Geoscience Reference
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JAMSTEC (http://www.jamstec.go.jp/). Since the pressure sensors are located on
the continental slope, the depths of the ocean at the sites, where they are established,
undergo noticeable changes within a single step of the ETOPO2 net. To estimate
the possible error in determining depths, the minimum and maximum depths were
calculated inside the square 2
2 angular minutes with the centre at the point, where
the sensor was established. The horizontal size of the square approximately corre-
sponds to the depth of the ocean in the area considered, which can be considered
an additional physical substantiation of the expedience of the choice of dimensions
of the square. As a result, the following values were obtained: H PG 1
×
min = 2 , 256 m,
H PG 1
max = 2 , 578 m and H PG 2
min = 2 , 170 m, H PG 2
max = 2 , 300 m. To estimate the error, re-
lated to values of the speed of sound, we assumed that it can vary within limits,
known in marine acoustics, from c min = 1 , 480 m/s up to c max = 1 , 545 m/s.
From the values of depths and velocities, determined by the aforementioned
method, calculations were performed of the ranges limited by the values
PGi
ν
0min =
c min 4 H PGi
0max = c max 4 H PGi
PGi
min . The maxima of the spectra, related to elastic
oscillations of the water column, must lie precisely within these ranges. In Fig. 3.16
the ranges are shown by thin horizontal lines. We immediately note that variations
of the near-bottom pressure occur at frequencies that correspond quite well to the-
oretically calculated ranges. This fact is evident that the sensors recorded elastic
oscillations of the water column. But if we mention the exact positions of the main
maxima of the observed spectra, they are seen to lie somewhat more to the left, than
predicted by the theory. The shift of maxima towards low frequencies is explained
by the acoustic base in the region dealt with being located under a powerful sedi-
mentary layer. Therefore, for theoretical calculation of the position of the maxima of
the spectra, it is expedient to consider not simply elastic oscillations of the water
column on an absolutely rigid bottom, but the related oscillations of two columns:
the water column with its free surface and the underlying sedimentary layer with its
rigid lower boundary. For such a two-column system the set of normal frequencies
γ
max and
ν
is determined from the following transcendental equation:
tan 2
tan 2
= ρ s c s
ρ
πγ
H
πγ
H s
c s
,
c
c
where H s is the thickness of the sedimentary layer, c s is the velocity of elastic lon-
gitudinal waves in the sedimentary layer,
ρ s is the density of the sedimentary layer.
According to the database of properties of sedimentary rock (http://mahi.ucsd.
edu/Gabi/sediment.html), the thickness of the sedimentary layer in the region con-
sidered, the velocity of longitudinal waves and the density of sediments vary within
the following respective limits: 47 m-2 km, 1.74-2.3 km/s and 1.816-2.053 g/cm 3 .
The space distributions of these characteristics are indicated by numbers in
Fig. 3.13. It is seen that the possible variations in the velocity of longitudinal
waves and in the density are insignificant, while the thickness of the sedimentary
layer can change by more than an order of magnitude. Therefore, in calculating
the value of the minimal normal frequency
γ
0 we took into account the uncertainty,
due to the thickness of the sedimentary layer, while the velocity of longitudinal
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