In a press release by Almannavarnir (Iceland Civil Protection) it is announced the lowering of the warning level around Eyjafjallajökull from danger area down to uncertainty level. There are also some travel restriction lifted that have been in place around Eyjafjallajökull volcano. The current warning level is the lowest warning level that Almannavarnir has.

The Press release by Almannavarnir in Icelandic. Use Google Translate at own risk.

Lækkun á almannavarnastigi frá neyðarstigi niður á óvissustig vegna eldgossins í Eyjafjallajökli (almannavarnir.is)

Icelandic News about this.

Almannavarnastig lækkað í óvissustig (mbl.is)

Almannavarnir lækka viðbúnaðarstig (Rúv.is)

Almannavarnastig vegna Eyjafjallajökuls lækkað (Vísir.is)

This is OT.

Referring back to the Krýsuvík swarm, I put together a rather weird plot of the quakes since 10/24/10 to present with the lat-lon vs date (z-axis).

Other than being handy in seeing how the stresses are moving around there, it’s mostly of entertainment value.

http://i56.tinypic.com/8zla4m.png

What if you kept the colour-coding for date, but used the z-axis for depth, a sort of four-dimmensional plot? Now that really would be interesting!

Well, I’m not going after a $1400 software package to do hobby plots.

But, if you can bear with the Excel date code format for the 4th D, here ya go.

http://i55.tinypic.com/2hxy80m.png

Thank you lurking, it’s exactly what I wanted! Albeit there is a concentration of quakes geographically, there is no temporal sharpening of the focus, i.e. the picture provided is not one of rising magma but could be one showing an inflating magma chamber or one where the pressure rises with time.

Ehh… simple enough to put the date into the same format as the GPS plots.

http://i51.tinypic.com/fmq74o.jpg

Really interesting! As time goes, the quakes seem to concentrate to a smaller volume, and simultaneously they are shallower. To me, this looks like a magma intrusion going on!

Not the easiest plot to pull off, but I’ve done it before. Sort of tied up with other things right now.

yes colour coding for and providing depth data time would be great.

http://www.sigmaplot.com/products/sigmaplot/graph.php

— the thumbnail alongside ‘function plotter’ shows the gray shadowing on the two walls as an aid to 3D visualisation.

There was yet another 4+ at Reykjanes Ridge.

Probably a complementary quake. It was 48 km away on the other side of the spreading center.

… seesaw… 🙂

Okay… web-spelunking.

Found a paper that discusses the formation of vertical or near vertical faults / cracks / surface expressions of extensional forces from sloping subsurface fault planes.

http://www3.hi.is/~oi/Pdf%20reprint%20library/Grant%20-%20Fault%20tectonics%20Reykjanes.pdf

It’s applicable to the Krýsuvík area as well as other “sprungar” areas.

Hey, that’s actually a pretty cool way of doing the 4D plot.

Again, the color is the date of the event, using the same format as the GPS plots. (fractional year)

Herðubreiðartögl, 2 perspective views June through December.

http://i52.tinypic.com/2gucozk.png

and

http://i51.tinypic.com/2bnzap.png

You can make out the sheet orientation of the quakes.

Thanks for all the cool plots, I am now in Nerdvana!

really loved when you put in the corner of Askja caldera as a red part of a circle in some earlier plots. Think you could do that more? It makes it so much easier to get a grasp of the coordinates for my old and confused head 🙂

It is indeed a very “cool way” of doing a plot and the results clearly show a change in location over time – although I’m not savvy enough to tell what that change really is due to… 🙂

Snicker….

Eyjafjallajökull – Katla – 17 April – December – 4D

http://i54.tinypic.com/33bmwl5.png

This is actually pretty informative! Apparently there has been no new intrusions of magma to Katla’s conduits/chamber, i.e. the next eruption could be at least a few months away…

Or years. Or decades. Or maybe even centuries. 😉

Katla is really quiet. But inflation wise that volcano is already at maximum I believe. But the most inflation took place in 1998 to 2003 I think.

Katla may be inflated, but IMHO it is not pressurized, as it is so quiet.

Lurking – wonderful plot, many thanks. I think its important. Heres why:

We should compare Lurking’s plot with the recent Nature paper, bits of which are on Erik K’s blog:

http://bigthink.com/ideas/25094

-look at the red patch in fig 3F

This is at longit. 19.4 to 19.5 – similat to Lurking’ plot, probably the same structure. But the Nature paper schematic has truncated the structure at 5km depth. Yet during the EQs in March – pre eruption – we saw EQS at depths down to 25-30km, very much as we see in Lurkings plot above. So I’m not happy with that Nature schematic. I suspect that red blob ( dyke) extend down to 30km depth and is reasonably the feeder conduit for magma, not the wispy wiggle depicted centrally under Eyjaf.

Lurkings plot ( april-dec ) shows clearly a cut off in EQs at 10km depth. The Nature paper focussed on horizontal sills that diverted rising magma laterally at around 4-6km depth. Lurking’s plot might be revealing another horizontal sill that extends out towards Katla (long 19.00). The focus of green spots are at correct longit to be under Katla (cant tell latit, from the plot.)

Could Lurking’s plot be revealing the long suspected Eyjaf-Katla link?

– a horizontal sill at 10km depth.??

The colour coding shows the time trend beautifully; up from 35 km depth, sideways at 10km, now halted at 10km under Katla……

They should re-jig and re-do their Monte Carlo reconstruction simulation to incorporate the locations of the seismic events.

Sheesh. I would think they have large seismic tremor and infrasonic sound data sets.

Well, since that one was well received, here is a set of my more traditional version of that same data. This should allow you to see past the ambiguity of the perspective plots.

Plan View (Lat-Lon-Time)

http://i53.tinypic.com/fd9iq1.png

View North (Lon-Depth-Time)

http://i51.tinypic.com/14m3onb.png

(Things are much clearer in that plot)

View East (Lat-Depth-Time)

http://i51.tinypic.com/106ltsl.png

There is something going on at the ≈12 – 8 km depth at a diagonal cant between the two, but I can’t say what it is. At the time those quakes happened I noted it but was told that it was too ephemeral to be much of an indicator.

It is clear, but it would just take removing very few quakes (perhaps only 5 – 10) for the pattern to disappear. I’m not saying that it is not the vertical extension of Eyjafjallajokull and Katlas tubinged magma reservoir meeting up. But the proof is a bit ephemeral as you said.

But save the data for all your worth. I think you will find it there on the day you can cross-reference that data with Katlas during a Katla eruption.

The data on all EQs are archived back to 1995. That would cover the epriod of inflation of Katla that Jon talked about. Would be neat to see EQs’ distribution whil kalta was inflating: when was that Jon?

So the 10km depth was illusionary. ‘Korf’ found a way of shadowing the loci on the walls of the cube, I’ll try to find the link.

What is the chances of Laki eruption or greater?

I have noticed that a lot of people are thinking about this all the time. And then we end up in discussions about this,. and people look at individual volcanos and see “cycles” and say things like “this and that volcano” will erupt with this frequency and then they look at the known ones with this propensity of large eruptions and do a summing/division average. And then we end up with the usual “not likely” during our life answer. But that answer is probably wrong due to 2 math stat phenomenons.

I will therefore start this my own mini thread in this thread to explain why it is wrong and do a little calculations out of this into the actual risk. This is just the first post out of perhaps many. So for those interested in theoretical speculation perhaps you should book-mark this for future reference.

First we start with the “Birthday problem”. Since we have at least 4 active volcanos (Katla, Bardarbunga, Grimsvötn, Theistareykjarbunga) that since the iceage have had large as Laki or larger eruptions and quite a few (at least 10) volcanos that can have a caldera forming event we must do a summing of statistical probabillities of a large-scale event happening. And here enters the Birthday problem.

http://en.wikipedia.org/wiki/Birthday_problem

Ie, the more “population” (volcanos) you have in the class-room (Iceland) the larger the likelihood of 2 of them having the birthday (eruption) at the same date. Of course I am not here talking about 2 of them having an eruption at the same time (even though it aplies to that too), instead I am talking about the effect on the summed risk of a large eruption happening over time.

If we say that we have 10 volcanos in our class that can have either a large scale fissure eruption or a caldera forming event we have fourteen instances in our class during a year (and the year here being the average of instances occuring). And then we clearly see that the likelyhood is larger than just a simple summing and division statistics here with a following increase in likelyhood.

In the next instalment I will go into gaming theory and the problem of winning lottery tickets being found more often in the last tickets sold, then among the first. Headache-warning, drink all-galactic gargleblasters…

Interesting..Just a thought though. The main difference between the “Birthday problem” as described above and these volcanoes is that the probability of two people having the same date of birth is more of a coincidence right? (Even though it can be mathematically calculated).

And when it comes to volcanoes there are so many more factors which needs to be included. And these factors are pure mechanics which can to some extent be measured with quite good certainty.

So in short my question would be: Is there a significant difference between the human brithday problem and the volcanic birthday problem? (Chance vs Fact)

Not sure if i am getting my point clear here but ill give it a shot..;)

Yes it is a difference, a huge difference. But only in the short run where we have those facts. We can with a bit of degree of certainty prognosticate an eruption being likely on facts for anything between 30 minutes (Hekla) to a year or two for Eyjafjallajökull.

But here I am totally into statistical math and probability prognostication and then we are working with unknowns (lottery tickets) and no facts known.

It is clear that Þeistareykjabunga is not doing anything. It is dormant and has not shown any signs of activity. So you can cross that volcano off your list.

No, why would I cross it of my list?

It is probably dormant as you say (even though it has had 2 quakes inside the caldera at mid depth the last month).

But it is after all known to be dormant for long periods, and it has had a huge eruption. The difference here is that it likes to erupt on average every 4000 years or so, as oposed to Bardarbunga and the rest that have a large amount of smaller eruptions inbetween the large one.

For the rest, Theistareykjarbunga has had two mid-sized eruptions and one huge in the last 12000 years.

So Jón, yes we can probably say that it wont be erupting soon, but it fits the bill to be in this theoretical statistical discussion.

After all, if it starts to show signs of leaving it’s dormancy it could erupt after 10 – 20 years and here we are talking about sums of statistics spanning thousands of years. And that is why it stays on the list.

Theistareykjabunga volcano has been quiet for almost 2700 years now and does not show any signs of changes it dormant stage.

If that where the case I would already have known about. As I do keep a good eye on the Icelandic volcanoes and what they are up to.

Earthquakes do happen in this area. But all of them so far are due to the tectonic processes in the area.

Sure. Theistareykjabunga might erupt tomorrow. But then again it might not erupt for the next 1000 years. But you can be sure that Theistareykjabunga is going to make a lot of earthquakes before it starts erupting again. So far it is all quiet and I don’t see any changes going on there. It also appears that Theistareykjabunga has on averge about 5900 years between volcano eruptions (last being 6800 BC and then 900 BC (+- 100 years). Given the data that I currently have.

All volcano eruptions from Theistareikjabunga are going to be Hawaiian in style.

http://www.volcano.si.edu/world/volcano.cfm?vnum=1703-09=

You are absolutely correct. But it fits the bill for this type of theoretical discussion.

I did not in any way say it would be erupting soon, or for that matter ever. I just think it deserves to be added since it can if it erupts produce a large hawaiian eruption.

And I also have a silly reason for liking Theistareykjarbunga… Imagine all the american newscasters trying to pronounce it? 🙂

If you want to a volcano to worry about. Add Esjufjöll to your list. There appears to be magma inflow into that volcano system. That magma inflow is at current rate really show. But that might change at any time without a warning.

But this is going to be followed by a lot of earthquakes.

Problem with Esjufjöll is that there is no known instance of a large eruption. So therefore I cannot use it in a statistic model directly. But it would be influencing the “unknown eruptive capabillity index” upwards a bit, but so does a lot of other volcanos.

I can either here do it in formulas proving my point, or I can do it “layman-way” without proof.

Years ago there was an electronic internet scratching lottery in sweden and norway where you could scratch a hundred tickets per day for free and win consumer goods. There was 1 million tickets and 1000 prices ranging from a sausage to a bike or something such. It was funded by selling ads. Since I pretty much never gamble out of being to good at math I had up untill then never really noticed the more quarky effects of gaming theory on lotteries where the tickets are sold with the price already pre-decided in them. (Here think volcanic eruptions)

My then girlfriend got hooked on this scratching lottery and I did not since I thought the chance was 1 in 10 to win a sausage after spending 30 minutes scratching the daily aloted 100 “tickets”. Not worth it really even if it is free.

What was different here was that they had a counter showing the statistical chance of winning in a percentage on an average ticket, and that is something that is normally keapt really secret and is only possible to show in an electronic game where the counter is affected by every scratched ticket. But the result in the end is the same in a “real” scratching lottery.

So I said to her, “why the hell are you scratching like mad when there is just a 0,1 percent chance of you winning on each ticket? We are talking about bloody sausages after all?”

And she answered… “What are you talking about, I have just won 14 sausages, 3 skin-creams and a bike! And the chance of winning is 37 percent, not 0,1 percent!”

I was by now certain of her either being crazy, lying to me, or the mathematical world as known to man being wrong… I looked at the counter (it showed 37 percent), I looked at her winners-list (yepp she had won), so I retracted into the kitchen to mix an all-galactic gargleblaster against my mathematical headache.

What had happened?

Well, after a while I started to remember some of the more obscure statistical things happening in large closed statistical systems and I calmed down.

What happens when you scratch that first ticket? Simply put you scratch a ticket with a 1 in 1000 chance of winning. Ie, 999 duds. So in the beginning you will scratch away more duds statistically then winning tickets and that slowly slowly alters the odds. So after you have scratched away your first dud the chance of winning is… 0,100001 percent of winning. And a strange phenomenon starts happening here in statistics given that on average you will normally find the first win among the latter tickets in a bunch of say a thousand, if at all… Remember that the chance in the beginning was 1 in 1000, then it is 1 in 999,999 and so forth…

And this is why Lotteries keap how many tickets they have left at a given time a secret. If they didn’t people would wait and buy when there are relatively few left since it is so much larger chance of winning then…

So what on earth does this have to do with volcanic large-scale eruptions in Iceland?

Well… Every year it does not happen it is like a scratching ticket coming up with a dud. Let us say that the average of a large eruption on a Laki or larger scale happening is 1 in 500.

First year 1 in 500 =0,2%

Second year 1 in 499 = 0,2004008%

Third year 1 in 488 = 0,2008032%

…

Twohundredtwentyseventh year 1 in 227 = 0,3663003%

Okay, there is a problem in here somewhere you are now saying. And yes there is. A big one. Volcanos are not a fixed number of lottery tickets type of lottery. Let’s say that on average a single volcano erupts on average in a large way every 2000 years. Problem here is that we do not know the amount of years (tickets) untill the next eruption so we do not know the amount of years (tickets) remaining well enough to calculate the percentage. So the numbers we crunch on the average is getting larger and larger uncertainty numbers. But this is just one volcano… The more volcanos and types of instances we add the closer we get to a closed number lottery with a smaller and smaller number of the uncertainty values as a result.

Now we can do numbers.

All-galactic Gargleblaster substitution recipé. Mixed at least 4 different sorts of vile tasting spirits of at least 40% in equal parts, ad one part 95% ethanol. Stir the result with a chilifruit. Drop down a sliver of lime. Drink. Call the emergency room. Pass out.

@Carl: “The more volcanos and types of instances we add the closer we get to a closed number lottery with a smaller and smaller number of the uncertainty values as a result.”

Well, not necessarily. The lottery organizer always knows the number of left-overs at each time the game is organized. And it is typically organized during a limited time (calendar, or as-long-as-coupons-last). And, different cases are not dependent on each other. Hence, the cases are always closed with previously known limits, both in time and numbers.

For volcanoes it is far more complex. We have only long-term average propabilities, which may change over time, e.g. due to continental, magma or hot spot movement. Various volcanic systems may have connected volcanoes, other don’t. The limits (start-up & shutdown, active periods vs. dormancy periods, etc.) vary, hence the cases are really never closed.

You cannot make a open system closed by adding more neighbours to it.

You are correct, but you can make it narrower by adding instances. Ie, diminish the uncertainty values into managable figures.

If volcanoes are considered to erupt in a quasi-periodic (episodic) manner, the probability of eruption increases as an eruption becomes ‘due’ and then ‘overdue’ … and tails away as no eruption suggests extinction.

The scratch and win distribution seems appropriate.

Carl, a more elegant/accurate way – yes I did statistical calculations as part of my job as an Army officer for some 15 years – is to do the calculation based on the chance of a non-eruption:

Chance of an eruption 1/500, i.e. the chance of no eruption is 499/500

The chance of two years in a row producing no eruption => 499/500 x 499/500 = 0.996004 or the chance of an eruption in any of those two years = 0.003006

The chance of the next 100 years producing no eruption => 499/500 ^100 = 0.818566804688 or the chance of an erution in the next 100 years is 0.181433195312.

The chance of the next 250 years producing no eruption => 499/500^250 = 0.606227065 or the chance of an erution in the next 250 years is 0.393772935.

Now, you’d think that if an eruption occurs on average once every 500 years, there’s a 50-50 chance it might go off after 250, but as can be seen the actual chance is less. Thus the likelihood increases towards the end, just as you say.

Now, with four volcanoes likely to go off after long intervals, the statistical probability that one of them will go off increases as the probabilities of an eruption add up.

Now, it should not come as a surprise that in first grade myself and my two best friends had birthdays on the 6th, 8th and 10th of Februari and that later in life, in a different context, it turned out the birthdays were 7th, 8th and 9th of february.

Infinitessimal chances do have a nasty habit of occuring far more frequently than a cursory glance might suggest…

Actually, for two first years it would be 499/500*498/500 and so on…

True, provided you were positive about the probability refering to “once every 500 years” and not “1/500 every given year”. If so, it’s a countdown rather than a calculation of probabilities. 😉

Right! A nice correction, thank you!

Nice version!

This is why many minds are good!

What you are saying in the end I have changed into this phrase many years ago… (Religious people stop reading)

Carls Law of Miracles:

(In Swedish first)

Osannolikt många osannolikheter kommer att drabba dig osannolikt ofta.

Improbabel amounts of improbabilities will happen to you improbably often.

Ie, there are more odd occurancies than normal in a large system. Let’s say you are waiting for the hangman, given a large enough amount of hangings things will happen. Sooner or later the hangman will fall off the podium and break his neck. There might also be a piano appearing at 20 metres hight before falling and crushing the audience, or pretty much any weird thing.

Problem is that “miracles” happen all the time, I see them every day, but people are too occupied with praying for them to notice them. Just remember that the miracle might happen to somebody in you vicinity… and that there are as many bad as good miracles out there.

Now I will run off to do some real work.

A quick note, I know about the uncertainties problems in this line of statistical mathematics being a large problem here. And my point was to problematize the simple sum/divide average people are doing with large volcanic instances.

To do it correctly I would choose to do a path-integral solution (heavy computations) and do a sum over history. But my point is that the chance over time increases instead of staying the same, by doing a summary of 2 of the problems with simple sum/divide in statistics.

Checking back tonight.

Intuitively speaking, it is self-evident for me (a former scientist in physics) that the probability increases over time. But I doubt that you can actually calculate the %-chance for an eruption at Iceland, e.g. during next year. I bet statistics will give you a better value!

And the difference being what exactly between statistics and probability?

Confused now.

Sorry… With statistics I meant data collected of past eruptions.

Ah, the statistical foundation onto you apply statistical mathematical models to get probabilistic answers 🙂

I have now calculated all the eruptions that meets the following criteria.

1. Lava and tephra at 10 cubic kilometres or larger.

2. VEI-7 (none!?!).

3. Caldera forming eruptions.

4. And 1 – 3 not happening to a dead volcano, ie. that had an eruption during the last 2000 years and if more than 1500 years old has a history of long intermissions.

So there is 51 known eruptions fitting these 4 criteria during the last 11500 years. That gives a raw number of 1 eruption per 225,5 years.

I noticed that there are more eruptions during the last 2000 years so I then decided that the phenomenon is caused by quite a few of hidden eruptions have not been found, and/or are covered by glaciers. Actually the occurancies are twice as common the last 2000 years. So I added 12 instances to the list to cover this and the possibility of a new large volcano suddenly forming was also added with a singular instance (this is after all Iceland). This number is really low. If I instead had added the full missing amount the number of instances would have been increased with 37.

Then I got the new number that covers missed eruptions at 179,7 years between eruptions.

And since the last eruption that fits the bill is not the infamous Laki eruption, but instead the Askja eruption and subsequent collaps of the Viti-caldera in 1875 we now have a point to start our statistical counter with.

Uncorrected value: 90,5 years.

Corrected value: 44,7 years.

As you notice I have not done any fancy mathematics yet. This is just simple sum/divide statistics. And as we have noticed these are not the best modell to use.

Next time I will do it with all the blows and stops.

Ie, one version that is Birthdayicized + statvariance-corrected and one that is a path-integer summing over multivalue history. (And Dicky Feynman would cry if he ever knew about it…)

@ Carl: I think you need to consider volcanic systems complex and add a little Chaos Theory to your maths.

Well, yes. But gaming theory is actually a mathematical modell to find instances of order out of chaotic systems. But we could probably instead do an “emergant order” analysis before going into the gaming theory.

But hell if my head can solve the “emergant problems” that would need to be solved first.

Or Bayesian propability theory, as there are so many unknowns.

Would not be out of my range, but I am just hunting the 2 most obvious fallacies that I have noticed people doing when trying to crunch the “average numbers” out of most people only knowing how to sum things and then divide with instances to get a number. And that here gets them wrong.

Here is another big eruptinon in historical times, Hallmundarhraun from Langjökull, close to the recent earthquake swarm:

http://www.vulcanospeleology.org/sym06/ISV6x19.pdf

In Vestmannaeyjar, Helgafell did erupt 5000 years before the eruption 1973 and most people did think the volcano extinct.

Thanks for that link 😉

i was in the Surtshellir & Stephanshellir Lavacaves this summer 🙂 its really impressive to walk trough this massive lava tunnel, only with a small light and your camera on the back. and there is allways this feeling of beeing trapped, what if there commes suddenly a new lavaflowt towards you. even if you know that its absolutely impossible. for those that were there to, have you met the cave-book? its like the book that you sometimes find on top of a mountain, where you write the date, time and your name in. so when you get back there some times later, you can look for your name in the book and how many people where there in the time between. 🙂

And this sets it’s finger on another problem.

What exactly is a large event?

Your lavarun was at 3 cubic kilometres, but with a really coolish feature.

My original idea was to use these numbers.

1. Total ejective volume (lava + tephra) > 10km^3

2. VEI-7 or larger

3. Caldera forming event producing more then 5km of tephra. Reason for this being the cataclysmicity of such an event on a large area.

But feel ultimately free to convince me to use other numbers. What is a large event? Hm…

Miffed, I have to do an inventory for tomorrow, (piecemeal, just a pain in the arse) but the stats and prob discussion is riveting. Please continue.