Civil Engineering Reference
In-Depth Information
Intensity-magnitude relationships were proposed by Ambraseys (1985, 1989) for European regions
as follows:
M
−
3
()
(1.22.1)
=−
1.10
+
0.62
I
+
1.30 10
⋅
r
+
1.62
log
r
S
i
i
i
which is applicable for north-west Europe, and
M
−
3
()
(1.22.2)
=−
0.90
+
0.58
I
+
1.10 10
⋅
r
+
2.11
log
r
S
i
i
i
for the Alpine zone, where
I
i
is the MM intensity of the
i
th isoseismal and
r
i
is the radius of equivalent
area enclosed by the
i
th isoseismal, in kilometres.
Local geological conditions and focal depths can signifi cantly affect the intensity of earthquake
ground motion. Semi-empirical formulations accounting for focal depths are available (e.g. Kanai,
1983 ). Sponheuer ( 1960) proposed to calculate
M
from the epicentral intensity
I
0
as follows:
MI
=
0.66
+
1.70
log
()
−
h
1.40
(1.23)
S
0
where the focal depth
h
is in kilometres and the intensity
I
0
is in the MM scale.
Attenuation relationships (relationships between a ground-shaking parameter, magnitude, distance
and soil condition) for different ground-motion parameters can be derived from intensity and magnitude;
they may account for distance, travel path and site effects. The most common attenuation relationships
formulated for active seismic regions worldwide are presented in Section 3.3 of Chapter 3 .
Problem 1.3
Calculate the surface wave magnitude
M
S
for an earthquake with
I
MM
of VII in an area that can be
approximated by a circle with radius 20 km for a site at the borders of the given isoseismal. This
site is located in the Western United States but you may use equation (1.22.1). Compare the ensuing
value with the estimations from relationships with other magnitude scales. Calculate the fault surface
displacements. Assume that the earthquake mechanism is normal faulting.
1.3 Source - to - Site Effects
The characteristics of seismic waves are altered as they travel from the source to the site of civil engi-
neering works, due to wave dispersion at geological interfaces, damping and changes in the wavefront
shape. The latter are referred to as 'distance and travel path effects'. Moreover, local site conditions
may affect signifi cantly the amplitude of earthquake ground motions; these are known as ' site effects ' .
Non-linearity of soil response and topographical effects may also infl uence ground - motion parameters
(Silva, 1988) as shown in Table 1.8. For example during the 26 September 1997 Umbria- Marche (Italy)
earthquake, signifi cant site amplifi cation was observed even at large distances from the epicentre (Sano
and Pugliese, 1999). Due to the geomorphological conditions in the epicentral area, located in the
Apennines, local soil amplifi cations related both to topographic and basin effects were present. During
the long aftershock sequence, a temporary strong-motion array was installed in the area where major
damage took place. Some instruments were deployed on different geological and morphological soil
conditions in two towns, Cesi and Sellano, to investigate the considerable localization in the observed
damage. Field investigations were also carried out to assess the geological profi les across strong- motion
sites. The recordings confi rmed the importance of site characteristics in the distribution of damage at
sites very close to one another. Large amplifi cation at the basin border of the Cesi site and an important
three-dimensional effect at the site in Sellano were observed.
