The Dead Zone

Updated 13 Sep 2012, see end of article.

In logic, an assumption is a proposition that is taken for granted, as if it were true based upon presupposition without preponderance of the facts. (Wikipedia)

Back around May of this year, Carl asked me to do a series of simulations using KWare’s Heat3D, a program written by Ken Woheltz and the Reagents of the University of California under the sponsorship of the US Governement. It’s a cool little program that allows you to run heat simulations of magma intrusions into rock of varying characteristics. I had been prompted to write an article about one of the more perplexing areas in Iceland (well, to me it is). Not feeling that I was up to the task, I offered to do the supporting graphics if Carl could find someone to write the meat and potatoes of the article. I killed off a weekend working up the plots, but two of the catch points that we ran into were; “What temperature of the intruding magma should we use?” and “What exactly is the geothermal gradient of the region?”

With those two uncertainties, and the bedlam of real life, the post never made it to the forum. Things happen.

Before I go on, I must warn each and every reader here that I am not a seismologist, geologist, or bona-fide expert in the field. I read a lot, have been “studying” geology and physics in some shape form or fashion for about 37 years. I am just an amateur like many of you, so there is ample room for error.

With that out of the way… now we discuss

First, “The Dead Zone” is not an actual named place. It’s just a colloquialism specific to VolcanoCafe. It’s that region of Iceland between Katla/Torfajökull and Bárðarbunga/Grímsvötn. I refer to it as “The Dead Zone” due to the seeming low number of quakes. Historically, and pre-historically, the region is quite active with fissure eruptions. Irpsit and others can give you more definitive dates and names about the area, but I am limited to what I can cobble together from various sources. There are many other features here, but the main ones that I can find data on are Veidivötn, Vatnaoldur, Skaftar, Eldgja and Trollagigar. (spelling as listed in GVP and may be missing some of the diacritical marks) Veidivötn, Vatnaoldur, and Trollagigar are part of the Bárðarbunga system, Eldgja belongs to Katla, and Skaftar belongs to Grímsvötn. (As parts of the parent volcanoes fissure swarms). As you can see from the overview plot, there just are not very many quakes in this region. (Ignore the dot dashed blue line, that was part of the original plot set and is not used here)

Now, why is the Dead Zone dead? Because it is really… really hot. Much more than you would think. When an eruption is completed, magma sits and cools after the eruption is over with. This cooling rate depends on the thermal conductivity of the surrounding rock. For Basalt, the heat capacity is 840 J/kg K. (this is what I used in the simulations), Granite, for comparison is 790 J/kg K. This is in part due to its lower density. How it works… in order to raise the temperature of one kilogram of the material by one Kelvin (same as one degree C), you need 840 Joules of energy (for Basalt). Since we are talking about heat capacity, Water is 4185.5 J/kg K and Ice (at 0°C) is 2090 J/kg , so you can see how water or ice can drastically affect what is going on. This is one of those “gotchas” that can throw this whole scenario off. This area has a high water table and that can seriously affect how accurate the simulations are. Keep that in mind as I continue.

Anyway… when a dike intrudes into rock, whether it erupts or not, it starts loosing heat at a rate that can be calculated (provided you have the skill, or a program written by someone with the skill). Heat3D runs through the iterations of how heat migrates into the surrounding rock.
Here is how a single intrusion works out over a few years.

In my original set of graphics, I used a temperature of 1600°C magma due to the runniness of the flows and how far they traveled. My original guess was 1100°C based on a statement that I had seen in a paper, and much discussion occurred between Carl and myself about what would be the sane value to use.

“Time constraints on the origin of large volume basalts derived from O-isotope and trace element mineral zoning and U-series disequilibria in the Laki and Grímsvötn volcanic system” Binderman et al (2006) places the temp in the 1120–1140 °C range based on a “Mg in glass” geothermometer. (calculating diffusion and formation rates vs temp and pressure). Another reference (that I can’t locate at this moment) implies a temperature of 1200°C at 250MPa for one of the clast minerals. 250 MPa is in the 10 km depth range. Still uncertain of what temp to use, I went with the program default of 1250°C.

I used a 10 meter dike width based off of the average of three known dike sizes contained in “Geodetic GPS measurements in south Iceland: Strain accumulation and partitioning in a propagating ridge system” LaFemina et al (2005). This produces a really crappy 95% confidence range of 0.5 to 10.2 meters. (three samples is horrendous, but it’s all I had) Since the size of the plot grid has a direct play in how long the simulations take to run, I used 10 meters in order to get the simulations done in one evening.

Okay… now the actual run. As noted, this is not the original, and for brevity, I focused on only one system, Veidivötn. In case you didn’t know it, Veidivötn is probably the most lively fissure system in the region. It’s responsible for many of the Tungnaárhraun tephra layers. (THc. THd, THe…) GVP places an event there at the following dates: -6650, -4800, -4600, -4550, -4400, -4200, -1200, 150. For each eruption, I placed a 10 meter wide dike and ran the program out until the next intrusion date, which was then added and the process repeated. Another “gotcha” that you should be aware of, the eruptions did not necessarily occur in the same part of the fissure. This simulation assumes that they did. In effect, this skews the region towards being hotter than it might really be (and don’t forget the possible effect of the water that I mentioned previously)
So… here is the final product for what conditions may be like under the Veidivötn fissure. The temperature scale from the previous plot applies here.

Pretty gnarly eh? This is the crux of why I think that you won’t really see many small quakes in this region. Each one of those fissure lines has a heat structure similar to this. The crust is for the most part, plastic and yields to any stress that comes along… until it arrives too quickly for it to give. Then you have the larger quakes and potentially an opening of the fissure if the conditions are right… such as a nearby parent volcano being at or near erupting and having a ready supply of magma to flow down the rift and open it the rest of the way up. Structurally, there isn’t really much there to hold the two sides together. Plate shifts can do it (tectonic), or a parent volcano.

---

From “IAVCEI General Assembly 2008 Conference Field Excursions, Excursion 1: Historical Flood Lava Eruptions The 1783-84 Laki and 934-40 Eldgjá events” August 14-17 2008

“In 1783 the people of south Iceland had enjoyed a favourable spring and were looking forward to summer. However, their destiny was about to change. Weak earthquakes in the Skaftártunga district in mid-May were the first sign of what was to come. The intensity of these earthquakes increased steadily and on 1 June they were strong enough to be felt across the region from Mýrdalur and Öræfi. The earthquake activity escalated up until 8 June when a dark volcanic cloud spread over the district, blanketing the ground with ash (Figure 18a). The Great Laki eruption had begun.”

I’ve worked out the distances to Mýrdalur and Öræfi from the Laki site and applied an Mw to MMI estimate based on a few real world quakes from the USGS catalog in order to get a feel for how the power drops off over distance. Based on the MMI levels at which a quake becomes detectable by an unaided person, the quakes leading into the Laki event were in the Mag 4.5 to 5.0 range.

It’s a bit of a reach, but extending the formulas from “New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement” Wells and Coppersmith (1994) down to Mag 4.5, you get the following numbers.

Mag 4.5 – Surface rupture length 0.5 km, Subsurface rupture length – 1.3 km, Downdip rupture width – 1.7km.
Mag 5.0 – Surface rupture length 1.3 km, Subsurface rupture length – 2.7 km, Downdip rupture width – 2.9 km.

THESE ARE ESTIMATES

There is a bit of slop in the formulas, it is an attempt to get a working estimate of the physical manifestations that you would see from a quake. These particular formulas are only considered reliable for events down to Mag 5.2, but they do track well with no oddities in the curves. Below 5.2 the confidence in what the formula says drops off.

From that, it seems that the Mag 4.5 to 5.0 quakes are what is needed to open the system up. They have the right sort of features; the crust itself has likely healed very little from the previous events and should not take a lot of energy to re-open.

All this rumination and reading is one thing… but there is always something missing when you think and talk about these fissure eruptions. That’s the scale of the things. Since none of us were around, we just don’t know or have a frame of reference. All we have are eyewitness accounts. From some of those accounts, we know how long or how tall the fire curtain was, but that’s it. Just numbers in a book. Here, I have scaled an image of a generic fissure eruption and placed a few well known silhouettes in front of it so that you can see just how big these things are.

Enjoy.

GEOLURKING

GL Edit: The silhouetted buildings are;
Empire State Building – 443.2 m, Taipei 101 – 449.2 m, Burj Khalifa – 829.84 m, Sears Tower – 527 m, Petronas Towers – 451.9 m

“GVP” = Smithsonian Institution – Global Volcanism Program

UPDATE:

Irpsit says:
September 12, 2012 at 18:26

From what I know Laki eruption could be observed from almost anywhere in Iceland, in distance. The reports even speak that you could see the fountains from far away, but probably not everywhere in Iceland, as 1km high is not enough for that.

This put me on a search for two of the images that I made for the original article. I was able to pull them from Google archive of my mail.

They are not as stunning as the scaled image, but they are worth pondering. The ruddy maroon rectangle represents the Skaftar (Laki) fire curtain anchored to the surface, as seen from a couple of locations.