.00E+18
6.7 1.40E+19
6.7 1.40E+19
7.9 8.81E+20
8.4 4.95E+21
6.8 1.97E+19
6.2 2.48E+18
7.2 7.85E+19
6.4 4.95E+18
6.7 1.40E+19
8 1.24E+21
6.5 7.00E+18
5.4 1.57E+17
4.6 9.89E+15
7.5 2.21E+20
6.7 1.40E+19
7.2 7.85E+19
6.9 2.79E+19
4.2 2.48E+15
5.9 8.81E+17
6.8 1.97E+19
6.6 9.89E+18
4.3 3.51E+15
6.7 1.40E+19
6.7 1.40E+19
5.2 7.85E+16
4.5 7.00E+15
8.1 1.76E+21
6.7 1.40E+19
7.1 5.56E+19
6.4 4.95E+18
6.5 7.00E+18
6.9 2.79E+19
7.5 2.21E+20
8.1 1.76E+21
6.9 2.79E+19
7.1 5.56E+19
8.3 3.51E+21
6.8 1.97E+19
4.5 7.00E+15
6.7 1.40E+19
6.7 1.40E+19
6.7 1.40E+19
3.8 6.24E+14
6.9 2.79E+19
5.8 6.24E+17
6.8 1.97E+19
7 3.94E+19
5.9 8.81E+17
4.8 1.97E+16
7.7 4.42E+20
6.3 3.51E+18
6.3 3.51E+18
6.8 1.97E+19
7.4 1.57E+20
8 1.24E+21
4.6 9.89E+15
6.1 1.76E+18
4.2 2.48E+15
6.7 1.40E+19
6.4 4.95E+18
7 3.94E+19
3.8 6.24E+14
7.6 3.13E+20
6.7 1.40E+19
6.6 9.89E+18
7.4 1.57E+20
3.6 3.13E+14
4.1 1.76E+15
6.5 7.00E+18
6.6 9.89E+18
6.8 1.97E+19
6.5 7.00E+18
6 1.24E+18
6.5 7.00E+18
6.9 2.79E+19
7 3.94E+19
4.5 7.00E+15
6.3 3.51E+18
7.6 3.13E+20
6.6 9.89E+18
7.5 2.21E+20
4.7 1.40E+16
7.6 3.13E+20
7.2 7.85E+19
5 3.94E+16
5.6 3.13E+17
7.2 7.85E+19
5.9 8.81E+17
5.1 5.56E+16
5.3 1.11E+17
6.7 1.40E+19
6.6 9.89E+18
6.6 9.89E+18
4.9 2.79E+16
7.2 7.85E+19
6.8 1.97E+19
7.8 6.24E+20
5.2 7.85E+16
6.9 2.79E+19
6.7 1.40E+19
4.1 1.76E+15
4.2 2.48E+15
6.7 1.40E+19
6.7 1.40E+19
8.6 9.89E+21
6.6 9.89E+18
4.9 2.79E+16
7.1 5.56E+19
6.8 1.97E+19
6.4 4.95E+18
6.5 7.00E+18
4.1 1.76E+15
6.7 1.40E+19
7.1 5.56E+19
6.6 9.89E+18
6.7 1.40E+19
9.3 1.11E+23
8.1 1.76E+21
6.8 1.97E+19
6.8 1.97E+19
7 3.94E+19
7.1 5.56E+19
7.1 5.56E+19
6.3 3.51E+18
6.4 4.95E+18
7.2 7.85E+19
7.5 2.21E+20
6.7 1.40E+19
6.9 2.79E+19
6.3 3.51E+18
6.7 1.40E+19
5.9 8.81E+17
6.6 9.89E+18
6.7 1.40E+19
7 3.94E+19
6.5 7.00E+18
6.8 1.97E+19
6 1.24E+18
3.7 4.42E+14
6.6 9.89E+18
7.4 1.57E+20
7.2 7.85E+19
3.8 6.24E+14
4.3 3.51E+15
3.6 3.13E+14
7.3 1.11E+20
4.9 2.79E+16
5.1 5.56E+16
6.8 1.97E+19
4.2 2.48E+15
5.1 5.56E+16
6.9 2.79E+19
3 3.94E+13
6.5 7.00E+18
6.3 3.51E+18
6.6 9.89E+18
4 1.24E+15
6.6 9.89E+18
6.4 4.95E+18
5.3 1.11E+17
7.3 1.11E+20
7 3.94E+19
6.7 1.40E+19
5 3.94E+16
7.3 1.11E+20
6.6 9.89E+18
6.6 9.89E+18
6.6 9.89E+18
6.8 1.97E+19
4.5 7.00E+15
6.7 1.40E+19
6.5 7.00E+18
7.8 6.24E+20
6.6 9.89E+18
7 3.94E+19
0.35 4.17E+09
6.7 1.40E+19
3.6 3.13E+14
6.7 1.40E+19
7.3 1.11E+20
8.3 3.51E+21
3.3 1.11E+14
6.4 4.95E+18
6.6 9.89E+18
3.4 1.57E+14
3.7 4.42E+14
4 1.24E+15
4.7 1.40E+16
3.9 8.81E+14
3.8 6.24E+14
7.2 7.85E+19
4.5 7.00E+15
5.9 8.81E+17
5.3 1.11E+17
6.3 3.51E+18
7.6 3.13E+20
6.8 1.97E+19
3.6 3.13E+14
6 1.24E+18
7.6 3.13E+20
6.9 2.79E+19
6.8 1.97E+19
7.1 5.56E+19
3.6 3.13E+14
6.6 9.89E+18
4 1.24E+15
3.7 4.42E+14
5.8 6.24E+17
3.4 1.57E+14
7 3.94E+19
3.8 6.24E+14
7 3.94E+19
4 1.24E+15
4.2 2.48E+15
4 1.24E+15
6.8 1.97E+19
3.9 8.81E+14
6.7 1.40E+19
6.4 4.95E+18
4 1.24E+15
4.6 9.89E+15
7.1 5.56E+19
4.6 9.89E+15
6.8 1.97E+19
6.3 3.51E+18
5.2 7.85E+16
6.6 9.89E+18
4.1 1.76E+15
6.1 1.76E+18
4.7 1.40E+16
7.6 3.13E+20
7.3 1.11E+20
6.3 3.51E+18
6.7 1.40E+19
3.3 1.11E+14
5.7 4.42E+17
3.6 3.13E+14
4.8 1.97E+16
3.9 8.81E+14
6.3 3.51E+18
7.3 1.11E+20
4.4 4.95E+15
7.9 8.81E+20
7.4 1.57E+20
5.8 6.24E+17
5.9 8.81E+17
6.2 2.48E+18
6.7 1.40E+19
4.2 2.48E+15
6.9 2.79E+19
7.6 3.13E+20
5 3.94E+16
4.1 1.76E+15
7.6 3.13E+20
6 1.24E+18
4.8 1.97E+16
7.7 4.42E+20
7.7 4.42E+20
4.5 7.00E+15
7.3 1.11E+20
6.5 7.00E+18
4.6 9.89E+15
6.6 9.89E+18
5.3 1.11E+17
3.7 4.42E+14
3.6 3.13E+14
6.2 2.48E+18
4.9 2.79E+16
7.1 5.56E+19
5.1 5.56E+16
7.1 5.56E+19
6.1 1.76E+18
4.6 9.89E+15
7.5 2.21E+20
7.4 1.57E+20
5.7 4.42E+17
5.3 1.11E+17
6.5 7.00E+18
7.2 7.85E+19
7.6 3.13E+20
8.4 4.95E+21
6.8 1.97E+19
6.6 9.89E+18
7.6 3.13E+20
7.7 4.42E+20
7.5 2.21E+20
7.6 3.13E+20
7.8 6.24E+20
8 1.24E+21
6.7 1.40E+19
5 3.94E+16
7.9 8.81E+20
7.9 8.81E+20
7.2 7.85E+19
7.1 5.56E+19
7.5 2.21E+20
7.6 3.13E+20
6 1.24E+18
6.9 2.79E+19
7.6 3.13E+20
6.7 1.40E+19
7 3.94E+19
7.1 5.56E+19
7.1 5.56E+19
7.3 1.11E+20
6.1 1.76E+18
5.2 7.85E+16
7.2 7.85E+19
7 3.94E+19
6.6 9.89E+18
7.5 2.21E+20
8.1 1.76E+21
6.6 9.89E+18
5.9 8.81E+17
7.1 5.56E+19
7.5 2.21E+20
7.8 6.24E+20
7.8 6.24E+20
6.4 4.95E+18
7 3.94E+19
5.8 6.24E+17
7.3 1.11E+20
7.9 8.81E+20
6.5 7.00E+18
7.1 5.56E+19
6.6 9.89E+18
5.3 1.11E+17
6.9 2.79E+19
7 3.94E+19
8.2 2.48E+21
6.7 1.40E+19
6.2 2.48E+18
6 1.24E+18
7.8 6.24E+20
7.8 6.24E+20
5.8 6.24E+17
7.6 3.13E+20
5.7 4.42E+17
7.3 1.11E+20
7.2 7.85E+19
6.2 2.48E+18
6.8 1.97E+19
7 3.94E+19
5.6 3.13E+17
7.7 4.42E+20
7.4 1.57E+20
2.5 7.00E+12
5.5 2.21E+17
6 1.24E+18
6.9 2.79E+19
5.4 1.57E+17
6.8 1.97E+19
5.9 8.81E+17
6.8 1.97E+19
7.7 4.42E+20
6.6 9.89E+18
7.8 6.24E+20
6.7 1.40E+19
6.5 7.00E+18
5.6 3.13E+17
5.9 8.81E+17
5.1 5.56E+16
7 3.94E+19
5.5 2.21E+17
5.7 4.42E+17
6.2 2.48E+18
6.1 1.76E+18
7.9 8.81E+20
5 3.94E+16
6.8 1.97E+19
8 1.24E+21
7.8 6.24E+20
6 1.24E+18
5.8 6.24E+17
6.2 2.48E+18
6.7 1.40E+19
6.9 2.79E+19
6.9 2.79E+19
5.3 1.11E+17
6.4 4.95E+18
6 1.24E+18
7.3 1.11E+20
6.9 2.79E+19
6.8 1.97E+19
6.5 7.00E+18
7.2 7.85E+19
7.7 4.42E+20
5.2 7.85E+16
6 1.24E+18
6.2 2.48E+18
5 3.94E+16
5.8 6.24E+17
5.8 6.24E+17
4.5 7.00E+15
6.4 4.95E+18
5.7 4.42E+17
7.5 2.21E+20
7.8 6.24E+20
6.6 9.89E+18
7.4 1.57E+20
7.2 7.85E+19
7.3 1.11E+20
7.9 8.81E+20
7.5 2.21E+20
7.1 5.56E+19
6.5 7.00E+18
3.5 2.21E+14
7.5 2.21E+20
7.2 7.85E+19
6.7 1.40E+19
5.8 6.24E+17
4.6 9.89E+15
6.1 1.76E+18
6.2 2.48E+18
7 3.94E+19
7.6 3.13E+20
6.2 2.48E+18
7.5 2.21E+20
8.1 1.76E+21
7.3 1.11E+20
6.8 1.97E+19
6.2 2.48E+18
6.2 2.48E+18
7.6 3.13E+20
7.2 7.85E+19
7.1 5.56E+19
7 3.94E+19
7.5 2.21E+20
7.5 2.21E+20
6.9 2.79E+19
6.3 3.51E+18
6.6 9.89E+18
8 1.24E+21
7 3.94E+19
7.4 1.57E+20
6.9 2.79E+19
7.5 2.21E+20
7.2 7.85E+19
4.5 7.00E+15
5.7 4.42E+17
6.4 4.95E+18
5.9 8.81E+17
6.4 4.95E+18
7.8 6.24E+20
5.3 1.11E+17
6.9 2.79E+19
6.6 9.89E+18
7.3 1.11E+20
7.1 5.56E+19
6.9 2.79E+19
6.3 3.51E+18
5.3 1.11E+17
6.5 7.00E+18
7.3 1.11E+20
8.1 1.76E+21
5.9 8.81E+17
6.8 1.97E+19
7 3.94E+19
6.1 1.76E+18
5 3.94E+16
6.9 2.79E+19
7 3.94E+19
5.1 5.56E+16
7.3 1.11E+20
6.5 7.00E+18
5.7 4.42E+17
7.3 1.11E+20
7.1 5.56E+19
8.7 1.40E+22
7 3.94E+19
6.9 2.79E+19
7.5 2.21E+20
5.1 5.56E+16
9.2 7.85E+22
8.5 7.00E+21
6 1.24E+18
7.1 5.56E+19
7.1 5.56E+19
7 3.94E+19
4.2 2.48E+15
9.5 2.21E+23
7.9 8.81E+20
5.7 4.42E+17
7.5 2.21E+20
6.8 1.97E+19
6.5 7.00E+18
7.3 1.11E+20
5.6 3.13E+17
7.5 2.21E+20
8.3 3.51E+21
7.7 4.42E+20
7.3 1.11E+20
7.1 5.56E+19
8.1 1.76E+21
7.9 8.81E+20
7.1 5.56E+19
7.6 3.13E+20
7.1 5.56E+19
7.1 5.56E+19
5.3 1.11E+17
7 3.94E+19
7.1 5.56E+19
7 3.94E+19
7.1 5.56E+19
8.6 9.89E+21
5.4 1.57E+17
6.5 7.00E+18
6.8 1.97E+19
7.1 5.56E+19
6.8 1.97E+19
6.8 1.97E+19
6.6 9.89E+18
7.1 5.56E+19
7.9 8.81E+20
7.4 1.57E+20
7.1 5.56E+19
7.3 1.11E+20
6.5 7.00E+18
7.1 5.56E+19
9 3.94E+22
5.8 6.24E+17
7.3 1.11E+20
5.5 2.21E+17
6.9 2.79E+19
6.7 1.40E+19
5.8 6.24E+17
6.2 2.48E+18
8.6 9.89E+21
6 1.24E+18
8.1 1.76E+21
6.8 1.97E+19
6.8 1.97E+19
7.5 2.21E+20
7.1 5.56E+19
7.3 1.11E+20
7.3 1.11E+20
7.3 1.11E+20
7.4 1.57E+20
6.3 3.51E+18
7.3 1.11E+20
7.2 7.85E+19
4.6 9.89E+15
7.3 1.11E+20
8.1 1.76E+21
7.3 1.11E+20
7.6 3.13E+20
8 1.24E+21
7.3 1.11E+20
5.9 8.81E+17
8.1 1.76E+21
8 1.24E+21
7.1 5.56E+19
8.1 1.76E+21
5.8 6.24E+17
6.1 1.76E+18
7.4 1.57E+20
7.4 1.57E+20
7.6 3.13E+20
7.4 1.57E+20
7.4 1.57E+20
8.2 2.48E+21
7.3 1.11E+20
7.6 3.13E+20
8.2 2.48E+21
7.2 7.85E+19
5.5 2.21E+17
5.5 2.21E+17
7.3 1.11E+20
8.2 2.48E+21
7.1 5.56E+19
7.8 6.24E+20
7.8 6.24E+20
8.2 2.48E+21
8.5 7.00E+21
6.8 1.97E+19
7.3 1.11E+20
5.4 1.57E+17
6.2 2.48E+18
6 1.24E+18
6.3 3.51E+18
5.9 8.81E+17
6.5 7.00E+18
7.5 2.21E+20
7.1 5.56E+19
6.1 1.76E+18
7.1 5.56E+19
6.6 9.89E+18
6.5 7.00E+18
8.1 1.76E+21
7.4 1.57E+20
7.4 1.57E+20
6.4 4.95E+18
8.4 4.95E+21
7.6 3.13E+20
7.2 7.85E+19
7.8 6.24E+20
6.4 4.95E+18
8.1 1.76E+21
4.6 9.89E+15
5.8 6.24E+17
8 1.24E+21
5.7 4.42E+17
6 1.24E+18
7.9 8.81E+20
7.8 6.24E+20
4.2 2.48E+15
6.5 7.00E+18
7.2 7.85E+19
7.3 1.11E+20
6.5 7.00E+18
7 3.94E+19
7.4 1.57E+20
7.8 6.24E+20
7.6 3.13E+20
4.5 7.00E+15
7.1 5.56E+19
7.1 5.56E+19
7.9 8.81E+20
7.6 3.13E+20
6.1 1.76E+18
5.5 2.21E+17
6.8 1.97E+19
6.6 9.89E+18
7.1 5.56E+19
6.3 3.51E+18
7.9 8.81E+20
5.7 4.42E+17
7.3 1.11E+20
8.5 7.00E+21
7.2 7.85E+19
8.5 7.00E+21
6.1 1.76E+18
7.3 1.11E+20
7.8 6.24E+20
6.4 4.95E+18
8 1.24E+21
7 3.94E+19
7.5 2.21E+20
3.8 6.24E+14
7.3 1.11E+20
7.5 2.21E+20
5.1 5.56E+16
5.2 7.85E+16
7.1 5.56E+19
6.3 3.51E+18
7 3.94E+19
7 3.94E+19
4.5 7.00E+15
7.8 6.24E+20
7.2 7.85E+19
6.5 7.00E+18
7.7 4.42E+20
4.5 7.00E+15
7.4 1.57E+20
7.8 6.24E+20
7 3.94E+19
6.8 1.97E+19
6.4 4.95E+18
7.6 3.13E+20
5.1 5.56E+16
5.1 5.56E+16
5.5 2.21E+17
7.3 1.11E+20
7.2 7.85E+19
8.2 2.48E+21
7 3.94E+19
8 1.24E+21
7.7 4.42E+20
6.5 7.00E+18
8.2 2.48E+21
7.8 6.24E+20
6.8 1.97E+19
8.8 1.97E+22
7.9 8.81E+20
8.4 4.95E+21
7.5 2.21E+20
7.3 1.11E+20
6.2 2.48E+18
5.1 5.56E+16
8.3 3.51E+21
5.8 6.24E+17
7 3.94E+19
6.4 4.95E+18
7.5 2.21E+20
7.1 5.56E+19
5.9 8.81E+17
4.2 2.48E+15
6.4 4.95E+18
7.7 4.42E+20

total MO = 6.87 x 1023 Joules
total seconds in 107 years = 3.38 x 109 seconds
average power = 2.04 x 1014 Watts

kzb
2008-Feb-18, 06:29 PM
Warren Platts: Good grief that must be the longest message I've seen on here!

<<Thus, the Earth earthquake system is pretty much a perpetual motion machine.>>

AND

<<That is, the energy released by earthquakes gets recycled and becomes available to drive tectonics in the future.>>

I have severe doubts about this. Not that I don't believe most of the earthquake energy is converted back to heat and is retained by the planet, that is not the issue. I argued that myself above.

My doubt is based on thermodynamics. If you have heat being converted to other forms of energy and back again, that depends on a heat FLOW. Because earthquakes are a "heat engine", that heat flow will have to be larger than the earthquake power.

Heat flows from warm to cold, and on the way a bit of it is used to make earthquakes. The difficulty of this picture is of course the heat flow must be over 200TW, (or whatever our current best estimate of earthquake power is !).

Warren Platts
2008-Feb-18, 07:30 PM
Warren Platts: Good grief that must be the longest message I've seen on here!:lol:


<<Thus, the Earth earthquake system is pretty much a perpetual motion machine.>>

AND

<<That is, the energy released by earthquakes gets recycled and becomes available to drive tectonics in the future.>>

I have severe doubts about this. Not that I don't believe most of the earthquake energy is converted back to heat and is retained by the planet, that is not the issue. I argued that myself above.
Yes indeed--it's your idea and you get the credit for it!


My doubt is based on thermodynamics. If you have heat being converted to other forms of energy and back again, that depends on a heat FLOW. Because earthquakes are a "heat engine", that heat flow will have to be larger than the earthquake power.

Heat flows from warm to cold, and on the way a bit of it is used to make earthquakes. The difficulty of this picture is of course the heat flow must be over 200TW, (or whatever our current best estimate of earthquake power is !).You are correct, sir, that the heat flow must exceed 200 TW. But it does: there is the 20 to 60 TW coming from radioactive decay; and then there are the 200 TW of energy released by earthquakes! So I misspoke when I said the Earth was a perpetual motion machine; it's just a superefficient regular machine. If only our automobile engines were were 99.998% efficient! But I guess that's what a grand scale of economy will buy you.

Remember, not all of the energy of an earthquake gets recycled. The energy measured by ES still gets radiated to space eventually. Only MO - ES gets recycled--not the entire MO. The surprising, counterintuitive thing is just how small ES is compared to MO (in the case of the 2004 Indonesian earthquake, the ES was only 0.002% of the MO); but apparently it is a fact. . . .

Since MO - ES is not radiated into space, it has to be accounted for in the interior Earth's heat budget. And how else are we to account for it, except as a positive heat source? That heat would then becomes available to produce strain in the crust, would it not? So you do in fact have a ~200 TW heat source (helped out of course by the much smaller [~20TW] but still significant radioactive decay heat) to produce more earthquakes and drive plate tectonics.

kzb
2008-Feb-19, 12:48 PM
Hmmmm.....I'm still not sure. M(o) is a measure of WORK according to your definition above. In thermodynamics, the energy available to do external work is proportional to the temperature DIFFERENCE.

If E(s), a much smaller quantity than M(o), is actually the mechanical work, then I think we might be getting somewhere.

Warren Platts
2008-Feb-20, 10:18 AM
Hmmmm.....I'm still not sure. M(o) is a measure of WORK according to your definition above. In thermodynamics, the energy available to do external work is proportional to the temperature DIFFERENCE.

If E(s), a much smaller quantity than M(o), is actually the mechanical work, then I think we might be getting somewhere.
Think back to the sanding block analogy. It is easy to directly measure the amount of work done by using a spring scale. Yet exactly what does that work do? It produces heat through friction with the wood. There is no other work done: no gravitational potential energy built up, no chemical reactions driven uphill, no kinetic energy built up, no strain stored.

We measure the work done directly by a sanding block with the spring scale; but we could also do it indirectly if we know the area of the sanding block, the resistance to movement (the friction), and the distance moved. That's the theory behind MO. There's a rupture within a section of Earth with a definite area, it moves a definite distance, and there is a definite friction between the surfaces of the rupture.

So, ES is most definitely not the amount of work done--it's just the energy that's actually radiated out to space: hence the name "radiative energy". (Well, don't quote me on the naming part--that's just a guess on my part.)

Think about it this way, a sanding block could be mechanically driven by a steam engine. However, it just so happens that the sanding block is rubbing up against a heat exchanger connected to the boiler that drives the steam engine. If the whole system were 100% efficient, it would be a true perpetual motion machine. Since such a machine would not be 100% efficient, it would require supplemental heat inputs from an outside source to make up for the inefficiencies--say a nuclear pile. But still, the heat generated by the sanding block would help the boiler heat up and thus help drive the sanding block in the future. This hypothetical steam engine would be lucky to be 10% efficient, I would guess. However, the Earth is in principle the same sort of machine--the only difference is that the Earth is 99.998% efficient.

It's the economy of scale. :D

JonClarke
2008-Feb-21, 01:21 AM
In request to a PM:

The Earth's average heat flow is 3 X 10e-2 W/m2 (wikipedia)

The Earth has an area of 5.10 X10e14 m2

Thus the total heat production is 15.3 X 10e12 W

About half is from radioactive decay, the remainder is gravitational.

Hope this helps!

Jon

kzb
2008-Feb-21, 06:37 PM
Warren Platts I'm afraid I still have severe doubts. Just imagine if the Earth were suddenly plunged into an environment that was at the same temperature as the core.

Heat flow would stop. It would be just as hot, but no work could be done because the heat sink is at the same temperature as the heat source.

Also I really doubt that Earthquake production (mechanical work, potential energy storage) can be anything like 99.998% efficient in the thermodynamic sense.

Warren Platts
2008-Feb-27, 11:58 PM
In request to a PM:

The Earth's average heat flow is 3 X 10e-2 W/m2 (wikipedia)
Which article?



The Earth has an area of 5.10 X10e14 m2

Thus the total heat production is 15.3 X 10e12 W

About half is from radioactive decay, the remainder is gravitational.

Hope this helps!

Jon
15 terawatts is in the right ball park. That's what we've been saying all along. As for half of the heat being from residual gravitational collapse, that was debunked a hundred years ago, was it not? When Lord Kelvin said Darwin's theory of evolution just had to be false just because the Earth had cooled way too fast for all that evolution to have occurred?

The geoneutrino results anyway suggest that there is 15 to 60 terawatts of power produced from radioactive decay alone--more than enough to account for the 15.3 x 1012 Watts of total heat production that the wikipedia says is going on.

But Jon, we could really use your geological expertise and have you weigh in on the question of what powers plate tectonics, because that's what's so perplexing: no matter how you slice it, more energy is released in earthquakes per year on average than is apparently released to outer space. . . . How is that possible?

I did take a geophysics class in college a long time ago from Prof. Richter (not the real Richter), and I must say that this thread is giving me major deja vu. I believe the view I'm presenting here is the theory I was taught back in the 1980's.



Warren Platts I'm afraid I still have severe doubts. Just imagine if the Earth were suddenly plunged into an environment that was at the same temperature as the core.

Heat flow would stop. It would be just as hot, but no work could be done because the heat sink is at the same temperature as the heat source.
Of course--but there is a heat sink: it's called outer space.


I really doubt that Earthquake production (mechanical work, potential energy storage) can be anything like 99.998% efficient in the thermodynamic sense.
My 99.998% efficiency figure is based on the USGS data for the 2004 Indonesian earthquake where MO/ES = 50,000.

Thus 1 - (1/50,000) = 0.99998 = 99.998%

How else should we account for it???

P.S. Sorry I didn't get back sooner--I just got back from New York City. . . .
:D