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ResearchTsunami Detection Algorithm
Deep-ocean Assessment and Reporting of Tsunamis (DART)
Tsunami Detection Algorithm
Introduction
Each
Deep-ocean Assessment and Reporting of Tsunamis (DART) gauge
is designed to detect and report tsunamis on its own, without
instructions from land. The tsunami detection algorithm in
the gauge's software works by first estimating the amplitudes
of the pressure fluctuations within the tsunami frequency
band and then testing these amplitudes against a threshold
value. The amplitudes are computed by subtracting predicted
pressures from the observations, in which the predictions
closely match the tides and lower frequency fluctuations.
The predictions are updated every 15 seconds, which is the
sampling interval of the DART gauges.
Background
oceanic noise determines the minimum detection threshold.
Based on past observations, a reasonable threshold for the
North Pacific is 3 cm (or 30 mm). If the amplitudes exceed
the threshold, the gauge goes into a rapid reporting mode
to provide detailed information about the tsunami. It remains
in this mode for at least four hours.
Form of the Tsunami Detection Algorithm
The
tides and lower frequency signals are predicted within a few
millimeters using a cubic polynomial that is fit to bottom
pressure observations over the past three hours
3
Hp(t')=
? w(i) H*(t-idt)
i=0
where
the asterisk denotes 10-min averages and dt = 1 hr. The prediction
time t' is set to 5.25 minutes, which is half the 10 minute
averaging interval plus the 15-second sampling interval for
the gauges. The coefficients w(i) come from Newton's formula
(II) for forward extrapolation. Using these temporal parameters,
the w-coefficients are
w(0) = 1.16818457031250
w(1) = -0.28197558593750
w(2) = 0.14689746093750
w(3) = -0.03310644531250
A
tsunami is detected if the difference between the observed
pressure and the prediction Hp exceeds the prescribed threshold
in magnitude (30 mm in the North Pacific).
The
gauges could use the most recent pressure observation to test
against the prediction. However, the next earlier value is
used so that the gauges can screen the pressure values for
instrumental spikes that might falsely trip the algorithm.
The threshold for these spikes is set at 100 mm.
Figure
1.
Theoretical
Pressure Series
Figure
1 shows the application of the algorithm to a theoretical
pressure series. The series consists
of an M2 tide with an amplitude of one meter and a short pulse
that has an amplitude of 5 cm and a duration of 15 minutes.
The pulse affects the difference both directly and through
its indirect effect on the prediction. Following the first
and largest differences, pulses continue to occur each hour
with diminishing amplitude until the pulse no longer influences
the predictions.
The
difference exceeds the threshold at the beginning of the theoretical
series. This is due to the mismatch between the time series
and the constant values placed initially in the H* array.
This phenomenon will also occur during field deployments of
DART gauges as they fall through the water column toward the
bottom.
However,
the difference will stabilize at sub-threshold values 4-5
hours after the gauges reach the bottom. Then, the H* arrays
contain only on-bottom pressure values, and the gauges are
in thermal equilibrium with the bottom waters.
As
shown in Figure 1, a software flag is set to -1 each time
the difference exceeds the threshold. In turn, this exceedance
flag controls a reporting flag that puts the DART gauge into
its rapid reporting mode. The reporting flag is set to -1
as soon as the threshold is exceeded and remains equal to
-1 until four hours has passed since the last time the threshold
was exceeded. The gauge then returns to its monitoring mode.
Figure
2.
Frequency
Response
As
shown in Figure 2, the pressure difference has a response
near unity over the tsunami band, which spans the periods
from 2 to 90 minutes. At lower frequencies, the attenuation
increases rapidly with decreasing frequency. Hence, tsunami
and higher-frequency signals dominate the pressure difference.
Figure 3.
Observed Tsunami
Figure
3 shows small-amplitude tsunamis observed by internally recording
gauges in the North Pacific. Relative to the high-passed data,
the background noise in the difference series is either equal
in amplitude or slightly enhanced. Neither tsunami is high
enough in amplitude to set a DART gauge into rapid reporting
mode.
Figure
4.
Observed
Rayleigh Waves
Figure
4 shows pressure differences observed at an internally recording
pressure gauge in the northern Gulf of Alaska. The two groups
of high-frequency fluctuations are seismic Rayleigh waves
caused by the 1996 Andreanof Island earthquakes in the Alaska-Aleutian
Subduction Zone. The first group was generated by the main
shock, while the second was generated by a smaller aftershock
that occurred about eleven hours later. A DART gauge would
be set into rapid reporting mode by the first group of Rayleigh
waves.
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