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based on ground acceleration measurements. In the proceedings of a meeting
held in Strasbourg in 1903, he wrote (Cancani 1904):
collecting these data
[on
macroseismic intensity]
, and performing some interpolations, I think I have found,
with enough accuracy, the accelerations corresponding to the ten degrees of the
Forel-Mercalli scale. These accelerations increase following a geometrical rule with
a common ratio of two. According to the seismologist's judgment, the tenth degree
of the Forel-Mercalli scale corresponds to an acceleration which is not larger than
2 500 mm
(sic)
)
where acceleration reaches 10 000 mm per second
(sic)
; this is why it was necessary
to add two degrees to the above scale.
Because this 1903s note linking degree XII to
10 m/s
2
is not easily accessible, we reproduce it in its original French language in the
appendix. One can find in (Sieberg 1912) a detailed description of the twelve-degree
scale of what became later on the MCS scale.
The Cancani 1903s factor 2 in ground acceleration between two degrees of
intensity may be compared with the factor 2.15 that can be inferred from a re-
lationship published by Richter (1958). It is not far either from the factor which
can be expected from the study of Alkinson and Sonley (2000) who established
a more sophisticated relationship taking implicitly into account the shift in fre-
quency with epicentral distance. Alkinson and Sonley's formula is established for
29 California earthquakes in the moment magnitude range 4.9-7.4. It links intensity
I, peak ground acceleration Y, epicentral distance D, and magnitude M through the
relationship:
,
while there are some earthquakes in Japan or South America (
...
I
=−
9
.
32
+
6
.
08(log Y
+
0
.
46D
−
0
.
03M)
.
(1)
The correction by the factor 0.03 M being negligible, one can infer from (1) that
one degree of intensity at a fixed epicentral distance D roughly corresponds to a
multiplicative factor 1.5 in peak ground acceleration.
The logarithmic relationship between ground acceleration and macroseismic in-
tensity has been thus known for more than a century. As the Richter magnitude
M is defined from the logarithm of the output of the short period Wood Anderson
seismometer with a flat response to acceleration up to 1.25 Hz (Richter 1935), it
corresponds to frequencies which are relevant for macroseismic effects and M may
be linearly related to intensity I. This is what many empirical relationships show,
such as the following general equation adapted from Musson and Cecic (2002):
=
+
+
+
,
I
a
bM
clogR
dR
(2)
where “a” and “b” are constants, R is the hypocentral distance, and c and d depend
on geometrical spreading and anelastic attenuation, respectively.
Most estimations of magnitude of historical earthquake rely on (2). Focal depth h
and magnitude M of small and moderate-size earthquakes are commonly estimated
from I versus D observations, taking in mind that R
2
h
2
. Most often, a mag-
nitude is estimated directly from the epicentral intensity I
0
after correction is made
from the focal depth h. By doing so, site effect at the epicentre and/or error in the
D
2
=
+
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