Green Gabbro

I’ve finally read Dr. Tom Chalko’s wackaloon manuscript. It was fantastic.

Chalko artfully combines common misconceptions about his subject matter with accessible yet impressively mathy-lookin’ slipshod data analysis, and produces an argument that appeals to the innate human desire to make sense of the natural world. His skill at subtly invoking people’s fear of a changing world and appropriating the power of existing cultural narratives – in this case, the discourse on climate change – places him among the crackpot screed-writing elite. That makes it worth discussing a few of his more beguiling errors.

So. What’s wrong with this picture?

i-a773ded9a9c82c388bb257164a09ce0c-chalko-fig1.png

To start, let me show you what Chalko’s graph is really measuring. I used the same procedure he did to estimate the total energy from all earthquakes of magnitude 7 or greater in the calendar years 2004-2005. This procedure falls apart on close examination, and I will show you why this matters in a few paragraphs, but it is good enough for a quick and hand-wavy sketch:

i-51c95bfa0685b39b350ab449ef2bd73e-2004-2005-seismic-energy.png

Earthquake magnitude is a logarithmic scale; each magnitude unit represents an approximately 30-fold increase in the total energy of an earthquake. So when you get one extremely large event, such as the Great Sumatra-Andaman earthquake, it completely swamps everything else. Its largest aftershock still contains more energy than all of the other earthquakes during that two year period on the planet combined.

It is a curious fact of seismology that there are always about 10 times as many M4 earthquakes as M5, and 10 times as many M5 earthquakes as M6, and so on. I’ve never heard a satisfying physical explanation for why this is so, but it is. So even though you could, in theory, find a million harmless M4 earthquakes to release the energy of one devastating M8, in practice you will always come up 990,000 little earthquakes short, no matter how hard you look.

In terms of total seismic energy release, only the very biggest earthquakes matter.

Now let me show you the same picture as Chalko’s Figure 1, this time going all the way back to the turn of last century:

i-c347d37682377493c552d26ea4663847-seismic-energy-timeline.png

Less impressive, isn’t it?

There are some problems with this figure. I used NOAA’s significant earthquake database for earthquakes prior to 1973, and it’s a bit quirky – compared to other sources, it seems to overestimate the size of many earthquakes, especially those that occurred during the dawn of seismology in the first few decades of the 20th Century. So there may be some shift in data quality or calibration that accounts for the apparent downward trend in earthquake energy in the first part of the 20th Century.

A bigger problem is the definition of “magnitude”. While most people are familiar with the Richter magnitude scale, that’s actually just one (and not a very popular one nowadays) of many magnitude scales in seismology. All of them are carefully crafted to be approximately comparable, but they’re not exactly the same. When I made all these graphs, I paid no attention to this whatsoever. It’s a bit like trying to figure out how many “1 meter” boxes I need to pack all of my stuff – most boxes are vaguely square-ish, so it doesn’t matter too much if I’m talking about the length, width, or height, but what about those long skinny boxes designed to hold floor lamps or random furniture parts from IKEA? In this analogy, larger earthquakes come in funnier-shaped boxes.

NOAA’s catalog uses a magnitude scale that is useful for structural engineering, but not so good at showing the differences between the very biggest earthquakes. It’s based on the peak amplitude of a particular set of seismic waves, the surface waves, which are usually the most damaging waves of an earthquake. As earthquakes get really big, though – bigger than about magnitude 8 – less of their energy goes into creating a big peak surface wave amplitude, and more goes into creating long-lasting waves and making the entire Earth ring like a bell and other stuff that doesn’t show up in the measurement of surface wave magnitude. Because of this, you don’t usually see surface wave magnitudes that are larger than the low 8s. So I cheated in a few places – notably, the 1960 Valdivia, Chile, and 1964 Great Alaska earthquakes, which are the largest earthquakes ever recorded – and changed the numbers to a different magnitude scale, one that works better for very large events. This is the moment magnitude scale; it’s determined using information from the entire seismogram, not just one set of waves, and it’s generally considered the best number to use when you’re describing really big earthquakes.

Now let’s return to the post-1973 world of Chalko’s figure. You’ll notice on both of our graphs that the 70s and 80s look fairly quiet. Is this because God really liked punk rock, but got pissed off at the rise of grunge and decided to punish us with earthquakes? Did Richard Nixon dig a hole all the way to China, and make a treaty with the Mole People on his way to normalizing diplomatic relations between the U.S. and the PRC? What did Bill Clinton do to piss off the Mole People?

Chalko’s data, and mine post-1973, are taken from a catalog maintained by the National Earthquake Information Center. It doesn’t use the same magnitude scale for every earthquake. Instead, each entry in the catalog provides both a magnitude, and a magnitude scale. A quick skim of the data reveals that until the 1990s, large earthquake magnitudes are mostly given as surface-wave magnitudes, and then the catalog shifts to reporting mostly moment magnitudes.

If you don’t pay close attention to the magnitude scale you are using, you will find that earthquakes seem to get bigger in the 1990s. This does not mean that Bill Clinton upset the Mole People or that global warming is responsible for increased seismicity, it just means we’ve gotten better at measuring big earthquakes.

Comments

  1. #1 BrianR
    June 27, 2008

    Very nice … some quality debunking is just what I was looking for with my morning coffee today.

  2. #2 Stephen
    June 27, 2008

    OMG. Earth quakes obey a power law distribution! Richter was sooo forward thinking in 1935 to make his famous scale logarithmic! That is so uncommon in nature! I mean other than sizes of stars, rocks, financial markets, internet networks, almost anything self organizing like life, etc.

  3. #3 Kerr
    June 27, 2008

    Can we really afford to be wrong, though? What with the upward trend and all, clearly the mole people are building Weapons of Mass Seismology! NUKE EM ALL!

  4. #4 Scholar
    June 27, 2008

    I was under the impression that each magnitude is 10 times stronger than the next.
    For example, a magnitude 6 earthquake is 10 times stronger than a magnitude 5.
    You spoke of “the total energy released” being 30 times greater for each magnitude.
    Care to enlighten me?

  5. #5 The Mole King
    June 27, 2008

    Now, now – you are wrong. We were upset over the treatment of Princess Lewinsky. That’s why we increased the Earthquake Machine and shook the world. We Mole People are not to be treated unkindly!

    PS – tell the Tick we said Hi.

  6. #6 Maria Brumm
    June 27, 2008

    Scholar: Oh! Yes! Thanks for asking that question, I totally should have thought of it while I was writing.

    Each magnitude step is a 10-fold increase in the amplitude of seismic waves, but that increase in amplitude requires a 30-fold (actually, 10^1.5) increase in total energy. I always think of it as because there are 3 directions for the seismic waves to move in, though that’s more a memory trick than actual physics.

  7. #7 Martin
    June 27, 2008

    Thanks, that’s a nice, satisfying read :)

  8. #8 themadlolscientist
    June 27, 2008

    What’s the spike in 1961? The Alaska quake? I read somewhere that it had been estimated at possibly as high as 9.6. I remember seeing the photos of Anchorage in National Geographic. OMFG.

  9. #9 Maria Brumm
    June 27, 2008

    The big spike is actually in 1960, from Chile – the axis labels are a little wonky. Alaska was in 1964. Chile is generally listed as a 9.5, Alaska 9.2 (moment magnitudes!), though I’m sure there have been higher estimates.

  10. #10 Martin
    June 28, 2008

    A random question – isn’t the real trend (over millions of years) in fact going to be downwards as the Earth ages? I’m guessing over a century or so that’s not going to be noticeable, mind.

  11. #11 themadlolscientist
    June 28, 2008

    OIC. Alaska was a wild-ass guess – it was the only major one I could think of from that general time frame. Thanks.

  12. #12 Silver Fox
    June 28, 2008

    When relating earthquakes or seismic energy to global warming, shouldn’t any increase actually have started at the beginning of the Industrial Revolution in the 1800′s — or at the end of the last ice age about 10,000 years ago? Any paper, like the one you’re debunking, trying to link the two things — hot air and seismicity — should go back a little farther than the last several decades! Your graph actually shows an overall flat line or even downward trend overall since 1900.

  13. #13 bigTom
    June 28, 2008

    I think most of the people looking for a secular increase are hoping to see a signal that God is warming up for an end-of-days finale.

    Back in the ancient days when I was a grad student in seismology: Richter scale was the log of the amplitude on a standard seismograph at a standard distance. The short period seismograph was used, and the amplitude only looked at the first couple of seconds of the wave train. A magnitude eight typically takes a couple of minutes to rupture along hundreds of KM of fault, so the Richter scale was really a measurement of the energy at initiation point of the quake.

  14. #14 BrianR
    June 29, 2008

    Martin says: “A random question – isn’t the real trend (over millions of years) in fact going to be downwards as the Earth ages? I’m guessing over a century or so that’s not going to be noticeable, mind.”

    That’s an interesting thought … I guess I would put that trend in the billions of years instead of millions … the plate tectonic ‘machine’ will keep churning for a long time to come. At least, that’s my speculation.

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