Lyttelton earthquake peak ground acceleration

By Grant Jacobs 27/02/2011 25


A light post introducing two maps showing the difference in shaking in the September 4th and February 22nd earthquakes.

If you are looking for my news feed on the Christchurch/Lyttelton earthquake, I post comments updating news here; older comments can be found on an older post.

During the 22nd February Lyttelton earthquake my uncle’s bath, half-full with water, was thrown up in the air to meet the taps on the wall.

We’re held on this planet by gravity, 1 G’s worth.

Any force that throws things up upwards has to be greater than gravity’s pull downwards.

One way geologists measure earth movements is to record the acceleration in movements of the ground.

Acceleration is the amount of change in speed. You plant your foot on the pedal in a car, the rate at which the speed increases is acceleration.*

Peak Ground Acceleration (PGA) is the amount of acceleration of movement of the earth at the point recorded, reported as a percentage of gravity’s acceleration (9.80655 m/s2).

Below are the peak ground acceleration maps for the Sep 4th earthquake and below it the February 22nd earthquake that I found on the GeoNet website (click on the image to see the full images at the GNS website):

PGA values for Darfield September 4th, 2010 earthquake; map from GNS GeoNet website (cropped, with legend moved)
PGA values for Darfield September 4th, 2010 earthquake; map from GNS GeoNet website (cropped, with legend moved)
PGA values for Lyttelton Feb 22nd, 2011 earthquake; map from GNS GeoNet website (cropped, with legend moved)
PGA values for Lyttelton Feb 22nd, 2011 earthquake; map from GNS GeoNet website (cropped, with legend moved)

These maps show the peak ground acceleration at particular points (coloured boxes), with a few landscape features sketched in. The black lines are coastlines and rivers, the red lines roads. The CBD is roughly the area of the right-hand half of that bounded by the two red lines (roads) at 90˚ to each other at the upper-left of the sections of the maps I’ve shown.

In the February 22nd earthquake the central business district (CBD), perhaps the part of the city with the largest group of vulnerable buildings, experienced a little shy of three times the ground acceleration it did in the larger magnitude September 4th event.

Earthquakes don’t just shake things sideways they toss them upwards too, like my uncle’s bath. Things that go up have to come back down; not everything is built to take that well. As Dr Hamish Campbell of GNS Science is quoted as having said:

“’No wonder so many stone churches were destroyed. They are simply not designed to be thrown up in the air and then go into freefall.’

The peak ground acceleration values in the CBD range roughly 18-28% of gravity’s acceleration in the CBD for the September 4th event. In the February 22nd event, the same area experienced a peak ground acceleration of 57-80% of gravity’s acceleration. (100%g is the same acceleration as gravity.)

The largest peak ground acceleration was recorded near Heathcote Valley Primary School: 220 %g, a little over twice the acceleration of gravity. This is apparently the highest ever recorded in New Zealand.

Aimee has written pointing to one possible cause of the particularly strong shaking observed: echoing from underlying basaltic rock. One good early summary of possible contributing factors is at The Landslide Blog. In time we’ll see more detailed accounts of precisely why this earthquake packed such a punch.

(* [Added later] It is the change in speed (acceleration) that you feel, not speed itself. Similarly, to travel upwards you need to accelerate against gravity.)

Update (2nd March 2011): Architect and fellow science blogger Ken Collins has written about ground acceleration in terms of effects on buildings and the building standards. Recommended reading. (At the very end he lets slip that he is another Blackadder fan!)

(Updated 7th March: corrected error in date.)


Other articles on Code for Life:

6.3 earthquake in Christchurch

Finding platypus venom

On alternatives to academic careers and “letting go”

Autism – looking for parent-of-origin effects

Capturing bodies – medical imaging data


25 Responses to “Lyttelton earthquake peak ground acceleration”

  • If any readers are curious about the direction of the acceleration reported in the PGA values shown on these maps GeoNet has told me, in their words:

    “PGA is made up of the vertical and two horizontal components.  For the images you are inquiring about, we report the MAXIMUM of these.”

    The up-shot is the acceleration values reported on the maps I’ve shown are either in vertical or horizontal directions.

    No promises, but If I’ve time (and it looks sensible to present them) I’ll might try dig out the vertical v. horizontal components out of their data.

  • Wow! 2.2Gs! If that was the highest of horizontal OR Vertical, what was the total force vector in the direction of movement!?

    I mean if it were say 2Gs vertical plus 2.2Gs horizontal, that would be 3G at a 42 degree angle to the ground.

  • Hi Bruce,

    I’m not a geologist, but I was struck by it too.

    Thanks for the wikipedia link. I was aware of the Kobe figure (0.8g), but not the 1994 California one (1.7g).

    I’m guessing that the highest of the values are more-or-less in the direction of the axes recorded; might motivate me to check! Been busy programming or distracted by the many conversations around here lately.

  • Interesting info on accelerations. These are obviously important wrt the loading on a structure, however, there is a lot more to how a given structure will respond to a particular event than just max acceleration. For example, if the foundations experince differntial movement due to ground displacement that can impose an addiitonal and very significant load to the actual seismic accelerations. If the structure is eccentric in shape or stiffness, then additional torsional loads can also occur as it responds to the ground acceleration differntially.

    The earthquake spectra (acceleration and direction vs time) is also important, especially if this happens to co-incide with the struture’s own “natural” frequency. As an example of how this works, take a flexible stick around 1m long and by holding it rigidly vertical but moving the base set it oscillating backwards and forwards. To get the swaying to magnify, (and eventually break the stick), the frequencies of the motion and the sticks natural swaying must be the similar.

    Typically earthquake sprectra have frequencies at peak ground acceleration of fractions of a second which means they develop a resonance and possible magnification with only very short stiff buildings. Mutistorey framed buidings usually have much longer “natural” frequencies than this. Try shaking the base of the stick really fast – nothing much happens. The plots I have seen of this earthquake however, which is influenced by the ground conditions where the seismometer is loacted for a given plot – well exceeded the “standard” design spectra at all frequencies – “something for everyone”.

    Modern reinforced concrete multistorey buildings are now designed to not only withstand a given seimic load in an elastic manner, (without failing), but when that load is exceeded they are designed to go post elastic (fail), in manner whereby the failure occurs in designated areas, so for example beams are designed to fail rather than columns to avoid the “soft storey” mechanism whereby a complete storey collapses to create a sandwich.

    A question I would like to see answered of the more modern building is not so much why did it fail, but rather why did it fail in such a catastrophic fashion.

  • Hi Stu,

    Thanks for your detailed comment!

    My rather simple post was just meant to highlight a difference in the September 4th and February earthquakes that might give a general reader a glimpse of why a lower magnitude earthquake had a higher impact.

    I’m sure a lot of people would like the answer to your question. I’m afraid I can’t help you as it’s well outside my knowledge and given the public interest in it I’d be cautious about speculating.

    I believe a Royal Commission Enquiry has been initiated to investigate the building collapses. These things take ages (!), so I wouldn’t be expecting a formal response any time soon.

    Your writing about resonance on structures reminds me of of the popular (but apparently disputed) example of army soldiers marching in time across (suspension) bridges e.g. the collapse of the Angers Bridge in France:

    http://en.wikipedia.org/wiki/Angers_Bridge

    It’s practice to ask the soldiers to march out of step as a result. The Millennium Bridge across the Thames had a related problem in 2000.

    (Now you’re reminded me of that story, it’s almost worth a blog post!)

  • Stu said….
    The earthquake spectra (acceleration and direction vs time) is also important, especially if this happens to co-incide with the struture’s own “natural” frequency. As an example of how this works, take a flexible stick around 1m long and by holding it rigidly vertical but moving the base set it oscillating backwards and forwards. To get the swaying to magnify, (and eventually break the stick), the frequencies of the motion and the sticks natural swaying must be the similar.

    Stu, I think that everyday familiar example of structure’s resonant frequencies (SHM – simple harmonic motion) to readers here is the swingsets from children’s playground. Once can observe a child on a swingset at a playground, rising up & lowering down him/herself (while standing) on a swing. If the frequency of the rising/lowering matches the natural frequency of the swing (pendulum) itself, then the child will experience a maximum point in his/her swinging.

    The swing (pendulum) itself, absorbs energy from the swinger (child) therefore it propels the swingset to the possible maximum/highest point. When the rising/lowering frequency doesn’t match the natural frequency of the swing, then the child swinger will not experience/reach the maximum point during his/her swing. We all experience this when we were kids.

  • Grant, the resonant in bridge structure is best demonstrated by the collapse of the Tacoma bridge in the US in 1940. It is being captured here on film (watch it on Youtube).

    “Tacoma Narrows Bridge Collapse”

    Every introduction Physics textbook in kinematics quoted the Tacoma bridge as an example of SHM (simple harmonic motion), where the wind-speed frequency matches the bridge’s structural natural frequency, therefore the bridge kept absorbing energy from the wind which lead to increased amplitude of its oscillation. At a certain point in time, the bridge structure couldn’t withstand this large amplitude swing, leading to breakage.

    I read somewhere else online that the collapse of the Tacoma bridge wasn’t an SMH phenomena.

  • Tacoma Narrows is apprently attributed to aerodynamic flutter, but my reading of that is that its still a case of sympathetic and magnified motion between the intitiating force, (wind), and the structure. Just in the case of aerodynamic flutter its not the wind force surging, (as with earthquake ground motion spectra), which creates the dynamic loading, its the structure’s respose to the wind. So the wind blows, the bridge flexes accross the deck, the bigger surface area catches more wind and flexes more in a cyclic fashion. Still same deal.

  • Does any one know if PGA has been recorded higher than this elsewhere in the world? Or how high the highest is?

  • I don’t know the answer to your question, but as an aside more entries have been added to the wikipedia page on peak ground acceleration. (And as an aside to my aside (!), it’s good practice to cross-check what’s on wikipedia: I’ve seen junk there.)

    http://en.wikipedia.org/wiki/Peak_ground_acceleration

    Among those listed are the Sendai magnitude 8.9 earthquake (now M=9.0, apparently), which they’ve listed a PGA of 0.35g. The 2.2g PGA from the Lyttelton earthquake remains the highest on that table. It’s possible that may not mean much if, for example, large earthquakes in, say, the Himalayas or Indonesia, the Aleutian Islands, etc., haven’t been recorded or recorded only partially. I also worry if there can be artefacts in how these are recorded. We’d need a geologist to fill us in.

  • Following comments on Ken Collins’ blog, it appears that the PGA values for the 2011 Sendai earthquake have been revised both at the USGS and the wikipedia entry I linked to in my previous comment.

    The wikipedia entry now offers 2.7g (single direction) and 2.99 (vector sum) PGAs for the 2011 Sendai earthquake. The page offers more background detail that it did at the time of writing my previous comment.

    This table now also reports a whopping 4.36 vector sum PGA for the 2008 Iwate-Miyagi Nairiku earthquake (magnitude 6.9/7.2), which perhaps belatedly answers Dani’s question.

    Taking nothing away from wikipedia: it’s a good source of leads, but what is reported there ought to verified against original sources – hence the wording of my previous comment. I haven’t time to revisit the USGS sources (and don’t know Japanese to tackle the Japanese sources!) – readers are welcome to fill this in if so inclined.

    I think I’m not alone in having a (minor) gripe with reports relying overly on magnitude rather than intensity measures (i.e. impact at a particular area on the ground) to convey the import of an earthquake. I pointed to a geologist writing about this March 2010.

  • Hi
    I am interested in knowing whether land settlement can be worked out from these PGA figures.

  • Hi Vivienne,

    I’m not a geologist, so I really couldn’t give you an answer. I suspect (I’m guessing*) they can’t and that even if the PGA values could be used that they are extremely local and so couldn’t be applied more than a modest distance from their location.

    (* for example, they are a maximum acceleration in the movements that occurred, not the overall shaking over time. I imagine the overall activity matters, as well as details about the soil and whatnot — all of which I know pretty much nothing about.)

    In another post I showed a map of vertical land movement before and after the main earthquakes taken from measurements from a satellite: http://sciblogs.co.nz/code-for-life/2011/03/08/christchurch-lyttelton-earthquake-ground-movement-captured-by-satellite-imagery/ Again, you’d really want input from a geologist, not me. (My guess is that settlement is localised and wants on-the-ground measurements. But that’s ‘common sense’, with all the trouble that gets you in!)

    While I’m writing, there is another map that gives the vertical and horizontal accelerations separately: http://sciblogs.co.nz/code-for-life/2011/06/29/christchurch-earthquake-buildings-and-acceleration-maps/

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