1. SEA WAVES AND LONG PERIOD VERTICAL SEISMOMETERS
Lorenzo Papa
Marina Pizzo
Istituto Idrografico della Marina
University of Genoa, Dept. of Physics, Italy
Genoa
14th –18th November 2006

2. The measurement of sea waves is of great interest in many environmental projects as:
the design of coastal structures
the harbour planning
the shoreline protection
predicting coastal vulnerability and map risk
Surf wave coast effects and deep water standing oscillations produce, according to the Longuet- Higgins’ theory (1950), primary microseism waves with the same dominant period as sea surface waves and secondary microseisms which have half this period

3. Longuet-Higgins’ theory
The stationary wave profile at the depth h, in Lamb’s notation, is given by:
For stationary waves (without compressibility) we have a dynamic pressure p:
where: a is the wave amplitude
w is the angular frequency
k is the wave number
r is the water density
h = a cos(kx) cos(w t) + O(a3)
p(t) = r a 2 w 2 cos 2(2w t)

4. The Physics Department of the University of Genoa uses
a long-period vertical seismometer (Teledyne Geotech, model SL210)
and
a prototype of variable capacitance accelerometer
to compute in real time the sea wave spectrum in the Gulf of Genoa

5. The SL-210 instrument operates on the moving-coil principle and has a natural period that can be adjusted from 10 to 30 seconds.
It employs a sensitive electromechanical transducer that converts long-period vertical motion into electrical output
This seismometer has been installed in 1989
The sampling time is 0.5 seconds
The power spectrum is computed serially on a buffer of 600 data (sampling window) by the FFT algorithm

6. A = electrode area
e = permittivity of air
X = internal sensing
element displacement
d = distance between
internal sensing
element and electrode
S = internal sensing
element
a = applied acceleration
It measures ground vertical accelerations caused by coastal sea waves. The variable capacitance accelerometer operates on a technique where the condenser capacitance (C ) of the internal sensing element (S ) changes in proportion to the vertical applied acceleration (a)

7. A coastal area can be studied with the following steps:
Monitoring of the environmental conditions
Database and computer graphic
Numerical models for the real time control of
the system
Mathematical and statistical algorithms for
forecasting of meteo-marine parameters

8. Gulf of Genoa – database
3806 mean daily values of significant wave height (HS)

9. 44 mean daily values of significant wave height (HS)
Example of a storm
44 mean daily values of significant wave height (HS)

10. Pattern matching for sea wave forecast
Pattern matching is a statistical technique (model free) used to check if a sample pattern finds relevant similarities in the whole historical database.
The comparison of the “sample pattern” with the “historical ones” is carried out by means of an algorithm that minimizes the standard deviation. When the historic pattern that matches the sample data has been selected, the time values of the following window are identified with the required forecast.

11. 10 days