Category Archives: earthquakes

posts tagged with “earthquakes” are related to the discussion of events we recorded.

A jupyter notebook to illustrate earthquake location

The  “textbook” method to estimate the epicentre of an earthquake is based on the arrival time difference between the primary and secondary seismic wave. From this time difference, we can estimated the distance from the station to the earthquake; in other words, from a single station, we know the earthquake happened anywhere on a circle centered on the station, where the radius is the estimated epicentral distance. The intersection of at least three station’s circles provides an estimate of the epicentre.

circles centered on each seismic station represent the epicentral distance to an earthquake. The intersection of all circles is at the epicentre.


But how do we get the radius for each circle? In the figure below, you can see the seismograms from several of the Ru seismic stations for an earthquake near Rotorua, plotted as a function of their distance to Rotorua. The red and blue curves are predicted arrival times for the primary and secondary wave, based on a spherically symmetric earth. We made this figure for a publication in the European Journal of Physics, but the jupyter notebook  that generates these figures is available here.

The distinct arrivals of the primary and secondary wave are matched with the arrival time curves predicted for a spherically symmetric earth.

M5.8, 30 km north-west of Wanaka

On May 4, 2015, at 2:29:10 UTC, an earthquake with magnitude 5.8 occured 30 km north-west of Wanaka.  Most of the TC1 seismometers of the Ru network recorded the resulting seismic waves.  Check out the map below, where the epicentre of the quake is shown as a red dot, and the stations in the Ru network are shown as black triangles.


The records of the earthquake motion are called seismograms.  Each “seismogram” is a record of the velocity of the earth at a particular time.  In the figure below, the seismograms are offset horizontally from the left of the graph.  This offset is the epicentral distance (distance from the epicentre) to each station.  The vertical time scale starts at the origin time of the earthquake.



There are two important things to notice about this figure.  First of all, Hokitika, Rangi-Ruru, and Ashburton museum stations are the closest to the earthquake and have very similar epicentral distances.   Therefore the the earthquake reaches them at close to the same time, and the stations are spaced close together on the horizontal axis.  Also, notice that these seismograms have large amplitudes and overlap each other.  By contrast, the two stations further away, in Auckland, record the earthquake at later times.  The amplitude recorded on these stations is also smaller, which makes sense because seismic waves spread out as they travel greater distances.

To see the waveforms more clearly, here is a simple plot of what all stations recorded.  Note that the vertical scale of the different plots is not consistent from plot to plot:



Also note that these plots do not look the same.  This is the result of path effects.  To begin with, as seismic waves travel through the earth, the earth attenuates (makes smaller) certain frequencies more than others, and which frequencies it attenuates depends upon which path the quake travels.  Since the waves took different paths to make it to our different stations, the recorded earthquakes look different.  But this is only part of the picture.  Notice that at the two stations which are further away, the seismograms are longer.  In addition to the primary wave (the fastest, which arrives first), there are other, slower waves that arrive later.  The further a station is from the epicentre, the longer it takes for all the waves to arrive, and therefore the recorded quake is longer.

And lastly, here’s a seismic section with data from our Taupo station included.  As you can see, it looks like the earthquake arrives a bit before it should.  The computer clock for this station was not accurate, which shows how important it is for professional seismologists to make sure their clocks are set right! (of course we at Ru understand that’s not always possible with the equipment we provide you).


Thank you to all the station managers who sent me data!  If you haven’t yet sent me your data, please do, and I can update the figures!

M6.5, 155 km east of Te Araroa

On November 16 2014, at 22:33:17 (UTC), an earthquake with magnitude 6.5 occurred some  155 km east of Te Araroa:
The stations of the Ru network recorded the resulting seismic waves, displayed  in the figure below. The so-called “seismogram” for each station shows the propagation of the vibrations caused by the quake:
The horizontal position of each seismogram represents the distance from the epicentre to each station. The vertical time scale starts at the origin time of the earthquake.

Black triangles indicate the location of the Ru stations. The red circle is the epicentre of the M6.5 earthquake. Click on the figure to see a larger version.

For example, it takes roughly 180 seconds for the first seismic wave to get to station kkvc1 in Kaikoria Valley, some 1200 km from the epicentre. This means the average speed of this primary (or P-)wave is 6.7 km/s! Over this relatively short distances,  you can almost draw a straight line through the onsets of energy on each seismogram, showing that the wave speed varies only by per cents  in the subsurface under our network.

Seismograms of each Ru station, organised by distance from the Earthquake. Click on the image to enlarge.

Also, notice how the seismograms change from station to station. For the close ones, the waves are bunched up in a relatively short time span, whereas for those stations with a greater epicentral distance, the “wave train” is longer.  It turns out that in addition to the primary wave, there are other, slower, waves in this wave train. These include secondary (or S-)waves, and surface waves.

Finally, we should mention that the amplitudes of each seismogram are equalised to show the arrival times the clearest.  In reality, the vibrations recorded closer the epicentre are much larger than those farther away.


M6.3 earthquake, 15 km east of Eketahuna


In the Science Centre of the City Campus of the University of Auckland we record seismic waves with the TC1 seismometer. Routinely, our station AUCK records seismic waves from earthquakes in New Zealand and beyond. On January 20th, 2014, an earthquake occurred on the South side of the North Island, 15 km east of Ekatahuna. Here is a map of the epicentre, our station location, and the great-circle path between them.




On the left you can see 10 minutes of recordings, starting at the origin time of this earthquake. The green marker annotated with a Pn is the predicted arrival of the first wave traveling 4 degrees from the epicentre, 15 km east of Eketahuna, to Auckland. This prediction is based on a spherically symmetric model of the Earth, by Brian Kennett, and certainly seems to mark the start of minutes of vibrations in Auckland from this earthquake. In fact, if you look carefully you see that the wiggles after 10 minutes are still larger than before the first wave from this earthquake arrived. Larger earthquakes can make the Earth “ring” for many hours.

In the image on the right, we zoomed in on the first-arriving wave, almost exactly one minute after the earthquake originated. Now, you can see that the prediction is actually a few seconds before the arrival. This means the lithosphere under the North Island of New Zealand is a bit slower (~3% on this path) than the average on Earth. In general, a hotter lithosphere is slower than a cold one. This makes seismic waves traversing old, cold, continents relatively fast, and those sampling younger lithosphere like ours in New Zealand, relatively slow.

In general, it is these small travel time differences that provide images of the (deep) earth through a process called seismic tomography.

A deep earthquake on the eastern margin of the Australian plate

Recently, we recorded seismic waves on our station AUCK from an Earthquake roughly 11 degrees to our North. This event is characterized by a strong P- and S-wave arrival as you can see in this figure:


Given the usual limitations of our (vertical) sensor when it comes to S-wave recordings, this is indicative of a very deep earthquake. The USGS estimates that this earthquake happened at a depth of 460 km. Now, under most places on Earth the rocks at those depths are too ductile to support the brittle breaking necessary for an earthquake, but in this case, the earthquake happened in — or on the boundary of — the brittle Pacific Plate subducted under the Australian Plate. Note that the epicentre of this event is about 500 km from the surface expression of the boundary between these plates. From the depth of the event and the offset to the plate boundary at the surface, we can estimate the angle of subduction may be around 45 degrees.


The P- and S-wave markers are based on the average wave speed in the earth. In this case, they are a bit earlier than expected, because the subsurface between earthquake and the AUCK recording station is slower than average. As discussed previously, this is indicative of a young, warmer (and thus slower) lithosphere.

Furthermore, such deep earthquakes cause relatively little surface wave energy. The signal after the S-waves is likely a guided wave in the Pacific plate called a “leaky mode.” If you want to learn more about leaky modes in the Kermadecs, you should read this paper.