Geoscience Reference
In-Depth Information
Eq. (8.23) can be written
A
=
A
0
e
−
π
t
/
(
QT
)
(8.24)
or
A
=
A
0
e
−
ω
t
/
(2
Q
)
where
is the angular frequency and
A
0
the amplitude of the wave time
t
ago.
By performing similar calculations on the spatial form of Eq. (8.21), one obtains
ω
A
0
e
−
π
x
/
(
Q
λ
)
A
=
(8.25)
where
x
is the distance travelled by the wave from the point at which it had
amplitude
A
0
, and
is the wavelength. Thus, after one allows for geometrical
spreading,
Q
can be estimated by taking the ratio of the amplitudes of a body
wave of a particular frequency at various distances or times. The quality fac-
tor determined by using Eqs. (8.24) and (8.25)isfor one particular wave type
(P or S) only.
Q
for P-waves,
Q
p
,ishigher than
Q
for S-waves,
Q
s
;ingeneral
Q
p
is approximately twice
Q
s
.Figure 8.5 shows the variation of
Q
p
, and
Q
s
within
the Earth.
λ
8.1.4 The three-dimensional structure of the Earth
Much more detailed velocity models of the mantle can be obtained by using
seismic tomography, a technique similar in method to the whole-body scan-
ning method used by medical physicists. The technique requires a network
of digital seismic stations. The number of such stations (compared with the
WWSSN) meant that the method was previously not capable of resolving struc-
tures in the Earth on a horizontal scale of less than about 1500 km and a
vertical scale of about 200 km. This has now changed with the establishment
of digital seismographic networks. First, the travel times, phase and/or group
velocities and/or waveforms are measured for hundreds of earthquakes and
recording stations. A best-fitting three-dimensional model of the velocity struc-
ture of the mantle is then constructed; the methods are varied and complex
and are summarized in Romanowicz (1991) and Ritzwoler and Lively (1995).
There are several current tomographic models of the mantle, each determined
using differing seismic phases, methods and approximations. There is, how-
ever, general agreement amongst them on the broad structure of the mantle
(http://mahi.ucsd.edu/Gabi/rem.html). Figures 8.6(a) and (b) (Plates 9 and 10)
show perturbations of an S-wave velocity from a one-dimensional standard Earth
structure. The model comprises eighteen layers of thickness
∼
100 km in the upper
mantle and 200 km in the lower mantle, each with an equal surface area (4
◦
×
4
◦
at the equator). The long-wavelength velocity perturbations that can be seen in
