Calculating Depths of Deep Earthquakes

N.Z. Version, 1998

The depth to very deep earthquakes is usually established by measuring the difference in arrival time of the P and pP wave. This is something you can do yourself with a bit of practice. You may be able to discover the deepest earthquake known so far! The best estimate for the deepest known earthquake is 684 km deep, under the Fiji Islands in the Southwest Pacific, on June 17, 1977. How do you go about this? First learn to recognize the pP wave. It has very much the same shape as the P wave (it reflects from the Earth's surface, very much like a reflection in a mirror, before going on its journey to the seismic station). Hint: sometimes it is much easier to see the pP and P similarity when you transform the seismogram to displacement rather than velocity. This is because pP spends more time in the "syrupy" upper mantle above the earthquake, where it looses some of the high frequencies (little wiggles).

We provide some selected pairs of P and pP waves from the Global Seismograph Network, presented in the following figure, for you to work through; NOTE: evdistgc is the epicentral distance along the great circle arc (ie; the angular distnce from the epicenter to the station).

Station	Date	evdistgc	P-pP time (sec)
ABKT	22 Aug 96	75.2	130
FFC	30 Nov 95	66.0	49
OBN	16 Mar 96	73.2	110

We measured the distance between the peaks of P and pP after transforming the record from ground velocity to ground displacement. You could also try to measure the difference between the onsets of the waves if these are not obscured by noise.

The next step is to translate the time difference between the arrivals of P and pP into the depth of the earthquake. You can use figure 1 below to do that. The figure shows the relationship between the epicentral distance, X-axis, and the time between the arrival of pP and P, Y-axis, for a range of depths (contours for 100km, 200km,...,800km depths).

To find out where your measurement should be plotted on the figure, first find the epicentral distance for the event along the X-axis. For example, the event recorded at station ABKT has epicentral distance of 75.2 degrees. You can draw a vertical line on the graph for this epicentral distance. Then, find the P-pP time (in seconds) you estimated on the Y-axis of the plot, and draw a horizontal line on the plot. In our example for ABKT, P-pP time is 130 seconds. The place on your graph where the vertical and horizontal lines you drew meet, gives you an estimate of the earthquake depth. For station ABKT, they meet almost midway between the 600 and 700 km contours on the plot, so you would conclude that the depth of this event is about 650 km. You can try to get a more precise estimate by using a ruler to measure how far away from the 600 km contour line your lines meet, relative to the total distance between the 600 and 700 km contours.
Another example, if your station is 70 degrees away from the epicenter, and you measure a time difference of 113 seconds, you are right in between the graphs for 500 and 600 km, so your estimate should be 550 km.

Once you have estimated the depth of the earthquake, ask yourself the question: "Is the depth I estimated realistic, given the geological features of the earthquake location?" Try to give arguments for why you think the estimate is correct, or what problems might be with it.

You can compare your results with the 'official ones', estimated by the National Earthquake Information Center (NEIC):

Station	Date	Depth (km)
ABKT	22 Aug 96	596
FFC	30 Nov 95	137
OBN	16 Mar 96	477

If you have large differences with the figures from NEIC, it is because NEIC did not use pP in establishing the depth, but their regular automated method. Using pP is generally thought to give more reliable depths.

Now that you know how to calculate the depth of deep earthquakes, you are ready for some original research! Try Research Idea #4 within the set of Research Ideas on Deep Earthquakes. Remember that this method will only work for earthquakes with hypocenters deeper than about 100 km, so events at subduction zones are the best candidates.

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