Geoscience Reference
In-Depth Information
Table 8.1
Volume, mass and density of the Earth
Volume
Mass
(10
18
m
3
)
10
21
Density
a
(10
3
kg m
−3
)
Depth (km)
Radius (km)
(%)
kg
(%)
Crust
0-Moho
Moho-6371
10
0.9
28
0.5
2.60-2.90
Upper mantle
Moho-670
5701-Moho
297
27.4
1064
17.8
3.38-3.99
Lower mantle
670-2891
3480-5701
600
55.4
2940
49.2
4.38-5.56
Outer core
2891-5150
1221-3480
169
15.6
1841
30.8
9.90-12.16
Inner core
5150-6371
0-1221
8
0.7
102
1.7
12.76-13.08
Whole Earth
0-6371
6371-0
1083
100
5975
100
a
After Dziewonski and Anderson (1981).
constitutes only 0.5% of the total by volume and 0.3% by mass. Uncertainty
increases with depth and mass.
8.1.3 Attenuation of seismic waves
In a perfectly elastic medium no elastic energy would be lost during the passage
of a seismic wave. However, in practice the Earth is not perfectly elastic, and
some energy is dissipated (i.e., turned into heat) as a seismic wave passes. The
amount of energy lost as a seismic wave passes through any medium is used to
define a parameter
Q
for that medium. The
quality factor Q
is defined as
2
π
×
elastic energy stored in the wave
energy lost in one cycle or wavelength
Q
=−
(8.21)
Thus, for a perfectly elastic material
Q
is infinite, whereas for a totally dissipative
medium
Q
is zero. A highly attenuative region in the Earth is often referred to as
alow-
Q
region.
Equation (8.21) can be written in differential form as
2
π
E
T
d
E
/
d
t
Q
=−
d
E
d
t
=−
2
π
E
QT
(8.22)
where
E
is energy,
t
time and
T
the period of the seismic wave. Integrating
Eq. (8.22)gives
E
=
E
0
e
−
2
π
t
/
(
QT
)
(8.23)
where
E
0
was the energy of the wave time
t
ago. Alternatively, since the amplitude
of the wave
A
is proportional to the square root of its energy
E
(Section 4.2.6),
