Geoscience Reference
In-Depth Information
When applying formulae (2.21)-(2.27) in geophysics, one should bear in mind
that the effect of the Earth's curvature is negligible for shallow events at distances of
less than 20
◦
, but that vertical stratification or lateral inhomogeneity can sometimes
considerably influence the deformation field.
For calculation of the bottom deformation the following parameters of the earth-
quake source are necessary: coordinates of the epicentre, the hypocentre depth,
the seismic moment or the moment-magnitude and the strike, dip, rake(slip) angles.
All these parameters are to be found in earthquake catalogues. The geometrical di-
mensions of the fault area (rectangular
L
×
W
) and the dislocation (or mean
|
D
|
) can
be estimated by empirical formulae [Handbook for Tsunami Forecast (2001)]:
log
10
L
[km]=0
.
5
M
w
−
1
.
9
,
log
10
W
[km]=0
.
5
M
w
−
2
.
2
,
(2.28)
log
10
D
[m]=0
.
5
M
w
−
3
.
2
.
Note that formulae (2.28) can be obtained from the definition of the seismic mo-
ment
M
0
=
DLW
, the relationship between the earthquake moment and moment-
magnitude
M
w
= log
10
M
0
/
1
.
5
µ
−
6
.
07 and then following empirical relationships:
10
−
5
(scaling law [Kanamori, Anderson (1975)]). The rigidity
of the crustal rock is assumed to be
L
/
W
= 2
,
D
/
L
= 5
·
10
10
Pa
[Kanamori, Brodsky (2004)].
In recent years methods have been developed that permit to determine, how
the fault at an earthquake source developed in time, and to reveal its space struc-
ture [Ji et al. (2002); Yagi (2004)]. In this case, the fault surface is divided into
a finite number (usually several hundreds) of rectangular elements, for each of
which Burger's vector D is determined. The bottom deformation, caused by each of
these rectangular elements, is calculated by formulae (2.21)-(2.27). Then, the con-
tributions of all elements are summed up. Digitized data on the structure of fault
surfaces for certain strong earthquakes (slip distribution) are presented on the site
http://earthquake.usgs.gov/regional/world/historical.php.
In Fig. 2.6 (see colour section), the example is presented of bottom deformation
calculations for the tsunamigenic Central Kuril Islands earthquake of November 15,
2006. According to USGS NEIC data the moment-magnitude of the earthquake
amounted to
M
w
= 7
.
9 (8.3 CMT), its hypocentre location: 46
.
616
◦
N, 153
.
224
◦
E,
26.7 km (depth). The dip and the strike angles were determined to be 14
.
89
◦
and
220
.
23
◦
, respectively. The fault plane dimension was 400 km (along the strike)
by 137.5 km, which was further divided into 220 subfaults (20 km by 12.5 km).
The maximum slip was 8.9 m. Data on the slip distribution are available from
http://earthquake.usgs.gov/eqcenter/ eqinthenews/2006/usvcam/finite fault.php.
Figure 2.7a (see colour section) demonstrates the space distribution of the hor-
izontal projection length of the bottom deformation vector. Figure 2.7b shows
the vertical component of the deformation vector. In both cases, the step, with which
the isolines are drawn, is 0.2 m. According to calculations, the maximum horizontal
bottom deformation amounted to about 3.8 m. The calculated maximum and mini-
mum vertical bottom deformations amounted to 2.7 m and
µ
≈
3
·
−
0
.
6 m, respectively.
