Page 6 - Visini_de Nardis_Lavecchia_2010

S248 Int J Earth Sci (Geol Rundsch) (2010) 99 (Suppl 1):S243–S264

this formula is that the full record of seismicity in any
where z is the standard Gaussian random vector, with
given region can be used, the a and b values of the
deviates produced with the polar Box–Mueller transform,
Gutenberg–Richter relation being the most important
C is the Cholesky decomposition of the covariance matrix
parameters in this calculation.
of the parameter vector V (symmetric and positive definite

The focal mechanism moment tensor F ij ; which is a
matrix), with a unique lower triangular matrix such that
function of strike, dip and rake of the fault plane solutions, T
V = C 9 C .
may be derived from the calculation of an average focal
mechanism starting from the available focal mechanism
dataset. Input data

The average seismic strain rate tensor _ e ij ; which is the
symmetric part of the velocity gradient tensor may be The application of the above procedure to any homoge-
calculated by means of Kostrov’s (1974) relation: neous seismotectonic province requires knowledge of the
1 shape and size of the seismogenic volume, possibly
_
_ e ij ¼ M o F ij ð2Þ
2lV deduced from integrated geological–seismological con-
straints, the moment tensor deduced from reliable fault
where V is the volume of the seismogenic deforming region
plane solutions, the values of the Gutenberg–Richter
and l is the rigidity modulus. In the general case, the
parameters and of the scalar seismic moment rate deduced
seismogenic volume V may be derived from the length
from the most possible complete record of historical and
(l 1 ),width (l 2 ) and the average thickness of the seismogenic
instrumental earthquakes over a certain magnitude
layer (l 3 ).
threshold.
The components of the velocity tensor U ij may be
calculated with the formula developed by Jackson and
McKenzie (1988): Dimension and geometry of the seismogenic sources
1
_
U ii ¼ M o F ii with i ¼ 1; 2, 3, and k 6¼ i;i 6¼ j; j 6¼ k ð3Þ In order to parameterise the dimensions (length l 1 , average
2ll k l i
width l 2 , average thickness l 3 ) and the azimuth with the
1
_
U i2 ¼ M o F 12 ð4Þ north of each deforming seismogenic volume, we have
2ll 1 l 3
assumed and schematised the 3D geometry given by
1 Lavecchia et al. (2007a, b) for the Marche–Adriatic and the
_
U i3 ¼ M o F i3 with i ¼ 1; 2 ð5Þ
2ll 1 l 2 mainland-southern Sicily seismotectonic provinces
(Fig. 2a, b, b5), whereas for the Southern Tyrrhenian
These equations are valid on the condition that l 3 is
province we have used the surface boundary and the
much smaller than l 1 and l 2 , and l 1 is much greater than l 2 .
average seismogenic thickness given by DISS3.0.4 (avail-
The reference system in Eqs. 2–5 is the province’s local

system (length/width/depth). Since F ij is usually calculated able online from http://legacy.ingv.it/DISS/).
By integrating constraints on tectonic style from seismic
in the north/east/down system, a rotation in the local
lines and geologic data with the traditional constraints from
province’s system is necessary.
historical and instrumental seismicity catalogues, Lavec-
The possible errors involved in the calculation of the
_
above equations are clearly controlled by errors in M o , chia et al. (2007a, b) have interpreted the mainland-
southern Sicily and the Marche–Adriatic seismotectonic
while the directions of the eigenvectors of the defor-
provinces as corresponding to active deformation volumes
mation are mainly influenced by errors in the focal
at the hanging-wall of an inward-dipping regional-scale
mechanism tensor (e.g. in F) (Papazachos and Kiratzi
basal thrust, named SBT and ABT, respectively (Fig. 2a4,
1992).
_
As evident from Eq. 1, errors in M o may derive from b5), which penetrate the crust to a depth of at least 25 km
with an average dip of nearly 20–25°. In both regions, the
errors in the a, b, c, d values and in the choice of the M max
thickness of the seismogenic layer deduced from seismic
and in the adopted M s –M o relationship. Use of the Monte
data coherently and slowly deepens from shallow depths to
Carlo simulation method and assumption of random errors
mid and lower crustal depths, well supporting such a
in these parameters, with known medians and standard
configuration (Parolai et al. 2001; Lavecchia et al. 2007b).
deviations, means that Gaussian deviates can be intro-
Therefore, in a 3D view, the Marche–Adriatic and the
duced. If m is the vector of mean values of the parameters,
mainland-Sicily provinces, also named ABT and SBT
the new parameter vector P = (a, b, c, d, M smax ) can be
provinces, may both be schematically represented as crust-
iteratively obtained by using:
scale wedge-shaped seismogenic volumes (Fig. 5). In map
P ¼ Cz þ m ð6Þ view, the two provinces correspond to arc-shaped, outward
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