At 8:33 pm GMT on 23 June 2001, an earthquake of magnitude 8.1 rocked the west coast of Peru and generated a tsunami that raced across the Pacific Ocean at an average speed of about 500 km/h, reaching the New Zealand mainland coast 16.5 hours later. The figure below shows the view from a satellite of the shortest propagation path.
The tsunami was picked up by several sea-level recorders on New Zealand’s eastern seaboard, including Sumner Head, near Christchurch. The plot below shows the sea-level record from Sumner Head after the tide has been removed. You can plainly see the arrival of the tsunami at about 16.5 h, when wave activity suddenly increased. However, the signal of the tsunami looks like random noise, with no discernible pattern.
To examine the structure of the tsunami, we decompose the signal into its various timescales using orthogonal wavelets. To do this, we fit a “mother wavelet” to the signal at various levels of magnification, just like using a microscope. In fact, wavelet analysis has been called a “mathematical microscope”. Below is the mother wavelet used for analysis of tsunami. It is called Daubechies No 5 after its inventor, Ingrid Daubechies, a pioneer in wavelet analysis methods. There are hundreds of mother wavelets. We have chosen this one because it looks like what we expect a tsunami to look like after it has propagated many thousands of km across the Pacific, namely a leading large wave, followed by an oscillatory tail.
The figure below shows the tsunami split up into its 7 wavelet “details”. Each detail is the contribution of the tsunami at a particular timescale. If you add all these up, you will get back the original signal. The timescale in minutes is in parentheses to the right. Thus, the top plot shows the contribution at 128-minute timescale. We see that even before the tsunami arrived, the sea was fluctuating at the 128-minute timescale by ± 50 mm. This is the ubiquitous Pegasus Bay seiche, driven by tide and weather systems as they propagate over the continental shelf and in to Pegasus Bay. These cause the bay to oscillate at its natural period (called a seiche). When the tsunami arrived, it also excited the seiche, but only for two oscillations before sea level resumed the oscillations that were present before the tsunami arrived. This is an important result that could only have been discerned using a method like wavelet analysis. It tells us that in Pegasus Bay, energy in the 128-minute timescale of a tsunami will be amplified, but there will be only one or two oscillations before they disappear. At lower timescales, we see quite different effects. For a start, they do not dissipate very quickly and most appear to have almost the same amplitude at 60 h that they do at 16.5 when the tsunami arrived, indicating that the tsunami made the whole southern Pacific Ocean oscillate for days.
You can find more details about this subject in:
Goring, D. G. 2002: The response of New Zealand waters to the Peru tsunami of 23-June-2001. New Zealand Journal of Marine and Freshwater Research 36: 225-232.
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Last Updated: 17 November 2003
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