Leave your sineful ways behind

It has been suggested by another of the editors that people enjoy images of cats and that if I posted one such it would keep the interest up for this dry series. The cat in question did not like the Haiti earthquake.

It has been suggested by another of the editors that people enjoy images of cats and that if I posted one such it would keep the interest up for this dry series. The cat in question did not like the Haiti earthquake.

Part 1 in the series can be found here: https://volcanocafe.wordpress.com/2014/06/06/earthquakes-or-wavy-gravy/

In the first installment I told a blatant lie, I thought someone would catch me, but alas not. The lie was put in on purpose so that I would have a point to start today’s wavy post with. In short, in the last installment I wrote that there are only 4 basic audio waveforms, and it was once believed to be true. But nowadays we know that all audio waveforms consist of the humble sine wave. So in a sense of it you have only ever heard one thing in all of your life.

Why now is that true? Well, let us just say that we can create all other waveforms from adding sine waves together according to specific “recipes”. I could either spend 3 pages on explaining this, or we just watch a brief video. After all, “what you hear is what you believe”. Video by Matt Mayfield from the Audio Kitchen.

In normal life you will basically only hear the sine wave, and the sine wave rules the longitudinal wave as we learned in part one of this series. As I mentioned last time the longitudinal wave travels as a mechanical sine wave and that it is the only possible way an audio wave can travel in gas or fluid media. There are a couple of exceptions but we can leave those behind.

But in solid media there is another type of mechanical audio wave lurking in the shadows and it travels in something called a transverse wave. It is time to enter the seductress of wave physics, the cosine wave.

Cosine waves

The sine and the cosine is in a way the same conundrum as the classical, “which came first, the hen or the egg?” Let us start with saying that the sine wave is a 2+1-dimensional wave and that the cosine is 3+1-dimensional.

The sine wave moves up and down (height) and forwards (distance), it also travels through time. This extra time dimension I added is just me being nitpicky, all macro-cosmal waves moves forward in time.

The cosine is a function as the wave spirals around in a drawn out circle, so you have height, width and distance (and time). But really, I can use words or I can give you this sexy little animation I found in Wikipedia. It will tell you everything you need to know.

Animation by Nashev, courtesy of Wikimedia Commons. Illustrating the cosine wave's fundamental relationship to the circle. Real sinusoid on a timebase, formed by a linear increment of complex argument in time.

Animation by Nashev, courtesy of Wikimedia Commons. Illustrating the cosine wave’s fundamental relationship to the circle. Real sinusoid on a timebase, formed by a linear increment of complex argument in time.

Now someone is probably muttering that a sine wave and cosine wave are just sinusoids of different phases, or that the cosine leads the sine wave or even that the sine lags the cosine. This is of course true, but in the end the cosine has one astounding difference as it carries the sound of the earthquake. Fasten your seatbelts; this will be an eye-opener that you will remember every time you see the simple representations of an earthquake on a drumplot, because now you will understand better what really is going on.

Transverse waves

Now that we have looked briefly on the cosine wave we are ready for the transverse wave. Now, remember that the cosine wave is a mechanical audio wave, and that the transverse wave is how the cosine propagates (moves around). But let us first take a refresher look at the creation and travel of the longitudinal sine wave through let us say Iceland.

Representation of a spherical pressure wave from a point source. This could be a drum, a stone dropped in a lake, or a small earthquake. Image by Thierry Dugnolle, Wikimedia Commons.

Representation of a spherical pressure wave from a point source. This could be a drum, a stone dropped in a lake, or a small earthquake. Image by Thierry Dugnolle, Wikimedia Commons.

Transverse planar wave by Christophe Dang Ngoc Chang.

Transverse planar wave by Christophe Dang Ngoc Chang.

As people set up new sciences they tend to want to differentiate themselves from the parent discipline. In physics it is a transverse wave, in Geologese it is a seismic S (secondary) wave. But basically it is the same shit with a different name.

The two most often occurring versions of transverse waves are the planar transverse wave (megathrusts produce these for instance) and the rather beautiful spherical transverse wave. One does not need to be a genius to understand why these waves really go heavy on buildings, one functions as a jolly trampoline and the other will twist the house upwards and sideways before the house is unceremoniously dumped back on the ground.

What is happening in the last animation is that the circular motion of the cosine is creating an expanding spiraling wave; this means that the sound from the earthquake will be Emediately separated into two distinctly different components with one wave travelling almost straight to the observer, and the second will be travelling a much longer way.

Spherical transverse wave by Christophe Dang Ngoc Chan.

Spherical transverse wave by Christophe Dang Ngoc Chan.

Think of it like this, you have one fireman named Mike Ross sliding down a fireman’s pole and another fireman named Mike Ross running down a spiral staircase, both Mikes are of course starting at the same time. The poling Mike Ross will come down before the transverse (spherical) spiral staircase Mike Ross even if they travel at the same speed. This is due to the spiral staircase being representative of a longer route to the finish line.

If you want to experiment on your own you can go outside and tie a rope to a tree, if you move your hand up and down you will see a planar transverse wave wandering down the rope, and if you move your hand in a circle you will see a spherical transverse wave move down the rope.

I think this will be enough for today. I just hope that my entire audience has not fallen asleep completely. Next time I will do my very best to envelope you all in the warm embrace of the third part that governs every waveform, the envelope. I seriously hope nobody got seasick from all the moving animations I used in this article.



81 thoughts on “Leave your sineful ways behind

  1. Two interesting small earthquakes.

    Wednesday 18.06.2014 06:45:48 64.222 -18.581 5.5 km 0.8 99.0 23.9 km NW of Laki
    This one is on the Bárdarbunga/Vedivötn fissure swarm.

    Wednesday 18.06.2014 05:51:58 64.341 -18.653 5.3 km 0.6 99.0 28.8 km NE of Sigöldustöð
    This one is on the Vonarskard fissure swarm.

    Interesting to see two individual swarms having earthquakes in the Dead Zone at almost exactly the same time. And no, it is not the end of the world.


    • There was another set of quakes a bit further north just a few days ago as well. Nothing big, but they were above the 1.0 threshold at least.

      • Reminds me of another prophesorial quip…

        “Soon will the waves of milk break upon the foot-soles of Bardi!”

        Reportedly stated by Katla, the housekeeper. She knew because she put him there after she killed him.

        • I have always wondered if not the rather clever Icelanders wrote in the general behaviour of their volcanoes in that sentence.

  2. 2 cents from the peanut gallery.

    Interesting take on the “cosine wave” aspect of it. I would equate that to a circularly polarized wave. In radio-electronics, you get maximum signal on a received transmition from an antenna that has the same polarization as the passing waveforem. Vertical antennas – vertical polarization, Horizontal antennas – horizontal polarization. Somewhere in that mess, someone came up with circular polarization. I have here hanging on the wall, a circularly polarized antenna that I built that have a pretty unique beam pattern. Pretty much a cardidoid. It’s intended to pick up signals equally well from horizon to horizon, with no drop off at the zenith. Great for snagging aircraft communications.

    In the more exotic field of satellite communications, you will see right hand or left hand circular polarization. Ground station antennas typically look like a helical coil with a reflector back.

    Flaming raven starts forest fire, cuts power to Yellowknife

    • DING!
      I skiped the polarization part of it to not overwhelm people, but you are absolutely correct. A transverse wave is polarized.

      • Woot! I got a virtual point!

        I think the best example of my polarization exploits was when I took an old 17 element TV antenna and flipped it so that the elements were in vertical orientation and attached it to my push-up pole with a director. After I cobbled together a rudimentary matching network in, I was able to pick off security up at Atmore speedway in Alabama chasing drunks around the facility on the scanner. It was entertaining. I no longer have that set-up because my mom got the idea that a co-worker of her’s needed a TV antenna due to the remote location that he lived at. I dis-assembled the set-up and hauled it to Mississippi and installed it as it was originally designed. Her co-worker got a free antenna set-up (and an install by someone quite familiar with working on exposed antenna systems) and it made my mom happy.

        As for long range TV reception, the most elaborate TV antenna I put together was a rhombic array. The basic design comes from “old school” trans-Atlantic HF communications links. I cut the antenna for the TV bands and had it small enough to make it directable. I could snag New Orleans or Montgomery quite easily. Eventually my street got cable and I disassembled it. The cool part about it was that all you had to do was to make your link resistor between the two legs match the impedance of the feed line and you could tie into it with 300 ohm twin lead with no matching network. Even though it could fit on a pole, it was still quite large. According to the specs, it had a 4 degree launch angle, that made it ideal for catching the forward scatter from the distant signals. (similar to headlight glow over the hill in dense fog)

    • It is also why you after some large earthquakes can see that all of the trees have been bowled over in the same direction perpendicular to the point of origin of the earthquake.

      Another possibility is that the earthquake causes a toroid (donut) transverse wave. I have on occation pondered if that might not have been the case with the infamous Bárdarbunga zero net displacement earthquake.

  3. I should though state that an earthquake is complex set of waves. That is why one part of a city can be affected by a planar transverse wave (trampoline) and another can get the “lift and twist” effect of the spherical planar wave. And also there are other versions beyond these two.
    As we progress with the series we will get to see even better what causes the effect that houses on opposite sides of a street can be affected so differently by waves even though almost everything is the same.

  4. Tohoku earthquake caused a planar transverse wave, but “the big one” will have a large spherical transverse wave component.

    • Ah, should perhaps explain the expressiong “the big one”.
      It means a big earthquake from the San Andreas Fault. The “really big one” will of course almost certainly be a planar transverse wave somewhere along the Chillean coastline.

      • Curious, are the earthquakes along the Andean coast actually bigger than the other largest subduction zones in the world, or is it just a product of more coastline?

        Also, why don’t we see any megathrust quakes in the mediterranean subduction zones? (Or do we?)

        • The Chilean earthquakes stands for roughly 50 percent of all released seismic energy, and if memory serves 8 of the 10 largest earthquakes in recorded history. And of course the largest earthquake ever.

          There are a couple of faultlines that produces thrust earthquakes in the med, but not on the awesome scale of Chile.

          • I guess I forgot to account for the fact that the Nazca plate is the fastest subducting plate on the planet. Add that in with the longest coastline for a subduction zone and I suppose that seems fairly logical.

            • If you take a look at the link below you will see that in the last 100 years the 1960 Valdivia earthquake released a whopping 22 percent of all seismic energy. Yepp, 22 percent of all combined seismic energy was released by just 1 Chilean earthquake.

              The 1906 “The Big One” of San Francisco is just a thinsy winsy little line in the pie chart.

            • Curious, is there any software out there that models worldwide seismic strain based off energy release, plate spreading rates, and subduction rates?

    • As for the seed files, with a bit of digging, you can find them from the Iris Buffer of Uniform Data site.

      Heads up, as far as I can tell, only a single station in Reykjavík is in the network.

      Also, SeisGram2K has the option of exporting the waveform as a wave file. (up-sampled) for use in audio applications. Just remember that the waveform is up-sampled if you try to glean any spectral data from it. Occasionally, you can detect what seems to be reflections from the strata too.

      I’ve used it on local quakes and fed the different channels into left or right ears. Sometimes, if you do it right, you can get a spatial effect as the waveform rolls by.

      One idea that I have yet to perfect, is syncing up the P wave for a single event as “heard” from two separate stations. If you succeed, you have in effect, a giant virtual head to listen to the waveform. (widely spaced ears)

        • Usually i use the “Synthetic Seismograms Network Map” in IRIS mda to view all available stations in a map. What i usually do..
          1) Visit this great blog to check for recent activity.
          2) Go to IRIS mda to see if is available seismic data for that volcano
          3.a) If data is available, great, use SeisGram2K to check for near realtime data or previous data. 3.b) If no data is available (99% of the times), spend a couple of minutes wondering why that agency do not share data with the world.

          But recently i found a great tool to check for seismic data in active volcanoes, Swarm (Available in USGS website), contains all seismic stations from many volcanoes in Alaska, its possible to see in near real time, up to 14 days and download the data to check in your favorite seismic analysis software. Currently checking high frequency events in Semisopochnoi (CERB SHZ station) and low frequency events (i think) in Pavlof.

          • Sounds like you have it covered.
            Could you write a short little article with your tips, I think people would love that as a light friday read?

  5. Thank you Carl! Trying hard to connect back to the deeply buried memories from physics and math classes 😉
    So do spherical transverse waves occurr in strike-slip earthquakes, perpendicular to the fault plane? Or what else causes the rotating jolt?

  6. By the way carl, you mentioned a few weeks back to remind you to do a post on the east africa rift :). If you dont have time, that’s fine however, but just figured I’d remind you since you mentioned to do so.

    • Keep on reminding me 🙂

      Right now I am really hard pressed for time, but sooner or later I will get around to it.

  7. I am actually starting to feel sorry for the Spanish… 7-1 in 3 periods, and on the road to the second trashing in a row.
    Chile are really handing them a Valdivia sized trashing. I can only come up with one paraphrase that covers what is happening.

    “All your asses are belong to us”

  8. About sine waves and sawtooth.. A friend of mine with good knowledge of math and physics explained this to me….. But you probably understand it better than me……

    • I am not going to go into fourier transformations, this is not the place and it is beyond the scope of explaining the basics of wave propagation.
      Perhaps way later one day when I want to explain waterfall graphs.

    • Whenever you get around to it, I’ll definitely read it. I’ve always wondered where that 13th harmonic requirement came from to get a nice clean square wave.

  9. Excellent post Carl. I don’t know why you think people don’t like this kind of thing. I love it. I bet there are hoards of us out here who have little more than stale knowledge of the physics we did at school and to be honest there is a huge gap in the literature out there between that and the full-blown scientific papers we get to read. This post fits the bill really nicely. More please!!

    So, if I have understood you correctly, all waves have a basic sinoid pattern but move in different axes.

    The primary wave is compressional and moves out in a one-dimensional ray from the point source:

    Secondary waves are much more noticeable as they have an amplitude or pitch to them. These are the waves we typically feel first. The jolt that wakes you up in time to hide under the bed.

    Now I am unsure if I got the next bit right.
    Finally we have surface waves which propagate much more slowly and can be polarized vertically, shaking things up and down (the sine element if you will or Rayleigh waves), and sideways, (the cosine or Love waves).

    … and of course everything in between and every interference pattern you can think of. Is that half-way right?

    .. and to stretch even further out on a limb and move from this to the beach balls. Because of the sine / cosine nature of a wave the region of primary thrust is not actually parallel to the fault line but at 45° to it, resulting in the dark quadrant of the beach ball. Is that correct? Or is it a product of 3D geometry that I just haven’t got my head round yet?

    • The dark bits of beach balls show the tension axis i.e. the minimum compressional stress axis. This is governed by how the fault slips. Don’t know if, or more likely how, it impacts polarisation of the waves. You would expect it could, as does the medium the waves travel through. Hopefully Carl can add more … 🙂

      • Really? I always thought it was the other way around. The black quadrant is maximum compression, i.e. the direction where the land first slips towards. Mind you, I wouldn’t be surprised if I have had that wrong all these years!

        • Now I know that the “P” caused my confusion.
          In another wikipedia graph it is drawn into the white quadrant of the beach ball. “P” stands for P-axis (pressure axis), that is the axis of maximal compression, or pressure prior to the earthquake. The axis along which the extensional stress, or strain, is greatest is called the T axis (tension axis).

          When the fault finally breaks, the first motion is away from the white quadrant of maximal pressure, hence causing a tensional first motion (indicated by “T” in the graph you linked to). I have the mental image if I hit the beachball in the white quadrant, then the first motion goes away from the fist and the pressure wave (P wave) propagates towards the black quadrant as a compressional first motion (“C” in the graph).

      • Yes, the polarization do affect how the beach ball will look like. For instance the planar transverse will be represented as a megathrust beach ball… And a spherical transverse wave will be represented as a strike/slip beach ball.
        Anyhoos… we are ahead of the installment schedule here 😉
        Also, I always need to remind myself what the correct “Geologese” term is for what I know at heart in the language of “Physicese”… So for me it is really confusing to remember the Geologese terms since I tend to always use Physicese in my shaggy and confused Noggin’ :mrgreen:

        • And to further be exact, the waves are caused by the type of initial break that in turn depends of the type of fault.
          So Fault under strain/stress/compression/etc -> Initial break -> Wave (polarization) -> Beach Ball…
          Nice little cause/effect/representation chain here.

    • Leaving the beach balls behind since that part is allready answered 🙂

      The initial wave (sine) (pwave in geologese) has amplitude and direction (and time) so it is a twodimensional wave, and it can and will be felt if the earthquake is large enough (around M2). The secondary (s-wave) wave is 3 dimensional. Hope that made that part clearer.

      You are absolutely correct that there can be any number of other flavours of waves involved, and there are, I will get back to how they come into existance in later parts.

      I am happy that you like the post. I agree that there is a bit of a need for explanations in between the physics behind it, and the effect we see on the instruments. More is coming 🙂

  10. Teams remaining in the Football World Cup that has a volcano:
    Costa Rica
    So, take your pick which team to route for 🙂

    I was routing for the Indomitable Lions, but they are now a lost case even though they have a honking big volcano.

    • Dear sir, aren’t you forgetting an important item in your list? Not a capital V kind of volcano, but we do indeed have Trindade to represent us and we’re not out of the context (yet) 😉

      • I happily stand corrected!
        Now we can all rout for the hometeam 🙂

        And I was anyhoos routing for Brazil due to the Manaus opera house (it counts as a volcano in my book) :mrgreen:

  11. A Russian Helicopter, a spectacular landscape, wingsuits and a base jump into an active volcano, you guys are going to love this 🙂

    Mutnovski volcano in Kamchatka had at least 12 mostly VEI-2 eruptions in the last 100 years.

  12. Ting… Small but not tiny quake near Godabunga.

    18.06.2014 10:20:53 63.653 -19.163 2.5 km 3.2 99.0 4.5 km ENE of Goðabunga

    This is the way that I like cats. Utterly dismayed.

    It’s as if their entire world-view has completely changed. What was once reliable firm ground is now tossing them around like detritus.

    • What I find interesting with the image is that the other two cats look totally depressed and sleepy, and the front cat is in the hyper “did you see that shit dude” state. This is also the two main states of human shock.

  13. I validated a simple idea tonight. The structure/airframe of a moth is poorly suited for supersonic airflow.

    My wife, who is hyper paranoid over anything bug sized or shape that moves around frantically called my into the livingroom to ID a bug on the ceiling.. To me, it looked roughly moth shaped and I IDd it as such,
    With no way to get rid of it that didn’t involve me prancing around the room, I popped it with a cloth in the manner that you snap a whip. The moth disappeared in a puff of dust.

    (reportedly, the end of a whip or towel used in such a way momentarily exceeds the speed of sound.)

    Image and video hosting by TinyPic
    In the eleventh century the Catholic Church got it into their head that the raving Vikings could do with a bit of Christening. So they pondered on how to do it and come up with the fairly obvious answer that Vikings really liked parties.
    The Midwinter Yuletide was a period of bathing, eating pork and getting drunk. That one the Catholic Church declared was the same time as the birth of Christ. So, remember that Christmas is due to drunken Vikings and in reality has nothing to do with the actual birth of Christ.
    Easter they put forth as a bonus party if we became Christian so that went down pretty well for both involved parties.
    But the Midsummer’s Eve was a bit taxing for the Catholic Church. It was after all a totally pagan ritual celebrating the fertility of mother earth. It involved getting drunk and general fornication. Back then a Pole with two balls adorned with leafs and flowers were driven down into the ground as a symbol of fertility.
    So what to do with it all? Banning it would only result in that the stubborn Vikings would chop of the heads of the priests. Making it a Christian party? Hm, not an option really… So, the Catholic Church compromised.
    So, almost 1 000 years later we still put up a Christian cross adorned with leafs and flowers with two flower wraths symbolizing a pair of balls. The symbolism is that the cross fornicates the ground to give a bountiful harvest. And we still get drunk and generally hump around that cross.
    Just keep that image in your head on Sunday.

    • Many years ago, I had an opportunity to take one of the organized tours of the antebellum homes in Natchez MS. Not sure what the big shin-dig was at an auditorium event, but it featured a maypole dance. At the time I wasn’t really into the cultural aspects of stuff, I was more interested in building architecture and the structural aspects of the female members of my class.

  15. Todays football teams with a volcano:
    Costa Rica
    So, if you are from a country without a team, or your team is a gonner, here are your volcanologically correct teams to rout for :mrgreen:

    I have a problem with the Costa Rica vs Italy match. Costa Rica is kind of the cool option, but then Italy has Mr Spock as a goal-keeper. Hm…

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