Geophysical Journal International
Geophys. J. Int. (2011) 186, 1415–1430
doi: 10.1111/j.1365-246X.2011.05125.x
Regression analysis of MCS intensity and ground motion spectral
accelerations (SAs) in Italy
Licia Faenza and Alberto Michelini
1 Istituto
Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata, 605, Rome 00143, Italy. E-mail: [email protected]
Accepted 2011 June 24. Received 2011 June 20; in original form 2011 January 7
SUMMARY
We present the results of the regression analyses between Mercalli-Cancani-Sieberg (MCS)
intensity and the spectral acceleration (SA) at 0.3, 1.0 and 2.0 s (SA03, SA10 and SA20). In
Italy, the MCS scale is used to describe the level of ground shaking suffered by manufactures
or perceived by the people, and it differs to some extent from the Mercalli Modified scale
in use in other countries. We have assembled a new SA/MCS-intensity data set from the
DBMI04 intensity database and the ITACA accelerometric data bank. The SA peak values are
calculated in two ways—using the maximum among the two horizontal components, and using
the geometrical mean among the two horizontal components. The regression analysis has been
performed separately for the two kinds of data sets and for the three target periods. Since
both peak ground parameters and intensities suffer of appreciable uncertainties, we have used
the orthogonal distance regression technique. Also, tests designed to assess the robustness of
the estimated coefficients have shown that single-line parametrizations for the regressions are
sufficient to model the data within the model uncertainties.
For the maximum horizontal component, SAxxhm , the new relations are
IMCS = (1.24 ± 0.33) + (2.47 ± 0.18) log S A0.3s hm , σ = 0.53,
GJI Seismology
IMCS = (3.12 ± 0.16) + (2.05 ± 0.11) log S A1.0s hm , σ = 0.36,
IMCS = (4.31 ± 0.10) + (2.00 ± 0.10) log S A2.0s hm , σ = 0.29.
For the geometrical mean SA, SAxxgm , the new relations are
IMCS = (1.40 ± 0.31) + (2.46 ± 0.18) log S A0.3s gm , σ = 0.53,
IMCS = (3.25 ± 0.16) + (2.08 ± 0.12) log S A1.0s gm , σ = 0.38,
IMCS = (4.46 ± 0.10) + (2.01 ± 0.10) log S A2.0s gm , σ = 0.30.
Adoption of the geometric mean of the horizontal components, rather than their maximum
value, results in a minor shift towards larger values of intensity for the same level of ground
motion; this difference, however, is contained within the regression standard errors of the
former. Comparisons carried out in various manners for earthquakes where both kinds of data
(macroseismic and instrumental data) are available have shown the general effectiveness of
the relations.
Key words: Earthquake ground motions; Seismicity and tectonics; Europe.
1 I N T RO D U C T I O N
Regressions between macroseismic intensity and ground motion
parameters are of great importance to make inferences on the level
of strong ground motion experienced after a larger earthquake in
localities where little instrumental data are available.
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Geophysical Journal International The calibration of these regressions, however, can be done only
for those areas where there are enough data to correlate instrumental data and macroseismic investigations. An example of such
an area is provided by Italy where there are both a long history
of macroseismic observations and a data bank of instrumental
data.
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The object of this work is to determine a relation between
the macroseismic Italian intensity data [INGV-DBMI04 data
available at (http://emidius.mi.ingv.it/DBMI04/) and the Italian
spectral accelerations (SAs), INGV-ITACA database available at
(http://itaca.mi.ingv.it/ ItacaNet/)] at the periods 0.3, 1.0 and 2.0 s.
The resulting relations appear also of importance for dedicated seismic hazard assessments studies such as those aimed at identifying
sites for nuclear power plants (e.g. the Pegasos Refinement project
in Switzerland).
The starting point for this analysis is the recent work of Faenza &
Michelini (2010, FM10 hereafter). In that work, the regression between Mercalli-Cancani-Sieberg (MCS) intensity and peak ground
motion values, such as PGA and PGV, was done using a technique
that implicitly takes into account the uncertainties of both dependent
and independent variables; the results are equations for conversion
of intensities to PGA and PGV with quantification of uncertainties in the analysis (i.e. epistemic uncertainties) and the standard
deviation of the relations (i.e. aleatory variabilities).
Moreover, the three spectral values selected in the correlations
presented later correspond to different bands of energy radiated by
earthquakes and relevant to the assessment of seismic hazard and
of interest to earthquake engineers.
Thus, this new work provides a range of regressions of MCS
intensity versus ground motion parameters that, together with the
results outlined in FM10, can be useful tools for calculating seismic
hazard maps, both in terms of peak values of ground motion and in
terms of spectral components. For what concerns Italy, this is the
first time that a regression analysis between MCS intensity and SA
is performed.
The paper begins with the data gathering and selection; the data
set used is similar to that of FM10, with the inclusion of the relevant
SA data and the addition of the L’Aquila 2009 M w 6.3 main shock
(Pondrelli et al. 2010). The second step consists of analysing the
quality of the assembled data set and the application of the Orthogonal Distance Regression technique. Our results are then compared
to other published regressions worldwide; this test is performed
even if the regression are based on different macroseismic scales
(e.g Mercalli Modified scale rather than MCS scale). Testing also
includes the residual analysis of the observed and predicted peak
SAs for 23 selected earthquakes.
The analysis is performed using two different data sets, which
differ in the manner the SA values are determined to be then paired
with the MCS intensities. In the first data set, each SA value is
chosen as the maximum between the two horizontal components; in
the second data set, the value of SA consists of the geometric mean
of the two horizontal components. The first option is performed
to satisfy shakemap’s code requirements (Wald et al. 2006); the
second procedure is applied for consistency with previous works, to
conform to the standards of the correlations used in seismic hazard,
and, finally, to make the comparison between our results and those
published previously straightforward.
2 D ATA S E T
2.1 Gathering and selection
Recently, the Italian accelerometric database, ITACA, has been
made available (Luzi et al. 2008). ITACA contains data acquired
in Italy by different national institutions, namely ‘Ente Nazionale
per l’Energia Elettrica’ (ENEL, Italian electricity company),
‘Ente per le Nuove tecnologie, l’Energia e l’Ambiente’ (ENEA,
Italian Energy and Environment Organization) and the ‘Dipartimento della Protezione Civile’ (DPC, Italian Civil Protection), see
http://itaca.mi.ingv.it for additional detail.
ITACA contains 2182 three-component waveforms generated by
1004 earthquakes with a maximum magnitude of 6.9 (1980 Irpinia
earthquake) covering the time period from 1972 to 2004. In addition
to the digital strong motion recordings, ITACA provides various
estimates of peak ground motion (e.g. PGA, PGV, PGD, Housner
and Arias Intensities). For what concerns the SA response values,
these can be extracted from the response spectra files provided on the
ITACA website, calculated with 5 per cent damping. In this work
we have extracted the spectral response values of the maximum
horizontal components at the periods 0.3, 1.0 and 2.0 s (i.e. SA03,
SA10 and SA20, respectively). As mentioned earlier, the analysis
is also performed using the geometrical mean of the two horizontal
components for the three periods.
In Italy there is a large and homogeneous macroseismic intensity
database—the DBMI database (Stucchi et al. 2007)—available at
http://emidius.mi.ingv.it/DBMI04/ (the revised release 1900–2008,
i.e. DBMI08, used in FM10, is no longer available). This database
is a revised collection of all the macroseismic analysis done for the
Italian Peninsula. It includes a total of almost 60 000 observations
from 12 000 earthquakes at more than 14 000 localities. Although it
is well known that local conditions can affect the amplitude (and duration) of the wavefield, we have made no attempt in the following
to subdivide further the pair association according to the different recording sites since the intensity values reported in DBMI04
represent already average values for the localities. The reported
intensities follow the MCS scale in classes spaced by 0.5 intensity units (e.g. 4, 4.5, 5, . . .)—nearly a standard in macroseismic
intensity studies.
In this work we used the DBMI04. The main difference between
the DBMI04 and DBMI08 databases regards the multiple main
shocks that characterized the Umbria-Marche (1997) and Molise
(2002) seismic sequences. In detail and for the 1997 UmbriaMarche, in DBMI04 only the macroseismic field of the morning
event (9:40 UTC, 1997 September 26, M L = 5.8) is reported (i.e.
the night event that occurred at 00:33 UTC on 1997 October 26,
M L = 5.6 is not reported). Similarly, for the 2002 Molise sequence,
the event M L = 5.3 of 2002 November 1, is also not reported and,
therefore, not included in our new database.
In FM10 the data set did not include the peak ground motion
and macroseismic data of the recent M w = 6.3 L’Aquila earthquake
(Chiarabba et al. 2009) that shook central Italy on 2009 April 6.
In the analysis later we have included these additional IntensityPeak Ground Motion (PGM) pairs. The three target periods we seek
determination of the regression values are the SAs at 0.3, 1.0 and
2.0 s. To this regard, we have performed some tests to assess the
robustness of the coefficients of the equations used. Our results have
shown that inclusion (or exclusion) of the L’Aquila data does not
alter the values of the coefficients appreciably.
As in FM10 and to the ends of this new work, the chance to
access and cross-match the two data sources above provides the
opportunity to assemble a new, homogeneous database consisting
of intensity and SA values (see S1 in Supporting Information).
To this end, we have extracted all the localities reporting intensity data which are located within 3 km from the accelerograph
stations that recorded the data and selected the closest if more are
available. Specifically, 43 of 264 pairs have more than one intensity
value located within 3 km from the station, 12 more than two and in
15 cases of 43 the reported intensities have the same value. This criterion was applied to all the events within ITACA and to the recently
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8˚
10˚
12˚
14˚
16˚
18˚
1976 Friuli
Earthquake
46˚
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46˚
44˚
44˚
1995 Gargano
Earthquake
42˚
42˚
40˚
40˚
38˚
38˚
8˚
10˚
12˚
14˚
16˚
18˚
Figure 1. Map showing the location of the analysed events (red stars) and of the stations (blue solid squares) used to assemble the intensity-SA pair data set.
The two boxes show the locations of the maps in Fig. 8 (1995 Gargano earthquake) and Fig. 9 (1976 Friuli earthquake).
acquired L’Aquila data. In practice, the SA files available on the
ITACA website (the new version that became available recently and
that adopts new, more accurate procedures for the determination of
the spectral values) were downloaded and the response acceleration
spectra at the target periods of our analysis extracted. Out of the
selected 87 events only one (1972 June 14) was not present in the
new version of the ITACA database and the spectral values reported
in the old database have been used. For the remaining events, in
three cases the spectral values were not available and they have
been similarly replaced by those of the old database.
Fig. 1 shows the spatial distribution of the selected events and the
location of the stations. 87 earthquakes in the time span 1972–2009
(3.9 ≤ M w ≤ 6.9) and intensity MCS ≤ 8 have been analysed, for a
total of 264 pairs intensity-SA (see Supporting Information, S1).
Fig. 2 shows the distribution of the data versus epicentral distance.
Overall, the database is well distributed although we note that there
are few intensity data at closer distances for small intensity values
(i.e. in the range 2 ≤ MCS ≤ 3.5). This follows from the DBMI04
data being compiled for damaging events (i.e. medium-large magnitude earthquakes producing macroseismic damage; e.g. Allen &
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not provide intensity-SA pairs at intensity levels larger than 8. Unfortunately, this is an inherent limitation of the assembled data set
and to some extent it prevents to constrain tightly the largest intensity values in terms of observed SA values. To this regard, inclusion
of the recent L’Aquila earthquake data did not solve this problem.
In fact and although some I MCS > 8 reports are available and have
been collected within 3 km from recording stations, we have found
that the same recording stations were to be paired, according to our
selection criteria, to closer intensity points which featured weaker
intensities.
2.2 Qualification
As mentioned in FM10 there are two distinct procedures to use the
data in the regression. The first consists of binning the data (BID
hereafter) into classes (e.g. at 0.5 intensity intervals) and calculating
for each class the SA mean and its standard deviation. The second
procedure does not involve any averaging and adopts the whole data
set although some robust statistics can be applied (e.g. remove the
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Figure 2. Distance coverage of the assembled SA-MCS intensity pairs data set. (a) MCS intensity; (b) log SA03; (c) log SA10; (d) log SA20. The distance
is calculated using the epicentral location of the events. Adoption of this distance for large events, rather than the fault distance, will introduce some differences
in the diagrams but it is inconsequential to the analysis carried out here.
tails of the data distribution) to remove the influence of the outliers.
In the following we adopt the geometric mean approach and refer
to FM10 for details on this choice. The geometric mean, μg , is
calculated as
μg =
n
1
log SAi ,
n i=1
(1)
where n is the number of data points for each intensity class.
The use of the geometric mean is motivated by the SA data
distribution about the arithmetic and logarithmic means as shown in
Fig. 3 for the maximum horizontal component data set. To compare
the whole data set at the same time, we have adopted the standard
), for the linear and logarithmic values
normal variable (i.e. z = x−μ
σ
of SA.
The corresponding normal distribution curves are also shown for
reference purposes and it is evident that the deviations from the
arithmetic mean are not approximated by a normal distribution. For
all the SA data the distributions about the arithmetic means are
skewed to the lower side of the mean value where the great majority
of the residuals fall. In contrast, the distributions computed using the
logarithmic mean agree well with the theoretical normal distribution
curve.
To test the likelihood of the normal distribution we have performed the 1-sample Kolmogorov–Smirnov test. We can reject the
null-hypothesis of a normal distribution for the maximum horizontal component of SA03, SA10 and SA20 with an α-value less than
1 per cent. Conversely, we cannot reject the null-hypothesis for log
SA03, log SA10 and log SA20 with an α-value equal to 90 per cent,
96 per cent and 96 per cent, respectively. Similar results have been
obtained when all three components are used to extract the maxima.
This all indicates that the data appear to be nearly log-normally dis-
tributed and will be treated as such in the following analyses. Our
results are very similar to those presented by Murphy & O’Brien
(1977) among many others and by FM10 for Italy.
In summary, 12 pairs of intensity and SA data are used to fit
using BID. The SA values are calculated using the geometric mean
average. The intensity standard deviations have been set equal to
the conservative value of σ I = 0.5. This value is in agreement with
the one roughly derived from the mean standard deviation of the
12 pairs out of 43 for which there are more than two intensity data
points closer then 3 km from the seismic station, which is 0.46.
The standard deviation for the SA values is determined for each
intensity class from the geometric standard deviation
⎛
⎞
n
2
(log
SA
−
μ
)
i
g
i=1
⎠.
(2)
σg = exp ⎝
n
Similar conclusions can be drawn using the second data set based
on the value of the geometric mean of the two horizontal components. For conciseness, the figures of this analysis are not shown.
3 METHOD
The methodology used in this work follows that recently proposed
by FM10 to convert PGA and PGV into MCS intensities and vice
versa. The technique adopts the ‘orthogonal distance regression’,
ODR, technique (Fuller 1986; Boggs et al. 1988; Castellaro &
Bormann 2007; Gomez Capera et al. 2007). Another useful approach for the analysis of categorical data is the Generalized Linear
Model, which analyses linear and non-linear effects of continuous and categorical predictor variables on a discrete or continuous
dependent variables (see Agresti 2007, for details or for a more
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Figure 3. SA data distribution. Original data (bottom) and after application of the logarithm in base-10 (top).(SA03: left, SA10: middle and SA20: right). For
each intensity bin, the data set is normalized to obtain standardized values, having zero mean and unit standard deviation. To the purpose of reference, the
corresponding normal distribution curves are also shown as thick solid lines.
general discussion of the treatment of categorial data). There are
two advantages which made us to prefer the ODR technique. First,
ODR gives the possibility to account for uncertainties both in the
dependent and independent variables and, secondly, the resulting
regression equations relating dependent and independent variable
are biunique, that is, the same coefficients can be used to convert
from one variable into the other.
In general, the technique stems on defining a data set (xi , yi ; i =
1, . . . , n) and a functional form yi = f (xi + δ i ; β) − i , which
explains the relationship of yi ∈ R1 versus xi ∈ Rm , and where δ i
and i are the errors of the independent and dependent variables,
distributed as δ i ∼ R(0, σδ2i ) i ∼ R(0, σ2i ) and β is the parameter
vector. In the ODR approach, the weighted orthogonal distances
of the curves f (·) from real data points yi is minimized. In the
following, we refer to the thorough description provided by Fuller
(1986), Boggs et al. (1988) and FM10 for additional detail on the
methodology.
4 A P P L I C AT I O N
We fit the data using a linear relation between the intensity (I) and
the logarithm in base 10 of the SA (i.e.,SA03, SA10 and SA20)
I = a + b log SA.
(3)
In all cases we have tested both single- and double-line regressions
since many works in the literature propose different proportionality
with SA at low and high intensities. Also, use of the ODR technique allows for the direct inversion between SA and I so that
the calculated coefficients can be used to express SA as func
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the same coefficients, for prompt conversion between the sought
variables.
Fig. 4 presents an overview of the two data sets, with the geometrical mean and the standard deviation. In the following, the
results of the application of the ODR to the two data sets are presented. As expected, the geometric mean data set provides values
always somewhat smaller than those of the maximum horizontal
component value.
4.1 Maximum horizontal SA
4.1.1 SA03
We fit the data using ODR using both a single- and a double-line
parametrization. With the single-line regression (Fig. 5, top panel),
we have obtained a = 1.24 ± 0.33 and b = 2.47 ± 0.18, with a
standard deviation of the regression line of σ single−line = 0.53.
As in FM10 we have tested the likelihood that a different scaling
applies at low and high intensities. This approach has been pursued
in other similar studies (e.g. Wald et al. 1999a; Atkinson & Kaka
2007, AK07 hereafter) by subdividing the data set into two parts—
intensities less than 5 and intensities greater or equal to 5. The
resulting coefficients from application of ODR using the doubleline regression are aI≥5.0 = −0.15 ± 1.83, bI≥5.0 = 3.06 ± 0.79 (7
data out of 12 belong to this group), and for the data with intensity
less than 5, the parameters are aI<5.0 = 1.62 ± 0.25, bI<5.0 = 2.01 ±
0.15. The standard deviation of the double-line fitting is σ double−line
= 0.60 (see Fig. 5, top panel).
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Figure 4. MCS intensity versus SA relationships for BID (i.e. the SA geometric mean binned data set). Data (small open circles), data geometric
mean (diamonds and squares for horizontal components geometric mean
and for maximum horizontal components, respectively) and standard deviations (error bars). Red and green colours used for horizontal components
geometric mean, and maximum horizontal component data sets, respectively. Diamonds, squares and the associated error bars are slightly shifted
for plotting purposes. SA03: top; SA10: middle; SA20: bottom.
Figure 5. MCS Intensity versus SA relationships for BID (i.e. the SA
geometric mean binned data set). Data (red solid circles), data geometric
mean (black solid diamonds) and standard deviations (black error bars),
single-line ODR (solid orange line) and double-line ODR (solid cyan line).
The associated 1-σ standard deviations (dashed lines) are shown on each
regression line. The diamonds and the error bars are slightly shifted for
plotting purposes. SA03: top; SA10: middle; SA20: bottom.
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Comparison of the standard deviations obtained using singleand double-line parametrizations supports the use of the single-line
since it is capable to fit the data equally well or better using fewer
regression parameters.
4.1.2 SA10
The procedure described for SA03 has been also applied to SA10
(Fig. 5, middle panel). The parameter for the single-line regression
using our binned data set are a = 3.12 ± 0.16 and b = 2.05 ± 0.11,
with a standard deviation of the model as σ single−line = 0.36.
The value of the coefficients of the double-line regression are
aI≥5.0 = 2.78 ± 0.61, bI≥5.0 = 2.20 ± 0.33, and for the data with
intensity <5.0, the parameters are aI<5.0 = 3.08 ± 0.18, bI<5.0 =
1.90 ± 0.18. The standard deviation of the model is σ double−line =
0.46. As for SA03, the similar or somewhat lower values of the
single-line standard deviation resulting from the ODR fitting when
compared to the double-line made us prefer the former as adequate
to fit the intensity-SA10 data set (Fig. 5, middle panel).
4.1.3 SA20
The parameter for the single-line regression using our binned data
set are a = 4.31 ± 0.10 and b = 2.00 ± 0.10, with a standard
deviation of the model as σ single−line = 0.29.
The value of the coefficients of the double-line regression are
aI≥5.0 = 3.98 ± 0.31, bI≥5.0 = 2.22 ± 0.24, and for the data with
intensity <5.0, the parameters are aI<5.0 = 4.16 ± 0.08, bI<5.0 =
1.81 ± 0.18. The standard deviation of the model is σ double−line =
0.39. Again the almost comparable values of the standard deviation
between single- and double-line ODR fitting and the relatively small
values of the uncertainties of the coefficients would suggest the
former to be adequate to fit the intensity-SA20 data set (Fig. 5,
bottom panel).
4.3 Discussion
Overall the values of the relation coefficients determined from application of ODR to the two data sets (maximum value and geometric
mean of the two horizontal components) do not vary significantly.
In Fig. 6 we present the regressions obtained using both data sets
and it can be appreciated that the difference is effectively minor.
The regression lines for all the three target periods of the analysis
are essentially subparallel to one another. The SA03 relations show
a maximum difference in intensity of the order of 0.25–0.3 intensity
units. Smaller differences are observed for SA10 and SA20.
In Fig. 6, we have also represented the standard deviations resulting from our analysis using the two data sets (dashed lines).
It can be observed that in all cases the regression lines fall inside
the standard deviations of that of the other data set (i.e. the geometric mean data set regression line falls within the bounds given
by the standard deviations of the regression determined from the
maximum horizontal component, and vice versa).
In Fig. 7 (top panel) we summarize the results of the ODR using
the maximum horizontal component (SAxxhm ) in comparison with
other works available in literature. The relations used are summarized below.
For SA03 obtained in Section 4.1.1 using the regression
IMCS = 1.24 + 2.47 log SA03hm
The same procedure was adopted for the second data set. As for
the maximum horizontal component, the regression was applied to
both single- and double-line parametrizations, and for all three SA
periods. As for the maximum horizontal SA component, comparison
of the standard deviations obtained using the single- and the doubleline parametrizations supports in all cases the use of the single-line
regression since it is found to fit the data equally well or better using
fewer regression parameters.
The regressions found for this data set (for clarity, we use the
SAxxgm below) are
IMCS = 1.40 + 2.46 log SA03gm
(σ = 0.53)
(4)
at 0.3s (σ a = 0.31 and σ b = 0.18);
IMCS = 3.25 + 2.08 log SA10gm
(σ = 0.38)
(5)
at 1.0s (σ a = 0.16 and σ b = 0.12);
IMCS = 4.46 + 2.01 log SA20gm
(σ = 0.30)
(6)
at 2.0s (σ a = 0.10 and σ b = 0.10).
The uncertainties expressed as ±σ bounds associated to each
regression are also shown.
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(7)
(σ a = 0.33 and σ b = 0.18) together with the regression obtained
by AK07. The uncertainties expressed as ±σ bounds associated to
each regression are also shown.
Similarly, in Fig. 7 (middle panel) we present the results for SA10
using the regression
IMCS = 3.12 + 2.05 log SA10hm
(σ = 0.36)
(8)
(σ a = 0.16 and σ b = 0.11) together with the regressions obtained
by AK07, Kaka & Atkinson (2004) and Atkinson & Sonley (2000).
Finally, in Fig. 7 (bottom panel) we show the results for SA20
using the regression
IMCS = 4.31 + 2.00 log SA20hm
4.2 Geometrical mean SA
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(σ = 0.29)
(9)
(σ a = 0.10 and σ b = 0.10) together with the regressions obtained
by AK07 and Atkinson & Sonley (2000).
The IMCSSA03 ≥ 5 range of values shown in Fig. 7 (top panel)
indicates that our regression line has a value of the slope coefficient
less than that of AK07 and at SA03 ≈ 101.8 = 63.1cm s−2 6.4
per cent g the intensity values predicted by our relation (I MCS ≈ 6)
are about one intensity degree larger than those predicted by AK07.
The two regressions lines intersect at IMCSSA03 8. In contrast, for
IMCSSA03 < 5 the slope coefficient of our relation is larger than that
of AK07 and the value in which the two intersect is at IMCSSA03 4.
We should note that the data set used suffers of poor resolution for
IMCSSA03 < 4 since the number of intensity-SA pairs available is
small and this is one reason why adoption of the double-line regression is probably meaningless with this data set. Nevertheless, if the
single data points and the geometric means used for the regression
are compared to the intensities predicted by AK07 (cf. Fig. 7, top
panel), the impression is that the latter tends to overestimate the reported intensity values. In summary, the largest differences between
the two relations for SAs at 0.3 s period are concentrated around
intensity 5 and these amount to about 1 intensity unit (iu).
The general behaviour observed for SA03 appears replicated
in the regressions performed using the 1.0 and 2.0 s period SAs
when compared to the regression coefficients of AK07. The only
relevant difference appears to be in the amount variation between the
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Figure 6. Comparison between the single-line regressions obtained using
the maximum and the geometrical mean processing of the horizontal components of SA. The geometric mean of the maximum horizontal components
is shown in orange colour and the maximum horizontal in blue. SA03, SA10
and SA20 are shown in top, middle and bottom panels, respectively.
intensity values at the kink of the double-line regressions determined
by AK07 (i.e. IMCSSA10 , IMCSSA20 = 5). In both cases the difference
exceed 1 iu reaching almost 1.5 iu for IMCSSA20 . As a result, the
spectral value interval (i.e. along the horizontal axis) between the
intersection points of our relations and those of AK07 are now
somewhat wider (cf . Fig. 7, middle and bottom panels).
Figure 7. Comparison of MCS Intensity versus SA relationships. SA03:
top; SA10: middle; SA20: bottom. The relationships plotted are listed in the
legend of each panel. See Fig. 5 for detail.
Comparison with the other relations available indicates that for
SA10 the relation proposed by Atkinson & Sonley (2000) features a
much steeper slope which, while meeting our relation at intensities
≈8 it does underestimate and falls off our data set at smaller intensity
values. In contrast, the Kaka & Atkinson (2004) relation predicts
always larger intensity values than ours—the point of intersection
being around (or beyond) intensity 10. Finally, comparison between
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the resolved relation for SA20 and that by Atkinson & Sonley (2000)
shows not only the remarkable difference existing between the two,
but also that the relation proposed by Atkinson & Sonley (2000) is
inappropriate to match our data set.
5 R E S U LT S A S S E S S M E N T
In this section we appraise the results obtained by following two different approaches. The first adopts the procedure of FM10 and it exploits both the observed data points and the predictions made using
the software package USGS-ShakeMap (Wald et al. 1999b, 2006).
The latter package, to provide maps of SA parameters and intensity
values, predicts ground motions on a regular grid of points (phantom
points) throughout the target area of the shakemap in addition to the
observed ones. The second approach we have used utilizes only the
observed data and we investigate the dependency of the residuals
versus magnitude and distance. It follows the analysis performed
by Douglas & Bommer (2009) in a report for the Pegasos Refinement Project where a comparison was made among several SAintensity equations to select the most appropriate ones for Switzerland. Specifically, Douglas & Bommer (2009) proposed a residual
analysis to compare the equations of Atkinson & Sonley (2000),
Kaka & Atkinson (2004) and Atkinson & Kaka (2007) for SA at
2.0 s, 1.0 s and 0.3 s, against the database of the French national
accelerometric network (http://www-rap.obs.ujf-grenoble.fr/) and
the SisFrance database (http://www.sisfrance.net/) of macroseismic
intensities.
5.1 Observed and predicted values using ShakeMap
USGS-ShakeMap (Wald et al. 1999b, 2006) is a package designed
to provide rapid estimates of ground motion parameters and intensities using observed instrumental data, ground motion prediction
equations (GMPEs) and some site effects corrections. The same
package, however, can be used as a tool to make comparisons between observed and predicted ground motions when both observed
instrumental and macroseismic data are available. It follows the relevance of such a package when the object of the study is appraisal
of intensity-SA relations such as in our case where correct calibration of the intensity conversions gives the opportunity to generate
meaningful maps of SA parameters. In fact, in our previous work
(FM10) the focus was on PGA and PGV and the purpose was to
define new relations between MCS intensities and SA to be then
adopted in the generation of shakemaps in Italy (Michelini et al.
2008). We then compared observed and predicted SA shakemaps
to assess the quality of the relations. A similar approach is pursued
below with the notable difference that, since object of the work is
the calibration of the SA relations with intensity, we had to modify the standard conversion from PGA and PGV to intensity used
in USGS-ShakeMap to utilize the SA relations determined earlier
(Sections 4.1.1–4.1.3) using the maximum horizontal components.
Therefore, we use the conversion eqs (7)–(9) within the ShakeMap
software package to predict (i) the SA (i.e. SA03, SA10 and SA20)
from the intensity values and (ii) the MCS intensities from the
available SA values. The two resulting sets of shakemaps (i.e. from
instrumental and macroseismic data) expressed in terms of SA and
intensity are then compared. To this end, we have modified the
relevant modules of the ShakeMap package to convert all-at-once
the SA03, SA10 and SA20 values to single value MCS intensities.
We have assumed SA03 most representative up to light perceived
shaking (I MCS ≤ 4); SA10 from moderate to strong shaking (4 <
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I MCS ≤ 6), and SA20 from very strong to extreme shaking (I MCS
> 6) (see legend in Figs 8a and 9a). This choice follows to some
extent that within the standard ShakeMap distribution (Wald et al.
1999b, 2006), that is, lower intensities are prevalently the result
of strong ground motions dominated by short-duration, pulse-like
peaks, whereas longer period shaking appears to be a more robust
measure of intensity for strong shaking. The GMPEs and the site
corrections from the geological V S30 (Michelini et al. 2008) have
been adopted. For the GMPEs, we have used the one Akkar & Bommer (2007a,b) for large events (M ≥ 5.5) and the regional equations
developed in the framework of the Probabilistic Seismic Hazard
Analysis in Italy (MPS Working Group 2004) for small events (M
< 5.5).
To show the validity of the regressions determined in this study,
we have applied eqs (7)–(9) to the data of all the earthquakes with at
least four instrumental records used in this study. In the following,
we follow very closely the procedure (and the description) adopted
in our previous work. In Supporting Information S2, we provide
all the shakemaps expressed both in terms of MCS intensity and of
SA03, SA10 and SA20 for the 21 earthquakes selected (in FM10, 25
earthquakes had been used but here we had to remove five and added
the L’Aquila main shock). In the following, we show two significant
examples (M5.2 and M6.4 in the Gargano promontory and in Friuli,
respectively, see Fig. 1) drawn form the calculated shakemaps (see
S2, Supporting Information). We consider these two earthquakes
representative of the seismicity occurring in Italy since M ≈ 5
earthquakes occur occasionally and are widely felt although they
generally induce only much awareness without causing sensible
damage; in contrast, M6+ earthquakes take place only a few per
century but result in extensive damage and large number of fatalities.
In Fig. 8(a) (top panels), we show the intensity shakemap for the
M5.2, 1995 September 30, Gargano event. We see a remarkable
similarity between the strong motion data and the intensity derived
maps of MCS intensity. The only notable difference between the two
maps lies in the level of local resolution that depends on the number of observations. The standard shakemap that relies on SA data
alone has been determined using many fewer data (green triangles
in the left panel of Fig. 8a) and this results in a much smoothed local
shaking distribution when compared to that obtained using the much
larger number of intensity data (green triangles in the right panel
of Fig. 8a). In Figs 8(a) (bottom panels) and 8(b), we compare the
SA data shakemaps with those obtained after converting the MCS
intensities into SA using the relations of this study. Again, we note
a remarkable similarity in the SA03, SA10 and SA20 shakemaps
obtained directly from the data and from the intensity to SA conversion. This result corroborates that the regressions found in this
study can be adopted to provide first order, maps of peak ground
motion although in these examples the level of local resolution is
hampered by the paucity of observations when using the SA data in
the standard ShakeMap manner.
In Fig. 9, we show the results obtained for the 1976 May 6 Friuli
main shock. This earthquake caused very extensive damage and
nearly 1000 fatalities. The PGM and intensity derived shakemaps
(Fig. 9a, top panel) are similar although there seems to be some
slight overestimation of intensities with the SA data derived intensity; in terms of SA03, SA10 and SA20 the maps are generally
similar although the large number of macroseismic points adds detail impossible to attain using the instrumental observations. To first
order, however, we feel that the SA shakemaps obtained from the
MCS intensities do provide, within the limitations imposed by a relationship calibrated using earthquakes throughout all Italy, a gross
description of the level of shaking experienced in the area. These
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L. Faenza and A. Michelini
Figure 8. Shakemap of the M L = 5.2, 1995 September 30, earthquake in the Gargano area in Southern Italy. We have applied the site conditions derived
from the geological V S30 and the ground motion prediction equation of Akkar & Bommer (2007b) (see Michelini et al. 2008), with standard deviation
σ SA03 = 0.22, σ SA10 = 0.33 and σ SA20 = 0.27. SA and MCS intensity derived shakemaps are shown in the left- and right-hand columns, respectively. The
green triangles are the stations (left) and intensity site (right) used as input in the analysis.
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Figure 9. Shakemap of the M L = 6.4, 1976 May 6, Friuli main shock in Northern Italy. We have applied the site conditions derived from the geological
V S30 and the ground motions equation by Akkar & Bommer (2007b) (see Michelini et al. 2008), with standard deviation σ SA03 = 0.18, σ SA10 = 0.19 and
σ SA20 = 0.20. (Same format as Figs 8a and b).
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L. Faenza and A. Michelini
SA
SA
SA
Figure 10. Comparison between MCS intensity (a), SA03 (b), SA10 (c) and SA20 (d) values determined from instrumental (inst) data and from macroseismic
(macro) surveys (e.g. [(SA03inst − SA03macro )/SA03macro ] × 100 using cumulative distributions. More than 110 000 data points are used in each graph. Mean,
standard deviation and median values are (8.53,12.17,8.12) for intensity, (17.48, 42.79, 14.03) for SA03, (25.90, 52.14, 28.59) for SA10 and (11.87,42.07,
5.95) for SA20.
conclusions are confirmed by the maps shown in S2, which show
an overall agreement between the intensity, SA03, SA10 and SA20
maps based either on instrumental records or on macroseismic data.
These results combined with the findings of FM10 suggest for the
future a thorough revisitation of the available macroseismic data set
of the strong historical earthquakes that have occurred in Italy in
the past and compiled, for example, in the ‘Catalogo parametrico
dei terremoti italiani’ (Gasperini et al. 2004).
To summarize concisely and assess more quantitatively the differences between the shakemaps determined using recorded data
and those derived from the macroseismic surveys using the relations found here, we have calculated the per cent differences for
all the data points used to draw the shakemaps shown in S2 and in
Figs 8 and 9. In fact, the points used to determine the differences include, in addition to the intensity-SA pairs, the phantom gridpoints
of USGS-ShakeMap (e.g. Wald et al. 1999b; Michelini et al. 2008)
within a radius of 80 km from the epicentre for a total of more
than 110 000 geographical points. Fig. 10 shows the residuals for
intensity, SA03, SA10 and SA20. The four cumulative distributions
show that the per cent differences for all but the SA10 parameters
are centred within ±15 per cent from zero. The SA10 mean and
median parameters differ more consistently although well within
the bounds of the standard deviation. In particular, we find that ≈90
per cent of the intensity values are comprised within ±25 per cent
(Fig. 10a). For SA03, SA10 and SA20, we find that ≈70 per cent,
50 per cent and 70 per cent of the values, respectively, lie within
±50 per cent differences (Figs 10b–d).
Finally, we have verified whether a correlation of the residuals
with distance and magnitude occurs in our analysis. To this end,
we have determined 2-D histogram of the residual distribution as
function of magnitude and epicentral distance; to investigate fully
this point we have included in the analysis all the available distances
without any limitation. The results shown in Fig. 11 suggest some
slight overprediction of intensities (≈5–10 per cent) up to 80 km
and ≈15 per cent beyond 80 km. Our results show also a near
independency upon magnitude.
It should be kept in mind, however, that in these comparisons
we have employed both predicted (through ShakeMap and, more
specifically, through the adopted GMPEs and local site correction
relations) and observed data. Thus, and in our opinion, this approach
appears adequate when the aim is the calculation of meaningful
shakemaps such as in FM10, but it should be taken with care when
Figure 11. Analysis of the dependencies of the per cent residual intensities
(cf. Fig. 10) versus epicentral distance (top panel) and magnitude (bottom
panel).
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Figure 12. Intensity residual plots for SA-MCS pairs with respect to eqs (4)–(6) (yellow diamonds). μ ISA03 = −0.16 and σ ISA03 = 0.94 (left panels),
μ ISA10 = −0.01 and σ ISA10 = 0.99 (middle panels), and μ ISA20 = −0.02 and σ ISA20 = 1.08 (right panels). To the purpose of comparison, the residuals using
AK07
the relationship determined by AK07 are also shown (blue squares). The associated bias and standard deviations are μAK07
IPSA03 = 0.59 and σ IPSA03 = 0.88,
AK07
AK07
AK07
AK07
μ IPSA10 = 0.73 and σ IPSA10 = 0.83, and μ IPSA20 = 0.74 and σ IPSA20 = 0.90.
the comparison between observed and predicted SA and intensities
is the effective target of the study. This aspect is pursued below.
5.2 Direct comparison between observed and predicted
values
This section addresses specifically the comparison between observed and predicted values for both intensity and SA. To this end,
we use the regression relations based on the geometric mean between the two horizontal components (eqs 4–6). The aim of this
section is to determine residual plots of the difference between (i)
observed and predicted MCS intensities with respect to magnitude,
M, the hypocentral distance, rhypo , and the predicted MCS intensities themselves (Fig. 12), and (ii) observed and predicted SA again
as function of magnitude, distance and regression predicted SA values (Fig. 13). To predict the SA values from intensity, we exploit
the biuniqueness property of ODR for our relations. To the purpose
of comparison, we also show the results of AK07 who adopted a
magnitude-distance-dependent relation (i.e. their eq. 3). We recall,
however, that their relations have been determined for the Mercalli
Modified scale and, moreover, that to predict SA, their eq. (3) has
been solved for SA. To summarize the results, we determine the
residual plots bias, μ ISA and μSAgm (i.e. the mean of the residuals),
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magnitude, hypocentral distance and predicted intensities or SAs.
The results shown in Fig. 12 indicate that the relationships determined in this work result in small values of the bias at all three
periods (−0.16, −0.01 and −0.02 for MCS intensities from SA03,
SA10 and SA20, respectively). The corresponding values of the bias
obtained using the AK07 relations range between 0.59 and 0.74 to
indicate that AK07 generally underestimate the intensity values.
For what concerns the standard deviations, it appears that the AK07
relationships perform slightly better than those determined here,
that is (0.88, 0.83, 0.90) and (0.94, 0.98, 1.08) for AK07 and this
work, respectively. For SA03 (cf. Fig. 12) there does not appear to
be any significant trend of the residuals for both magnitude and
distance. For SA10 and SA20, our results show some small trend
for magnitude which seems to be missing when using AK07. For
what concerns the intensity predictions (bottom row of Fig. 12),
there appears an overall overprediction when using both our new
relationships and those of AK07 for intensities larger than ≈6 and,
vice versa, underprediction for intensities less than ≈6.
In Fig. 13 we show the results of the residual analysis when
predicting SA from the intensity values. The residuals for the
three periods examined here show basically no dependence upon
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L. Faenza and A. Michelini
Figure 13. SA residual plots for SA-MCS pairs with respect to eqs (4)–(6) (yellow diamonds). μSA03 = 0.06 and σSA03 = 0.38 (left panels), μSA10 = −0.003
and σSA10 = 0.47 (middle panels), and μSA20 = 0.01 and σSA20 = 0.53 (right panels). To the purpose of comparison, the residuals using the relationship
AK07
AK07
determined by AK07 are also shown (blue squares). The associated bias and standard deviations are μAK07
PSA03 = −0.27 and σPSA03 = 0.42, μPSA10 = −0.43
AK07
AK07
and σPSA10
= 0.51, and μAK07
=
−0.46
and
σ
=
0.53.
PSA20
PSA20
magnitude for M > 4. Within the same magnitude range the AK07
relationship tends to predict somewhat larger SA values (top row
in Fig. 13). For rhypo (middle row panels in Fig. 13), we observe
no dependency for SA03 throughout the entire distance range. At
longer periods and at distances >100 km, our relations appear to
underestimate by roughly 0.5 units (logarithm in base 10 of acceleration expressed in cm s−2 ) the observed values (middle row panels
in Fig. 13). In contrast, AK07 seems to overestimate slightly the SA
within the same distance range. The predicted values of SA (bottom row in Fig. 13), appear to match well, within the limitations
imposed by this kind of analysis, the observed values throughout
the range of the observed values. The AK07-predicted SA values
appear to overestimate slightly those observed. In summary, the bias
values calculated using our relations are nearly zero (see caption in
Fig. 13), whereas those obtained using AK07 range between −0.46
and −0.27 to indicate an overall and slight overestimation of SA. In
contrast, the standard deviations of the residuals obtained using the
two sets of relationships are comparable in value—(0.38, 0.47, 0.53)
and (0.42, 0.51, 0.53) for our new relations and AK07, respectively.
In conclusion, the bias values calculated using our relations are
nearly zero (see caption of Fig. 13 for the proper values), whereas
those obtained using AK07 range between −0.46 and −0.27 to
indicate an overall and slight overestimation of SA. In contrast, the
standard deviations of the residuals obtained using the two sets of
relationships are comparable in value.
6 C O N C LU S I O N S
In this study we have performed regression analysis between MCS
intensities and instrumentally recorded peak ground motion data
expressed in terms of maximum horizontal and geometric mean
values of the horizontal components at the periods 0.3, 1.0 and
2.0 s, (SA03, SA10 and SA20, respectively). The data set has been
assembled for earthquakes that occurred in Italy in the time period
1972–2004 while including the 2009 L’Aquila M w 6.3 earthquake.
The work follows from the need to complement the conversions
between the MCS scale intensities and the SA parameters recently
proposed by FM10 with conversions based solely on SAs for earthquakes occurring throughout the Italian territory.
The data set used in the analysis has been assembled from two
thoroughly verified data sources—the database of the Italian strong
motion recordings, ITACA (Luzi et al. 2008) and the Macroseismic Database of Italy 2004 (Stucchi et al. 2007). Compilation
of the data set resulted in 252 SA-I MCS data pairs plus 12 more
data pairs from the recent M w 6.3 L’Aquila earthquake (note that
analysis performed with and without these additional data did not
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evidence any significant difference of the results). The compiled
data set appears to be the most complete data set for Italy and to the
authors’ knowledge the first which relates SAs and intensity values
for Italy.
Because both the intensity and the SA data are affected by inherent uncertainties, we have adopted the ODR technique which
explicitly takes into account the uncertainties in dependent and independent variables. As in FM10 and to apply the technique, we
have chosen to bin the data using the geometric mean since the
assembled SA data set conforms to a log-normal distribution.
We used two separate data sets that differ in the manner the
values of the SA are determined. The first data set uses the maximum
horizontal component and the second the geometrical mean of these
two components. Although adoption of the geometric mean of the
horizontal components, rather than the maximum value, does shift
the regression line to predict somewhat larger values of intensity
for the same level of ground motion, we have found that this shift
is minor and, perhaps more importantly, it is contained within the
regression standard errors.
The results show that, with the available data and for both data
sets, a single-line regression is sufficient to fit the data without
introducing two regression lines, that is, for low and high intensities
(or SA), respectively.
To appraise the determined relations we have inserted them in
a modified version of the USGS-ShakeMap procedure currently in
use at INGV (Michelini et al. 2008). The modifications include the
determination of maps of the SAs from the reported intensities and,
conversely, the determination of MCS intensities from the recorded
instrumental values. In the latter case and to provide a single conversion between the spectral values at the different periods and the
sought MCS intensities, the resulting scale has been set to adopt
progressively longer periods at increasing intensities. In general,
we have found that (i) the instrumentally derived MCS intensity
maps agree in general with the reported macroseismic data and
maps, and, vice versa, (ii) the regression relations can be used to
predict SA maps which we have found to be generally consistent
with those from observed instrumental data. The analysis of the
residuals made on the shakemap values shown in this work appears
to prove an overall consistency of our regression equations, both for
intensity versus SA and, vice versa, SA versus intensity. In addition
we have verified that the found regressions do not depend significantly on either magnitude or distance. The latter findings have
been confirmed by an analysis of the residual intensities (and SAs)
in which observed and predicted values are compared.
The results of our study evidence also that, for the macroseismic fields reported in Italy using the MCS scale, there exists a
difference of ≈1 iu for intensities around 5 at all periods analysed
here when compared to similar relationships determined using the
Mercalli Modified scale. This difference agrees well with our previous findings described in FM10. More specifically, the residual
analysis showed an overall bias of ≈0.5−0.6 iu of the AK07 relationships for all the three periods analysed. This bias is somewhat
smaller than that observed for AK07 by Douglas & Bommer (2009)
for PGA and PGV (i.e. 0.78 and 0.70 for PGA and PGV, respectively) using the data set of FM10.
In conclusion, we find that the results obtained from application of the regressions determined in this study do strengthen the
results of our previous work [FM10] and, within the limitations inherent to this kind of analysis (i.e. regression between a subjective
classification of effects and instrumentally recorded values), they
likely provide a first-order estimate of the level of ground shaking
quantified through the MCS intensity scale in Italy. Perhaps more
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importantly, the regressions developed here can be used to predict
additional parameters of ground motions from intensity data alone
and be of value in the retrospective assessment of past, historical
earthquakes.
AC K N OW L E D G M E N T S
This study has been financed by swissnuclear. We would like to
thank Philippe Renault for comments provided during the course of
the work which helped to improve the analysis. We would like to
thank Ingo Grevemeyer, Abdul-Wahed and one anonymous referee
for reviewing the manuscript and providing constructive criticism.
Some of the figures were constructed using the free software of
Generic Mapping Tools (Wessel and Smith 1998).
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S U P P O RT I N G I N F O R M AT I O N
Additional Supporting Information may be found in the online version of this article:
S1. Assembled data set table (pdf and csv formats).
S2. Shakemaps obtained from application of the relationships of this
study using instrumentally recorded and macroseismic data [panels
containing intensity (top-left); SA03 (top-right); SA10 (bottomleft); SA20 (bottom-right); in each subpanel the left is determined from instrumental data and the right from macroseismic
intensities].
Please note: Wiley-Blackwell are not responsible for the content or
functionality of any supporting materials supplied by the authors.
Any queries (other than missing material) should be directed to the
corresponding author for the article.
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