Magnitude of Historical Earthquakes, from Macroseismic Data to Seismic Waveform Modelling: Application to the Pyrenees and a 1905 Earthquake in the Alps - Historical Seismology: Interdisciplinary Studies of Past and Recent Earthquakes - page 361

Fig. 3 Epicentral distance D
versus intensity I inferred
from Fig. 2 for the pair of
earthquakes Bigorre (1660) -
Argeles-Gazost (2006).
Dotted line for the
uncorrected intensity

radius to D 200 km according to the farthest unambiguous macroseismic obser-

vations in France (Rodez, D

=

200 km).
As explained in the previous section, at a fixed epicentral distance D, we ex-
pect that the differences of intensities depend on the differences of magnitudes

= 255 km; Bordeaux and its vicinity, D =

M
only. The curves D(I) should thus be parallel. From this respect, the recent Argeles-
Gazost curve is abnormal at intensity III. Unreliable answers to the macroseismic
questionnaires received at BCSF for distances between 50 and 100 km is the most
likely reason for this anomaly. Within this distance range, the answer “not felt” is
often quoted by local city officers while reliable reports of intensity II (felt) are sent
by individuals. This lack of information from local city officers could explain the
abnormally too small area of intensity III in Fig. 2. In order to check the effect of this
possible underestimation of intensity III area we test below what is the consequence
of increasing the intensity by half a degree at a distance of 50 km from the epicentre.
The average difference of intensity between the pair of earthquakes Argeles-
Gazost (2006) - Bigorre (1660) is estimated to

= . ± .

29 from a set of
five epicentral distances D in the range 30-200 km (Fig. 3). From the relationship
(3) we found that the difference between their magnitudes is

I 3 59 0

= . ± .

13
(rms deviation). Starting from the 4.5 M W Argeles-Gazost (2006) earthquake, we
thus find a magnitude M W

M 1 63 0

13 (rms deviation) for the Bigorre (1660)
earthquake. Following the same procedure with the corrected intensity III 1

= 6 . 13 ± 0 .

/ 2 we get

06. Within an rms deviation around 0.1, one
can thus conclude with a quite good confidence that a magnitude 6.1 M w is expected
for the Bigorre (1660) earthquake. If one adds an uncertainty around 0.1 for both

M = 1 . 56 ± 0 . 06 and M W = 6 . 06 ± 0 .