Geoscience Reference
In-Depth Information
periods of
3200 s (S mode). Other modes jointly contain
(but not in a simple way) the body-wave phases. Thus the interference pattern
obtained by summing together all the theoretical normal modes and including a
model of a particular earthquake source yields a synthetic seismogram for that
earthquake: these generally compare well with recordings.
∼
2600 s (T mode) and
∼
4.2 Earthquake seismology
4.2.1 Location of earthquakes
The
earthquake focus
or hypocentre is the point in the Earth where the earthquake
nucleated. It is specified by latitude, longitude and depth beneath the surface. The
earthquake epicentre
is the point on the Earth's surface vertically above the focus.
Foranearthquake beneath California, the focus might be at 37
◦
N, 122
◦
W and
10 km depth. The epicentre for this earthquake would be 37
◦
N, 122
◦
W. In fact,
earthquakes do not occur exactly at points; rather the stress releases occur within
small volumes or along fault planes.
Assume that an earthquake occurs at the surface at time
t
0
. There are three
unknowns: time of origin, latitude and longitude. To determine these three
unknowns, we need to know the arrival times of seismic waves at three nearby
seismometers. If the shallow P-wave velocity is
α
and the shallow S-wave veloc-
ity is
, then the time taken for P-waves to travel from the focus to seismometer
1atdistance
r
1
is
r
1
/α
β
. Similarly, the travel time for the S-waves is
r
1
/β
. The
arrival time of P-waves at seismometer 1 is then
t
0
+
r
1
/α
, and the arrival time
of S-waves at seismometer 1 is
t
0
+
. The difference between the P- and
S-wave arrival times at seismometer 1,
t
1
,
S
−
P
,isgivenby
r
1
/β
r
1
β
r
1
α
t
1
,
S
−
P
=
−
(4.8)
α
β
and similarly for seismometers 2 and 3. If we assume values for
,wenow
have three linear equations with three unknowns,
r
1
,
r
2
and
r
3
,which can easily
be solved:
and
r
1
β
r
1
α
t
1
,
S
−
P
=
−
r
2
β
r
2
α
t
2
,
S
−
P
=
−
(4.9)
r
3
α
It would be simplest to solve this simple example graphically by drawing a map
of the area, marking the seismometers and then drawing an arc of a circle of radius
r
1
about seismometer 1, another radius
r
2
about seismometer 2 and another radius
r
3
about seismometer 3. The focus of the earthquake is then at the intersection of
the three arcs (Fig. 4.8).
In reality, things are not quite so simple because the Earth is neither flat nor
homogeneous with globally constant P- and S-wave velocities. In addition, there
r
3
β
t
3
,
S
−
P
=
−
