Ruminarian IX? Musings on Hekla.

The upturned boat hull shape of Hekla. Image from Wikimedia Commons.

The upturned boat hull shape of Hekla. Image from Wikimedia Commons.

I grew up hating math. Detesting it’s very existence with an unbridled passion that knew no bounds. I was like this all through school… until Junior and Senior years. Those years, our new Principal, Mr Pendergast, put together a couple of courses to prepare us for what we may run into if any of us ever got up the gumption to try college.   In retrospect, I think what he was doing was a last ditch effort to help some of the more idiot minded, such as myself, get up to a point to where at least our eyes didn’t glaze over when we ran into it. What Mr. Pendergast taught us was “Analytic Geometry.” About halfway through that course, I came to the realization that there was actually a useful purpose in moving numbers around on paper. If you did it right, it could actually tell you things that you didn’t know, such as where the collective debris ball from a car collision would wind up at. (which direction it would go). I never did get very far in college, managing to drop out and join the military. At the time I dropped out, I had a horrendous GPA. The only two classes that I managed to get decent grades in were Psychology and Calculus. A pretty odd combination of skill sets. After doing 20 years in the Navy, I found interesting uses for math, such as component failure rates and managing to sort of predict what spares I would need to have on hand when we deployed.  Getting tasked with attending quality control inspector classes for a shipyard period that we were on allowed me some exposure to statistical analysis and the world of Dr Deming. Deming is one of the reasons that Japanese automakers were able to overcome some manufacturing issues that they were having. I rank Dr Deming’s work up there with the likes of William Sealy Gosset. Where Dr Deming brought us Japanese autos that were not lemons, Gosset’s work gave us consistent tasting beer. Gosset worked for Arthur Guinness & Son. In order to prevent loss of trade secrets, Guinness would not allow Gosset to publish any of his work under his own name, but they did allow him to use the pseudonym of “Student” in his published material.

Now, why this article? Simple really. Following my Rumerian “The Crapshoot” article, and Albert’s “Once in a Blue Moon” article, it seemed appropriate to tie them in. Only this time, I’ll drag a volcano along for the ride.

As frequent readers know, I have a thing for “Black Swans.” Not the actual events, but just sitting in amazement and awe at the phenomena. Preferably before they play out, but while they happen is just as good. I’ve written about the 2011 Tohoku quake and tsunami and lamented how preparing for something that remote in probability is hard to sell to the investors. Recently, a perceived potential Black Swan made the news as millions of terrified New Yorkers huddled down and braced for a storm that delivered an epic four inches of snow. For the most part, this was caused by a media that literally ate up the warnings from the Mayor… who actually believed forecast that the weather guessers told him. If you look at the historical record of New York’s “massive” snow storms, and then look at what they were claiming was coming at them, it would have been a one in one point five million sort of event. Yeah, that would have been epic… only it wasn’t. Do note that the overall region did get a sizable snowfall… just not where they predicted that it was going to occur. I have a feeling that like volcanoes, snowstorms don’t really care about statistics either. They do what the prevailing conditions dictate, no matter how hard anybody wants it be how they think it should. This is a key thing that you really really need to remember whenever anyone starts spouting off terms like “overdue” for an eruption. Volcanoes just don’t give a rat’s patootie what so ever. There is always something there that wasn’t taken into consideration or evaluated.

Before I forget to mention it… according to Google’s calculator gizmo, one in a blue moon is 1.16699016 × 10-8 hertz. Taking the reciprocal you get 85,690,525… so by their calculations, a “one in 85,690,525” event is a once in a blue moon fit. This is based off of the “number of full moons in a season” definition. But, one in 85,690,525 roughly equates to a roughly 5.6 standard deviation event. That’s in the realm of Black Swans, so “nyah!”

Okay, time to pick on a volcano. Back before I realized just how little volcanoes cared about stats, I took a look at Hekla’s repose intervals. Using the Global Volcano Program’s listing of known eruptions, I get this.

Notice that as the years crawl by, the probability of having had an eruption start to climb. On the right hand side is the probability that hekla would have erupted by that year. Seems pretty straight forward, but it’s not. It only uses data back to the 1104 eruption, and Hekla is far older than that. There is a lot of Hekla’s history that is just not represented by the available data. Another insidious thing is that Hekla is not a generic run of the mill volcano. It doesn’t follow the same sheet of music that other more well known volcanoes do. Hekla is technically, an overgrown fissure cone row. Sure, it has the mass of a stratovolcano, but that is not how it was formed, and not how it operates. Tectonic stresses do just as much to govern Hekla’s action as does magma chamber pressure. That’s the reason IMO has strainmeters monitoring Hekla. Watching those and you may get an indication before it erupts… if you know what to look for. For Hekla 2000, the Burfell strainmeter took a serious dive and someone happened to notice. Seismically, absolutely nothing happened until about an hour before it went. The characteristic was due to the fissure line that makes up Hekla opening up.  When the quakes did start to occur, they were only detectable by instruments. In fact, the quakes did not cross into the realm of human perception until about 15 minutes before the actual eruption. That would have been a really bad place to be standing.

One item that has come up in discussion on the forum, is that the size of Hekla’s eruptions are strongly dependant on the length of repose time.   That’s not a bad statement, and it is supported by the records over at GVP.

The linear curve (it’s a line) has a correlation coefficient of about 0.56. Not a strong fit, but it does show some merit. I imagine that if we had access to actual volume data, it would be somewhat better. The “3.5” point is an artificial point. It was used to fill a gap in the data so that the repose interval data would not have a massive break halfway through the listing. “3.5” was an average data value. Little stunts like that are what some people do to get the formulas to work. Where it bites you is when you don’t consider how the data was massaged in order to get it to work. Media people tend to gloss over stuff like that, even though it is quite important to note it because that could throw the whole analysis approach completely off. I did it to make it work and to illustrate that point.

Will Hekla erupt? Well, yeah, eventually. When it’s good and ready. The tectonic stress changes that caused Bardabunga to erupt out at Holuhraun could become manifest around Hekla, and if she has the pressure, she might erupt. Several months ago, I tracked a wad of magma via GPS data that mysteriously took off to the Southeast and disappeared somewhere under the plains out there. I have no idea what that was about, but it was pretty wild seeing the GPS illustrate it so well.

This is”the lump” when it moved/slid out from under Hekla over a year ago.   Dunno where it eventually went.  Red is uplift, blue is down.  GPS data is interpreted from IMO plots and represented by a poly sheet overlying a Google 3D image of the area.

Enjoy!

Geolurking.

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281 thoughts on “Ruminarian IX? Musings on Hekla.

      • I remember when this eruption first began the quakes around Askja seemed to be in an arc pattern. I was absolutely certain that we would be hearing from Askja before too much longer because it just seemed like a tectonic-target being bracketed and sooner or later a quake would hit it in its sweet-spot and set it off. Instead it has proven to be a hard-arse that refuses to budge. It’s no wonder that volcanoes might be the last thing our sciences ever conquer.

  1. And a rehash to lead into something interesting regarding the Canaries.

    At one time, a long time ago, the area that the Canaries sit in was once a basin. Basin’s generally collect stream run-off and any sediment or sand that is in transport. In basins, this usually settles out and forms layers along the bottom of the basins. The oceanic crust underlying the islands has a layer of this likely sand and silica rich bedding underlying the oceanic sediment, upon which the volcanic islands are then built. Back during the formation of “Bob,” odd floating rocks appeared on the waters surface. They were termed Restolingas as some way to refer to them. (probably a media invented term, we just called them Bob’s floaters.) Bob was also an invented term that we came up with here in order to discuss it. Analysis of the Restolingas showed that they had the visual consistency of vanilla ice creme mixed with swirls of chocolate syrup. Some disagreement came up between two geophysical groups about the actual mineralogy of these floaters. One group called it Trachyte, another called it Rhyolite. The difference being primarily that of the silica content of the magma. Rhyolite is a more viscous magma and could be indicative of a potentially more violent eruption coming down the pike. Naturally, those that wished to downplay the seriousness of the eruption were in the Trachyte camp. In all liklihood, both groups were correct. The additional silica content probably came from remobilized sand from the sediment bedding that underlies the region from the time when it was “just a basin.” The magma had to go through it to get to the vent we called “Bob,” and it’s had millions of years to compact and compress into something akin to Phyllite, a foliated (layered) metamorphic rock. Not quite to the Schist level of metamorphosis, but getting there. (I did some calculations of the lithopheric pressure and that region falls short of Schist, but fits quite nicely with Phyllite).

    Now, in a stunning article about those restolingas:


    “A new study published today in Scientific Reports, an open access journal of the Nature Publishing Group, by a team of scientists from the universities of Uppsala, Las Palmas de Gran Canaria, Lisbon, and the Research Council of Spain, uses these fossil time-travellers to date the sedimentary layers beneath El Hierro and, in turn, shed new light on the long-standing puzzle about the origin of the Canary Islands.

    The origin and life cycle of oceanic volcanoes, such as the Canary Islands, has long been a source of debate among natural scientists. There are two competing models for the origin of the Canaries – one in which ocean floor fractures control the location of volcanic activity, and another in which an anomalously hot plume of molten rock from the Earth’s mantle feeds island growth from below.”

    http://www.brightsurf.com/news/headlines/105377/Fossils_survive_volcanic_eruption_to_tell_us_about_the_origin_of_the_Canary_Islands_.html

  2. And, just to lighten the mood…

    As you all know, Holuhraun it the topic at hand. It’s the current show of interest. We know that on it’s trip to the eruption site, the dike made a side-trip over to the fissure swarm associated with Grimsvotn before tracking north to where it erupted.

    Keep that in mind… now wander into the archives and re-read Carl’s article about the other side of the Grimsvotn fissure swarm… to the Southwest. For additional commentary, please do so in this thread.

    https://volcanocafe.wordpress.com/2012/03/20/icelands-forgotten-volcanoes/comment-page-1/

    • Isn’t this an exciting article! Found it in the archives and read it last fall, after I discovered this blog and went looking for history on Laki.

      • And if you poke around in Google Earth at that region you will note that the terrain is not unlike the rest of the dead zone. Old fissure lines and rift areas. Some of them quite wide. But the brunt of the area was paved over by the Skaftar Fires.

    • Reading this old article shows how much volcanocafe was build by Carl and the dragons. Please let them come back.. And please open up the blog again without requiring a log in. GL does an excellent job keeping it going but the work involved in a blog like this is more than one person can do. Carl is marvelous at though provoking, informative articles and at inspiring others to contribute.

      • Dunno about that log-in thing. It might be WordPress wide. I never really see it because I use cookies and usually stay logged in. I’ve run across it on other WordPress sites that I frequent.

        As for Carl, well, marriage is a game changer and each person taking up that activity has to work out how that changes their lifestyle.

        For example, when I got married, I had to cut down drastically on the number of dancers that I went out with…

        As for the dragons, they have always been free to move about as desired. We did have a structural collapse of one of the roof beams in the dungeon, so we had to evacuate that for a bit due to safety concerns, but most of us are still wandering about. I’m even in contact with one of them trying to elicit a post that is not about statistics and my groupie like affection for William Sealy Gosset.

      • Without discussing “what”, I guess i’ll just say that there has been some stuff going on behind the scenes that have left this place in its current state. It would be pertinent to say that there has been a lack of communication and clarity, even among many people who run this site as to what happened on a lot of things.

    • Thats pretty good. A few of the related links at the end of the story mention studies about how iron trickles through grains in the rock and form rivulets. Another mentions that iron oxide can form metal like characteristics at extreme heat and pressure.

      Quite interesting. The main article that you linked could have some connection to the Thea theory of moon formation. (Mars sized impactor shearing off a sizable quantity of crustal material and the Earth keeping the impactors core) Something that is neither proven or disproven from their work, but could help explain the odd crystal alignments that they are perceiving in the inner inner core and the outer inner core.

  3. Hello again. This might be a little off-topic.

    As most of you here knows, i love volcanoes. But that’s far from the only thing i really likes. Infact, i love everything that have with planets, moons, comets, asteroids, meteors, stars, galaxies, sun or the space in general.

    Because of that, i also play a game that i have been playing since 2004. This game is really great because you are playing that MMO game in space where you have 7929 solar systems, 67253 planets and 342170 moons.

    This is the only Sci-Fi MMO game that is in space that i have been liking good enough to keep playing it for so many years.

    So i have been making several videos from the game through the years. But the last video i made was a visual video that shows how the new asteroids graphics and the asteroid effects are in the game.

    Enjoy the video…..

    P.S: There is one spelling error in the video.

    • If I might ask two questions..what is the game called, and what screengrab software do you use. If we are not at liberty to post offtopic outside-links here, just email me at volcaccino (at) gmail (dot) com.

      • Since this is somewhat related to what we occasionally do here, it’s not off topic. For the animated plot sequences that I used back when El Hierro was the hot topic, I used the AVS software suite. One of the functions of the editor is grabbing video off of a screen area. I don’t know what Tom-Helge Andersen used, but it looks pretty good. For snagging video off of a game, there is Fraps, which is made for that purpose. I had toyed around with using it for the plot grabs but gave up and went with AVS.

        Nexroth used Fraps to capture this video from a stint as my gunner in BF1942 with the DC mod. He added the music and video cuts in a different editor.

      • The funny part of this particular game was that I had a habit and reputation of flying so low that occasionally the gunners point of view was from under the terrain. One of the benifits of getting a respawn upon death is that you can push the envelope of the simulations performance without actually dieing. I thought for some time that what I did in that game would be suicidal in reality, until someone posted a video of a guy actually flying what appeared to be a smaller airframe through even more radical maneuvers through a valley somewhere in Germany. Though it was quite impressive, I still think it was suicidal. No room for error.

  4. Maybe this is old news for you regulars. But in case it isn’t.
    “Published February 9, 2015
    Both Snæfellsjökull and Lóujökull are active volcanoes according to a new study by German scientists, Vísir reports. Volcanologist Haraldur Sigurðsson wants improved monitoring of Snæfellsnes, for public disaster protection and science.
    The youngest lava from Snæfellsjökull is 1700 year old Háahraun, according to Haraldur. He says that we have to treat the volcanoes on Snæfellsnes as active and that this is an important confirmation. “There is seismicity under the glacier and that’s new info” Haraldur ex­plains.
    Up until now the Icelandic Met Office has only caught the largest earthquakes on Snæfellsnes, due to a lack of detailed tracking. “German scientists placed seismographs on Snæfellsjökull and Ljósufjöll two years ago. And wouldn’t you know it: Turns out that there are small tremors in both of these volcanoes. So they are both active.” said Haraldur.”
    http://grapevine.is/news/2015/02/09/seismic-activity-in-snaefellsjokull/

    • The most interesting aspect of this to me is that at one time, Snæfellsjökull and the associated peninsula were the location of the MAR as it came ashore in Iceland. Later, the Reykjanes penensula became the active location of the MAR. Eventually, the rift will likely jump/shift to an area near Vestmannaeyjar.

  5. Thanks for posting this. I have often wondered if newer monitoring instruments and techniques might one day redefine “active” in volcanism.

    Also, it seems I need to spend more time here. I’ve found all sorts of fascinating articles just looking through comments today.

    • “Technology Skew” (my term) can be seen in a lot of earthquake lists. As new instruments come on line, you can actually see the effect in long period listings. It’s known about and compensated for in some studies. I first saw it accounted for in a paper about Italian quakes.

  6. Fully OT, and I will not get up on a soapbox over it, you draw your own conclusions.

    “Adolescents who chronically use methamphetamine suffer greater and more widespread alterations in their brain than adults who chronically abuse the drug-and damage is particularly evident in a part of the brain believed to control the “executive function,” researchers from the University of Utah and South Korea report.”

    http://www.sciencedaily.com/releases/2015/02/150211131854.htm?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+sciencedaily+%28Latest+Science+News+–+ScienceDaily%29

    Chronic → medical : continuing or occurring again and again for a long time

    I really hope that the Medical “professionals” who use Aderall (and related ADHD drugs) as a panacea to control kids have taken this into consideration. Nothing like having a generation of Zombies in our future. {Generation Z}

    {okay, but it was a small soapbox}

    • OT I had to listen one whole afternoon to a mother’s saga about Ritalin and her child, every so often interrupting herself to yell playing instructions to the rather timid and fearful little girl. I had met them once before without knowing who they were, and after the second meeting I came to the same conclusion as after the first one. Maybe the mother should be on Ritalin.

    • Hard to call, but a mag 3.9 is sufficient to open the fault face 839 meters above and below the hypocenter. If there is enough pressure down there, it might herald a surface breach… if not now, in the near future.

      (using Wells-Coppersmith, normal mode faulting)

    • There has been a pattern that has culled through at least 5 times where the quakes trend from deep to shallow, we are in a shallow phase right now. I see the cause being the collapse of the chamber roof, so the quakes slowly cascade upwards as the rock above sinks.

      This can be since clearly in this plot

      mag and depth

      There have been 1420 quakes less than 2km deep in the caldera
      772 less than 1km
      and 415 less than 200m since the start of the event

  7. seems to have gone very quiet lately on here – I’m guessing that’s for 3 reaasons
    1) no sign of Carl
    2) nothing new in terms of well monitored and enigmatic volcano events
    3) having to sign in with wordpress/twitter/facebook/google plus every time you want to comment

    • 1 Carl has things to take care of. This blog is a leisure time activity for all of us.
      2 Well, thats about right. How the overall changes in the tectonic stress field affect the other systems in the region has yet to be seen. Remember, Iceland historically goes through periods of heightened activity and this could just be the first act.
      3 Might be an issue WordPress wide. I’ve seen similar vagaries on other WP sites.

    • I’m still here. Just busy through the day. Then get on here to check on things. Don’t always feel like commenting. 🙂

  8. It looks totally calm now and Holuhraun is barely puffing. But something is up. There was a large number of “wet” tremors at very shallow depths this morning before all the seismographs went silent:

    Jon Frimann’s geophones show the tremors continuing and while they are very susceptible to wind, it could be magma moving.

    • These are very small quakes listed at IMO but are spread out far and wide

      12.02.2015 10:22:03 64.673 -17.475 0.3 km 1.6 99.0 4.5 km NE of Bárðarbunga
      12.02.2015 10:03:07 64.709 -17.506 0.1 km 0.1 99.0 7.7 km N of Bárðarbunga
      12.02.2015 09:52:45 64.686 -17.488 2.5 km 0.8 99.0 5.4 km NNE of Bárðarbunga
      12.02.2015 09:49:41 64.676 -17.469 0.1 km 0.1 99.0 4.9 km NE of Bárðarbunga
      12.02.2015 09:41:19 64.680 -17.436 0.7 km 0.9 99.0 6.2 km NE of Bárðarbunga
      12.02.2015 09:35:45 64.673 -17.412 1.4 km 1.3 99.0 6.6 km ENE of Bárðarbunga
      12.02.2015 09:34:08 64.684 -17.429 0.1 km 1.4 99.0 6.8 km NE of Bárðarbunga
      12.02.2015 09:32:14 64.677 -17.423 0.1 km 1.0 99.0 6.4 km NE of Bárðarbunga
      12.02.2015 09:19:00 64.635 -17.637 8.8 km 1.1 99.0 5.2 km W of Bárðarbunga

  9. For anyone interested here are up to date plots

    Note how we are in a phase of shallower quakes about to go back to deep if this pattern continues

  10. In the beginning of the eruption, I liked to think of the subsidence as an exponential function, mainly because many examples of physical systems show that kind of behavior. But the longer the eruption has progressed, the more I started to think of the subsidence as a quadratic function instead. If you study the subsidence graph more closely, you can see that the derivative looks quite linear in time. This is consistent with a quadratic function, and I have mentioned this before in previous posts.

    I did a small thought experiment to see how a simple model can explain what is happening and it’s the good old plug model. Below is a simplified figure of the model. A plug of rock and mush rests on top of a magma chamber. From the chamber, there is an open conduit feeding the Holuhraun eruption.

    The pressure required to support the plug of rock and mush is proportional to the height of the column, the density of the rock and mush, and the gravitational acceleration constant.

    p = K*h,

    where K is some constant depending on density and gravity. If h is reduced, it means p also has to reduce.

    If we now assume that the subsidence is even for the entire cross section of the plug (it’s not), the rate of the subsidence is related to the magma flow as

    F = dV/dt = -A*dh/dt,

    where A is the cross section area of the plug.

    If we model magma in the dyke as a fluid in a pipe, then the dynamic pressure of the fluid, and the pressure losses due to friction etc, both are on the form

    p = C*F^2,

    where C is some constant depending on cross section area of the dyke, magma viscousity, friction, etc.

    Combining all three expressions, we get a differential equation:

    dh/dt = -B*sqrt( h ),

    where all other constants have been absorbed in the constant B. The solution to this equation is on the form h( t ) = a*t^2 + b*t + c, i.e. a quadratic function!

    I agree there are a lot of simplifications going on here, but it always feels nice when a simple model matches the measured data. 🙂

    The key to getting a quadratic function instead of an exponential, is that the pressure in a pipe is proportional to the square of the flow as opposed to directly proportional to the flow. Based on the best quadratic fit, the subsidence will stop just before the beginning of March. This also seems consistent with Ian’s quake energy plot. If this also stops the eruption depends on if there is an inflow of fresh magma from below. In that case it is possible that the plug reaches equilibrium, but the magma flow continues.

    I will, however, not promise to eat anything strange if the prediction turns out to be wrong 🙂

    GL Edit: {grin}

    • This all makes sense to what we are seeing.

      The one thing that would alter this model substantially and would become another variable in the equation is the “plug” is not a cylinder dropping straight down thus accounting for the offset sink and difference in quakes north and south

      As the plug sinks, the south side slides down the inward sloping fault but the north falls away from the outward sloping fault. The north wall of the plug collapses more than the south creating more seismic activity

      at least this is the way I see it

      I would expect the seismic activity to keep going even if the subsidence and eruption halts completely, it will take a while for this huge area of rock to settle in place.

    • Thank you fkavirtuals. Another lovely interlude. I found it almost hypnotic. Very relaxing.
      Interesting lighting with the moon shadows and reflections on the snow and ice. I don’t normally like the music that backs up clips but this music is lovely and goes well with the dreamy quality of light.

      As to Lurking’s comments about this being people’s leisure activity. How right he is. Most of us are very busy people and like the volcanoes we have times of high activity where everything is erupting and almost no time to take a breather in private and work life. Followed by times of , perhaps not dormancy, but certainly periods when there is time to spend at the keyboard and screen purely for interest , relaxation and rumination.

      Tomas and Ian . Thank you both for your comments and plots. Aren’t those quake phases fascinating. I’m now waiting to see if they do become deeper again. That then poses the question. What causes this pattern?
      Tomas. I am not good at equations but again it will be interesting to watch and see if your prediction is correct. That’s what I like about this site. Ideas that are clearly explained and an attempt at predictions in this unique happening. It’s like a geological “who Dunnit?” 😀
      Please keep commenting. I am pretty sure there are lots of readers/Lurkers who pop in and appreciate all the time given by our many contributors

      I have no problem with having to Log in. I have noticed that when Microsoft does it’s updating thing, or I have cleaned up my PC I often have to log in again. Those Microsoft updates that quite often cause hiccups on my PC are a pain in the…..proverbial.I dread the next morning when I switch off the PC at the end of the day and it informs me not to unplug as there is an update going on 😦

    • One day is too short a time to judge this, but over several days there is also little indication of subsidence. And the earthquake activity has ceased: no M3+ quake since Wednesday. At the least this strengthens the case for close connection between the shallower quake activity and the surface subsidence. If this continues, it would be interesting to see how the Holohraun eruption rate develops. Bardarbunga may beginning to receive new magma at the same rate it flows out through the dyke. But it should be looked at for at least a week before drawing conclusions.

      Regarding the need to login to WP, this is a setting in the blog. It is a tick box under ‘Options/General’ which needs to be unset. Nothing to do with WP oversight – it is done by the blog administrator

  11. Even the background tremor drop suddenly around midnight last night to a level that was considered normal pre-eruption.

    Yes, it will be interesting to see what happens next

  12. Excellent read regarding the 1996 Gjlap eruption coming from a chamber 10km deep. If you google the title there are free access pages

    Crustal deformation associated with the 1996 Gjálp subglacial
    eruption, Iceland: InSAR studies in affected areas adjacent
    to the Vatnajökull ice cap

    “Subsidence at Bárdarbunga is
    not observed before October 6, suggesting that the dike
    originated either from a subsidiary magma chamber
    located southeast of Bárdarbunga or directly under
    Gjálp where deformation signals cannot be detected by
    InSAR due to ice cover.
    InSAR analysis indicates that significant deflation
    occurred at Bárdarbunga but only after October 6, when
    most of the magma had already been erupted at the
    Gjálp site. Modeling results indicate that a 10 km deep
    deflating Mogi source can explain most of the
    deformation with a volume decrease of the source of
    0.07 km3.”

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