Lost Weekend…

Photograph from Wikipemedia Commons. Menengai Caldera in Kenya, one of the largest calderas on the planet.

How to kill a weekend.

As some of you have observed, last week I asked for anyone running across a caldera size and eruption volume to give me a quick shout here on the forums. Ostensibly, I was going to compile a spreadsheet in order to look at Hagstrum’s hotspot list compared to large caldera locations. Despite Carl’s disdain for the Antipode Impact idea, I think Hagstrum’s hotspot list is still pretty good, and it collates several other lists and weeds out some of the less than accepted ones.

While trudging through the calderas that were readily supplied, grabbing what info I could and trying to stay focused on DRE, the question of DRE again came up again in discussions. It wasn’t an actual argument or disagreement, but it did give me enough doubt in my data to seek other sources. Along the way, I found “Sulfur dioxide initiates global climate change in four ways” by Peter L. Ward. Well, to be truthful, I didn’t find that first, I found his table that supports his paper. I had to dig around to find the paper. I HIGHLY recommend the table. It is awesome. While the focus is on SO2 and climate change, they include the names of the tephra deposits that go with specific eruptions. Not all, but quite a few.

From his table, and with the re-worked VolcanoCafe user provided data, I came up with this (distraction#1) :

The first thing I would like to point out, is that it’s a log-log plot. The formula is a bit cantankerous to work with in Excel or on a calculator. (uses 10 raised to a power from a function that then has a logarithm in it.) The log-log plot was the only way to make it come out halfway usable. This formula was derived with DPlot, and in order to minimize the sigma fight (which I lost, quite readily) I left the individual points in place so that you can see just how far the estimate can be off. In one incarnation, I came up with the estimated value being within 0.77 of the actual value, 75% of the time. At this point I needed a beer and would continue later.

Moving back to the plot, and poking around in the text of the paper, I found that Professor Yukio Hayakawa of Gunma University (Japan) had compiled a list of large eruptions covering the last 2000 years. I had to go find that. Unfortunately, the list cuts off at 1999 with the eruption of Hudson in Chile. Distraction #2 involved updating the list with everything that happened since. While using his calculation of eruption magnitude, I decided to look back at how some of the calculations compared to fresher data from GVP. The paper uses M=log(m) -7, where m is the erupted mass in kg.

That’s actually a pretty handy formula. It sort of tracks with the VEI range, (but it’s not VEI, that’s different) Eyjafjallajökull comes in at 4.62, Merapi at 4.55, and Sarychev Peak at 5.04 when using GVP combined lava and tephra (DRE) volumes.

Photograph from Wikimedia Commons. The Somma caldera of Mt Aso in Japan.

I did find a problem with the data though… it wasn’t lining up with GVP info very well. In general, it was running 1.13 times the Hayakawa data when redone with GVP info. Then I ran into the problem of GVP not having anything more than a guesstimate for the VEI of some of the volcanoes with no tephra or magma volumes listed. (and these were pretty recent eruptions) Since Hayakawa used a lower cutoff of M=3.8, anything less than a VEI-4 would not get that high. (VEI=3 yeilds an M of 3.43). Ehh… give up and go find something to gnaw on. I did find out that my stepson had retribution against the Pelicans. I had skipped the King Mackerel fishing since I was “in the groove” with the data. The bait fish they were using had a tendency to attract the Pelicans attention but was so swift that it would be gone by the time the bird got to it.

Referring to Carl’s “Did you notice the erupting Supervolcano?” post, you will note that in the reference, it doesn’t state what the size of the Tondano Caldera eruption was. Being focused primarily on the geothermal energy capability of the system, that is understandable. Using the outline from Figure 5 of the paper, and applying our handy formula, we can get a ballpark estimate of how much “stuff” was involved. At roughly 30km by 9km, it comes in at 197km³… give or take. Solid VEI-7, but the calculation has a sigma of 351km³ so it could quite easily have been large enough to be withing spitting distance of VEI-8. (900km³ is within 2 sigma, and VEI-8 is 1000km³) 

[Editors remark (Carl): I actually was a bit more devious than that. For this caldera I have a bit more data. Through drill core samples I know how much of the caldera is infilled with original ash and later ash. That gave me the actual depth of the original caldera bottom. One should recognize the difference between a subsided caldera and a blow out large caldera event. The first one gently drops with lost material, the other ejects more material due to explosion, in this case when the ocean hit the magma inside the magma chamber. I then calculated the amount of DRE by size. To get a low enough number I did not assume that there was anything ontop, ie. that the volcano was flat with the surrounding landscape. I then got a 918 km^3 of ejected DRE. Size is not everything as I discovered, depth is equally important. Add a couple of the known active volcanoes before the large caldera event and you are comfortably at the 1000 cubic range for a comparatively small caldera. I then did a sanity check against known ash depths for the layer across distance, and fount it to be within the ballpark.]

Okay, back to the data. In 2009, Deligne, Coles, and Sparks put out a paper entitled “Recurrence rates of large explosive volcanic eruptions”. Yet another kick arse piece of work. In it, they use Extreme Value Theory to attack the problem of recurrence rates of large eruptions. Now that is something that I can appreciate. Extreme Value Theory deals with the failings of the Gaussian curve… out there in the tail, the realm of the infamous Black Swan that I am always yammering about exists. I have to go back and read that paper. Anyway, they mentioned Hayakawa’s list, and then using those methods, took the list back to the last 10000 years. Hmm… what can we do with that? I have the Greenland Temperature from the ice core data available, so I plotted it. It didn’t look that interesting until I ran an integral of the M value, then detrended it. That brings out the relative change in the sum that is going on without the actual data trend obscuring it. Plotted against the temperature, it look… “interesting”

There are a couple of peaks that seem coincidental, but for the most part, not a flipping thing there. I found it interesting that there was a peak in activity about 3527 BC and over all, volcanic activity has been declining ever since. I don’t know why that is. That’s just what it looks like. Being a glutton for punishment, and since it was “just sitting there,” I ran a couple of correlation routines on it to see if anything was present, but not obvious. Pearon’s correlation coefficient of 0.0111. Okay, I didn’t really expect a linear correlation. Spearman’s rho is supposed to be able to detect non-linear relationships, and I expected a higher score. I got 0.0017. What? It’s worse? “Wow.”

I have, on this computer, a program called “Formulize” by Eureqa. It’s free, unless you want to use a server farm. You can set it up and run it on your on PC and it will churn through whatever data you feed it and try to find a formula that relates the data sets. It’s the ultimate “beat the data with a stick” program. It can yield garbage… (generally if you feed it garbage) but it’s pretty good at coming up with something. So, I turned it loose. It turns out, that if you have a delay of 1405 days, it can roughly predict the temperature in Greenland from the running detrended integral of the Volcanic activity with a correlation coefficient of 0.7177. (Actually pretty good considering where we started out from) I calculated a sigma for the function based on what the formula predicted and what the actual data was.

That… was distraction 3.

What’s it all mean? Beats me. Greenland is just one point on the globe. There seems to be a 1405 and 1422 day delay relationship in the data, or about 3.8 years. Formulize also ground on a 4.13 and 4.44 year offset for a while. It was quite fun watching it dance back and forth with the delay. Make of it what you will.

And now the all important caveat: I am not a Geologist or trained in any of the fields that have been touched on in this post. My specialty is electronics and cross correlating threats… if you must know. (such as the 230 knot Shvall torpedo tested by Iran having been designed for 533mm torpedo tubes postulated as a design criteria… and the the Kilo class sub launched from Bandar Abass last week or so, having six 533 mm tubes. And that’s all from published data in various sources on the web.) But.. I don’t do that anymore. Volcanoes will have to do.

What to take away from this post, something that can be used by my fellow volcanophiles, is the first plot. You can find a hole in the ground in Google Earth and do a ballpark estimate of how much material may have come out of it when it initially formed. Remember that it may not have all happened at once.

Several thousand years of activity can produce the same effect.

Enjoy!

GEOLURKING

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Sulfur dioxide initiates global climate change in four ways – Ward (2009)
http://tetontectonics.org/Climate/SO2InitiatesClimateChange.pdf
And the table:
http://www.tetontectonics.org/Climate/Ward2009TableS1.pdf

Hayakawa Paleovolcanology Laboratory
http://www.edu.gunma-u.ac.jp/~hayakawa/English.html

Recurrence rates of large explosive volcanic eruptions – Deligne, Coles, and Sparks (2010)
http://www.globalvolcanomodel.org/documents/Deligne%20et%20al%20(2010).pdf
Data Set
ftp://ftp.agu.org/apend/jb/2009jb006554/2009jb006554-ds01.pdf

El Hierro and the Physics of magma chambers

Image from Nature GeoScience. From Phillip A. Allens article Geodynamics: Surface impact of mantle processes.

Part 1

Not many people think about what is great with physics. People are normally more occupied with buying Prada hand-bags to carry their rat-sized yapp-dogs than physics. The great thing with physics is that the laws of nature are universal. And with that I mean that they can be transferred easily from the school books into real life, and from one part of science into another.

I am as most of you know not a volcanologist or a geologist, but I am a physicist. So every time I try to understand a volcano I do it from how it is behaving from the point of perspective of the laws of nature.

This time I would like to write about a few things regarding how magma chambers must be formed according to physics. I will mainly not talk about magma chambers because they are fairly hard to visualize since nobody has seen one in real life as it is forming. But most of us have for instance blown up a balloon.

In this case we will be talking about magma chambers that come from hotspot volcanism; the process will be slightly different in a subduction volcano. But first we need some background, this post will be about precisely that background.

Hotspots, weightlessness and Blobs

Let us start with what is required for a magma chamber to even start forming. And as a physicist I am always talking about basic forces. And there is only one basic force, and that is energy. There are of course many types of energy, and in this case we are talking about energy as mechanical pressure and heat.

Thankfully for the poor fledgling magma chamber there is one thing that causes both pressure and heat, and that is your basic magma. So, let us drop up a ball of nice hot juicy magma from the hotspot under El Hierro.

It is not entirely clear how magma travels upwards via a hotspot, but we know there are two types of hotspots. First we have the deep Icelandic type that brings up material from the depth, this magma is hot and arrives at high (relatively) speed and with great force. It brings with it an assortment of rare and heavy metals from deep down at the boundary between the core and the mantle. The other type is a colder and less deep hotspot. The magma here is either brought up from within the mantle, or created as the hotspot heats up material close to the MOHO boundary either through heat or pressure, perhaps even a mixture between them. This type creates magma that is low in precious metals, and gives a low Uranium-Thorium (UrTh) count which in turn is a dead giveaway that it comes from a shallow source. The Canarian hotspot seems to end up somewhere in the middle of these two types, it is definitely not melting crust as a part of the magma creation, the almost pure basic basalt tells us that, on the other hand it is not from the core/mantle boundary since the UrTh count is wrong for that option. Let it suffice to say that the Canarian hotspot is a bastard mongrel of a hotspot.

So, where does now the pressure to drive any hotspot come from? Well, once again the answer is not simple. We have at least two sources. The first is heat; the Earth is producing loads of juicy heat due to at least 3 different processes. The first one is UrTh and other atomic nuclear processes. Yepp, we live on an atomic reactor. The second one a form of pressure called overburden pressure. That is the combined weight of the planet pushing downwards, this creates compression heat. The third is through the dear old gravity slowly massaging the planet, this is by far the smallest of powers creating the heat. Here I have simplified a bit, there are more forces at play than this.

Image of nested magma.

So, how come then that magma travels upwards? The answer might surprise you a lot. If you are getting a headache from this it is normal. Let us imagine that you where hanging at the exact mid-spot of the planet. The pressure would be phenomenal from the overburden pressure; still you would notice something odd. For the first time in your life you would be completely weightless. This would be due to the entire planets gravitational pull would be affecting your entire body in every direction at the same time, effectively cancelling out any gravitational effect.

What does this now have to do with magma? Well, you have magma under tremendous pressure that does not weigh a lot. A cubic decimeter of magma at the mantle/core boundary is considerably more lightweight than the same volume of water. And at the same time it is squeezed by tremendous pressure.  Here we enter a nice little simple physics, when you squeeze a fluid it will try to run away, in this case it can’t go down, it is fairly buoyant and will try to float. Now we just need one small thing, a conduit. Enter the heat.

Energy will always go from a high state to a lower state; this is the nutty little physics law that also gives that order will always go towards disorder, in other words, entropy and enthalpy. So, the core will try to lose heat, and the heat will always be able to escape, and once a convective current of heat has started to run upwards it will jolly well keep on going. When magma finds a stream of heat going upwards it will follow that stream because the fluid will follow the point of least resistance. And that is why a mantle plume and a hotspot is the same thing (simple physics). The mantle plume cannot exist without a hotspot, and the hotspot will sooner or later create the mantle plume.

Now our blob of magma is finally moving upwards towards El Hierro, the trip started a long time ago, it takes a while to go through all that semi-permeable heated pipe that runs up through the mantle. One day, let us say on the 24^th of June 2012 our blob of magma arrives at the bottom of the crust under El Hierro.

The speed with which it arrives is very slow even compared to a human walking, but the weight is enormous, the same goes for the amount of heat energy and the buoyancy pressure. Let us just say that it is like a comet sized blow-torch hitting the almost melted MOHO boundary. It will cut through the first layers in a rather short time. As it goes on up through the bottom of the crust it decelerates fairly quickly, and that is the point where all the fun starts, the formation of the magma chamber.

Until the next time!

CARL

Urban volcanism!

The ironically named Mount Eden, near downtown Auckland.

Most people in the world agree on one thing: it is safer to live far from a volcano then it is living right on top of it. Living next too, or on top of a volcano is like sleeping in a cave with a friendly bear. Sure, it has it’s advantages, you stay nice and warm, you don’t have to worry about other predators, a good part of the year it is nice and quiet, but still….. you know that some day he will grab you and eat you. The inhabitants (some more permanent than others) of Herculanum, Pompeï, Heimaey and the Hawaiian Royal Gardens have found out the hard way.

New Zealand is, apart from being stunningly beautiful, one of the least populated countries in the World. When Western settlers arrived they could have chosen any location to go and build large cities. For some reason however, the inhabitants found it neccesary to build their largest city directly on top of a volcanic field with about 50 scoria cones, maars and tuff rings dotting the landscape. I suppose the knowledge of volcanism was not as developed back then as it is today, but nevertheless it is quite unfortunate.

Photograph by Mollivan Jon. Mount Taranaki.

New Zealand is dominated by subduction volcanism, with famous Mount Taranaki (or Egmont) as one of the most visually stunning stratovolcanoes in the world from both the ground and above, and with the infamous Taupo Volcanic Zone, best known for being one of the worlds “super” volcanoes. At 250 km from Auckland this is already quite a hazard on itself.

The Auckland Volcanic Field is a monogenetic volcanic field, meaning that an eruptive episode only happens once through a vent. Each eruptive episode generates a new vent somewhere within the volcanic field as opposed to “normal” volcanism where a volcanic vent has succesive eruptive episodes causing a volcano to build up and blow up occasionaly. The Auckland Volcanic Field produces basaltic scoria cones, maars and tuff rings (with the exception of the island of Rangitoto which erupted several times). All three are caused by the same type of magma, basaltic magma in this case, but the location the surface penetration, the eruptive flowrate and the total volume of the basalt determine the type of surface expression. The volcanic field has been active for about 150.000 (0.15M) years now. Older volcanic fields are found towards the south; South Auckland (1.5-0.5M), Ngatutura (1.8-1.5M) and Okete (1.8-2.7M).

The source of the basalt is not quite clear however. Basalt is normally not associated with subduction volcanism. Petrology and earthquake data have practically ruled out the possibility of the lava having an origin in melt generated by the subducting Pacific Plate. The Auckland volcanic field also sits some 200 km behind the active volcanic front of the Taupo Volcanic Zone. Furthermore, there is no evidence that the subducted Pacific plate reaches all the way to the Auckland volcanic Field.

Basalt is usually associated with mid-oceanic ridges/spreading centers or hotspot volcanism. Again, petrology has not been able to find much evidence for hotspot volcanism either. Additionaly, the propagation of the volcanic fields is directy opposite to the relative motion of the plate; the oldest volcanic field should have been in the north and the youngest in the south if a hotspot or mantle plume was involved. It is possible that the complex geology with major plates subducting, twisting and turning in the area is causing localised decompressional melting , leading to magma migration upwards right below the city of Auckland. There is some extention ongoing in the area, so this seems like a plausible explanation.

The Pacific plate and the Australian plate in a complicated geological setup

This image shows the subdution margin, the strike-slip faults to the southwest and extention(volcanic back-arc) to the northwest of the subduction margin.

Monogenetic volcanic fields are very interesting and highly unpredictable. The eruptions are not very large or extremely violent, but they can occur pretty much anywhere within the field at any time. With a large city with hundreds of thousands of inhabitants spanning the field, this is exactly what you don’t want. Paricutin in Mexico is the most famous example of this type of volcanism. One day you are happily working your crops, the next day you have to flee from your land because a volcano decided to take over your land. Bad luck, deal with it. Any new eruption within the Auckland Volcanic field will have as much compassion with buildings, streets, highways, parks and emergency shelters as Paricutin had with the crops that were growing there. This is what makes Auckland a relatively dangerous place to live in because it is not clear how much warning time there will be and how accurately the location of an eruption can be predicted with modern equipment.

The reason why new volcanoes pop up at random has to do with the generation of the magma. It is important that the generation occurs very slow. Slow enough to be unable to build a plumbing system that would efficiently conduct the magma to surface. Every new, hot, fresh slug of magma finds it’s own path to the surface, erupts and that’s it. The conduit cools and is no longer usable for the next slug of magma that arrives several decades or hundreds of years later below a slightly different part of the volcanic field. There is not enough magma flowing into one area to create a magma chamber in which the magma can evolve and produce more silicic types of magma.

Ridiculous in Los Angeles, not so ridiculous in Auckland. Bring out Tommy Lee Jones!

We have all seen the Hollywood movie “Volcano” and no doubt that many Los Angeles citizens have had a very good laugh at it (the La Brea tar pits are the surface expression of a leaking oilfield through a fault, it has nothing to do with volcanism whatsoever), but for the citizens of Auckland, those images are not even very far from the truth. The past gives an excellent example of what can happen. The next eruption in the field will most likely follow this scenario:

1 – Magma is forced upward through weak points in the crust.

2 – Either the magma contacts ground-water, or reduced pressure near the surface causes gases to bubble out of solution. The result is a phraetic or steam-blast eruption. The heaviest material is thrown out horizontally to form a tuff ring. Lighter material is blasted vertically to form an eruptive column. After a few days, weeks or months, the volcano falls quiet. Several of Auckland’s volcanos became extinct at this point.

3 – Additional magma may rise in the conduit. If enough magma is supplied, fire fountaining starts through one or more vents. Small lava flows may be produced, which do not escape the tuff ring. Sometimes the eruptions build scoria cones.

4- If fire fountaining continues beyond this point, the scoria cones can coalesce to rise and bury the tuff ring. Lava flows can also fill the surrounding valleys.

5 – Sometimes the outflow of lava is so great that it undermines the cone, which collapses into the flow and is carried away, leaving a horseshoe-shaped breached crater. If lava flows for long enough, nearby valleys are totally filled in and the lava floods the entire area with a large sheet.

Isn’t that just wonderful right in your own neighbourhood?

Map showing the city of Auckland and the eruptive centers.Pick your favourite spot to build your house.

The big question that remains is then: When is the next eruption going to be? Well, you will have to chop off one of the arms of a geologist to get a clear answer on that, but there are usually several hundred to several thousand years between eruptions in this field. The last one was about 600 years ago, so it might be a while before it is “overdue”, but it might be soon as well.

El Nathan