Civil Engineering Reference
In-Depth Information
Table 1.2
Velocity of primary (P) and secondary (S) waves in Earth's layer.
Layer (type)
Depth (km)
P - waves (km/s)
S - waves (km/s)
Crust
10 - 30
6.57
3.82
40
8.12
4.42
Upper mantle
220
8.06
4.35
400
9.13
5.22
670
10.75
5.95
Lower mantle
1,200
11.78
6.52
2,885
13.72
7.26
2,890
8.06
0.00
Outer core
3,800
9.31
0.00
5,150
10.36
0.00
Inner core
5,155
11.03
3.50
6,371
11.26
3.67
vv
vv
t
PS
Δ
x
=
Δ
(1.3.1)
−
PS
thus, if the wave velocities
v
P
and
v
S
are known, the distance
x
is readily evaluated. Velocities of P-
and S-waves in the Earth's interior layers are given in Table 1.2. For a quick evaluation, Omori' s formula
may also be used (Kanai, 1983 ):
Δ
Δ
x
≈ 742
.
Δ
t
(1.3.2)
with
t
expressed in kilometres and seconds, respectively. Equation (1.3.2) assumes that body
wave velocities are almost constant within a limited area. A comparison between the coeffi cient ' 7.42 '
used by Omori in equation (1.3.2) , the coeffi cients that are computed by using the fi rst term on the
right-hand side in equation (1.3.1), and the values of
v
P
and
v
S
given in Table 1.2 is provided in Figure
1.10. It is proposed to make use of a step-function to take into consideration the variability of the body
wave velocities in the Earth's interior. The suggested coeffi cients for equation (1.3.2) are 9.43 and
13.88, for depths below and above 300 km, respectively.
The procedure to locate an earthquake epicentre and origin time, i.e. time of initiating of fault rupture,
is as follows:
Δ
x
and
Δ
(a) Obtain seismogram records for a given observation site.
(b) Select the arrival time of the body waves on the record traces.
(c) Compute the time delay
Δ
t
in the arrival of P- and S - waves.
(d) Subtract the travel time
Δ
t
from the arrival time at the observation site to obtain the origin
time.
(e) Use equations (1.3.1) or (1.3.2) to evaluate the distance
x
between the seismic station and the
epicentre. The use of either equations (1.3.1) or (1.3.2) depends on the data available for the soil
profi le and approximation accepted.
(f ) Draw a circle on a map around the station location (or centre) with a radius equal to
Δ
Δ
x
. The
curve plotted shows a series of possible locations for the earthquake epicentre.
(g) Repeat steps (a) to (f ) for a second seismic station. A new circle is drawn; the latter intersects
the circle of the fi rst station at two points.
(h) Repeat steps (a) to (f ) for a third seismic station. It identifi es which of the two previous possible
points is acceptable and corresponds to the earthquake source.
