Geoscience Reference
In-Depth Information
Figure 4.8.
A map showing the location of seismometers 1, 2 and 3.
The earthquake focus is at distances
r
1
from seismometer 1,
r
2
from
seismometer 2 and
r
3
from seismometer 3 (
r
1
,
r
2
and
r
3
are given by
Eqs. (4.9)). The focus can be located by drawing an arc of a circle of
radius
r
1
about seismometer 1 and then repeating this for
seismometers 2 and 3 (radii
r
2
and
r
3
, respectively). The point at
which the three arcs intersect is the focus.
arc radius r
1
arc radius r
3
arc radius r
2
Seismometer 1
Seismometer 2
Seismometer 3
is a fourth unknown, the focal depth: earthquakes do not conveniently occur at
the surface. Errors in arrival times have to be allowed for. In practice, therefore,
several seismometers are required in order to locate an earthquake. Locations
are routinely calculated using as many travel times from as many stations as
possible. The distance between the epicentre and the seismometer is called the
epicentral distance
. The shortest distance on the surface of a sphere between
any two points on the sphere is along the great circle which intersects the two
points. The epicentral distance is therefore the length of this great-circle arc and
is usually quoted in degrees (except for local earthquake studies, in which case
it would be quoted in kilometres).
With a measurement of
t
s
−
p
at any seismic station it is possible to make an
initial estimate of the epicentral distance by using a compilation of the global
travel times (Fig. 4.16). For example, when
t
s
−
p
is 3 min the epicentral distance
is about 16
◦
(1800 km), whereas when
t
s
−
p
is 5 min the epicentral distance is 30
◦
(3300 km).
Focal depths can also be determined from measurement of the difference in
travel time between the P phase and the pP phase (pP denotes a P-wave reflected
at the Earth's surface in the vicinity of the earthquake, as in Fig. 4.9). The P phase
travels along path FS and has arrival time
t
P
,whereas the pP phase travels along
path FRS and arrives at time
t
pP
.Atteleseismic distances FR is small compared
with FS; so, to a first approximation, the length FR is given by
2
(
t
pP
−
t
P
)
FR
=
(4.10)
For shear waves (using phases sS and S), the corresponding distance would be
2
(
t
sS
−
t
S
)
FR
=
(4.11)
The focal depth
h
is then given by
h
=
EF
=
FR sin
θ
(4.12)
In practice, travel times of all the earthquake wave phases are tabulated: The
Jeffreys-Bullen
(1988) tables (often called J-B tables and shown graphically
in Fig. 4.16) are probably the most complete (they are a revision of the first
