Introduction to Acoustics

Acoustic-to-seismic coupling ratio (m/s / Pa)
×10 –6
8
7
6
5
4
3
2
1
0
10 2
8 9
Measurement
FFLAGS prediction
10 3
2 3 4 5 6 7 8 9
Frequency (Hz)
Fig. 4.8 Measured and predicted acoustic-to-seismic coupling
ratio for a layered soil (range 3.0 m, source height
0.45 m)
applied. These are
1. Continuity of total normal stress
2. Continuity of normal displacement
3. Continuity of fluid pressure
4. Continuity of tangential stress
5. Continuity of normal fluid displacement
6. Continuity of tangential frame displacement
At an interface between a fluid and the poro-elastic
layer (such as the surface of the ground) the first four
boundary conditions apply.
The resulting equations and those for a greater
number of porous and elastic layers are solved numerically
[4.58].
The spectrum of the ratio between the normal component
of the soil particle velocity at the surface of the
ground and the incident sound pressure, the acoustic-toseismic
coupling ratio or transfer function, is strongly
influenced by discontinuities in the elastic wave properties
within the ground. At frequencies corresponding to
Table 4.1 Ground profile and parameters used in the calculations for Figs. 4.9 and 4.10
Layer Flow resistivity
(kPa s m −2 )
Porosity Thickness
(m)
Sound Propagation in the Atmosphere 4.6 Ground Effects 127
Normalized impedance
P-wave speed
(m/s)
S-wave speed
(m/s)
Damping
1 1 740 0.3 0.5 560 230 0.04
2 1 740 0.3 1.0 220 98 0.02
3 1 740 000 0.01 150 1500 850 0.001
4 1 740 000 0.01 150 1500 354 0.001
5 1 740 000 0.01 Half-space 1500 450 0.001
600
400
200
0
–200
–400
–600
1
10
Real rigid
Real elastic
– Imag. rigid
– Imag. elastic
100
Frequency (Hz)
Fig. 4.9 Predicted surface impedance at a grazing angle of
0.018 ◦ for poro-elastic and rigid porous ground (four-layer
system, Table 4.1)
peaks in the transfer function, there are local maxima in
the transfer of sound energy into the soil [4.78]. These
are associated with constructive interference between
down- and up-going waves within each soil layer. Consequently
there is a relationship between near-surface
layering in soil and the peaks or layer resonances
that appear in the measured acoustic-to-seismic transfer
function spectrum: the lower the frequency of the peak
in the spectrum, the deeper the associated layer. Figure
4.8 shows example measurements and predictions
of the acoustic-to-seismic transfer function spectrum at
the soil surface [4.12]. The measurements were made
using a loudspeaker sound source and a microphone positioned
close to the surface, vertically above a geophone
buried just below the surface of a soil that had a loose
surface layer. Seismic refraction survey measurements
at the same site were used to determine the wave speeds.
The predictions have been made by using a computer
Part A 4.6