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Geophysical Journal International

Geophys. J. Int. (2017) 210, 1765–1771 doi: 10.1093/gji/ggx201

Advance Access publication 2017 May 11

GJI Seismology

Frequency ranges and attenuation of macroseismic effects

Patrizia Tosi, Valerio De Rubeis and Paola Sbarra

Istituto Nazionale di Geoﬁsica e Vulcanologia, Via di Vigna Murata 605, 00143 Rome, Italy. E-mail: patrizia.tosi@ingv.it

Accepted 2017 May 9. Received 2017 April 5; in original form 2017 January 10

SUMMARY

Macroseismic intensity is assessed on the basis of the effects caused by an earthquake. These

effects reﬂect the expression of both the intensity and frequency of the ground motion, thus

complicating prediction equation modelling. Here we analysed data of several macroseismic

transitory effects caused by recent Italian earthquakes in order to study their attenuation as a

function of magnitude and hypocentral distance and to obtain a speciﬁc prediction equation,

of simple functional form, that could be applied to each of the effects under analysis. We

found that the different attenuation behaviours could be clearly deﬁned by the values of the

specially formulated magnitude-distance scaling ratio (S), thus allowing to group the effects

on the basis of the Svalue. The oscillation of hanging objects and liquids, together with

the feeling of dizziness, were separated from most other variables, such as the effects of the

earthquake on small objects, china and windows, which were caused by a vibration of higher

frequency. Besides, the greater value of S, associated with the perception of the seismic sound,

explained the peculiarity of this phenomenon. As a result, we recognized the frequency range

associated with each effect through comparisons with the ground motion prediction equations

and, in particular, with the 5 per cent damped horizontal response spectra. Here we show

the importance of appropriately selecting the diagnostic elements to be used for intensity

assessment in order to improve the correlation with ground motion.

Key words: Earthquake ground motions; Seismic attenuation; Wave propagation.

1 INTRODUCTION

Macroseismic scales are based on the observation of the effects

caused by an earthquake and the intensity degree is routinely as-

signed when a prescribed set of diagnostic elements occurs in a town

or city. The speciﬁc set of effects associated to each macroseismic

degree has been established on the basis of empirical observations

and training based on a long-standing experience. The existence of

several macroseismic scales and the differences among the diagnos-

tic elements of each (Musson et al. 2009) highlight the complexity

of the topic. On the other hand, the effects caused by earthquakes are

the expression of the shaking, allowing the existence of a correlation

of macroseismic intensity with ground motion. This correlation has

been investigated by many authors (Douglas 2003). Among others,

Trifunac & Brady (1975), in particular, underlined the broad scatter

of data points in the correlation. Nevertheless, although the topic

has been studied for decades, both the intensity-to-ground-motion

conversion equations and the opposite ground-motion-to-intensity

conversion equations (GMICE) have yet to reach a formulation

that is unambiguous. The differences among the proposed formu-

lations can be mainly ascribed to the selection of the data that is

generally restricted to regional areas. Another reason for the dif-

ferences observed derives from the statistical methodologies and

processing of data adopted (Faenza & Michelini 2010). Moreover,

as highlighted by Wald et al. (1999) and by Caprio et al. (2015),

medium macroseismic intensities (<VII) are better correlated to

peak ground acceleration (PGA) while higher intensities (>VII)

are more related to peak ground velocity (PGV). The presence of a

correlation between intensity residuals and magnitude or distance

has suggested the inclusion of appropriate magnitude and distance

terms (Atkinson & Kaka 2007; Dangkua & Cramer 2011; Worden

et al. 2012). The weakness of prediction models has also been as-

cribed to the frequency content of the shaking, as is explained by

Sokolov&Chernov(1998), who showed that each intensity level

may be characterized by a ‘representative’ frequency, as well as

by Boatwright et al. (2001), who showed how the correlation be-

tween intensity and pseudovelocity response spectral ordinates may

change for different periods.

Our aim in this work is to show how the frequency content plays

a key role in the formulation of a GMICE by speciﬁcally analysing

each macroseismic effect and by performing the calculation of the

scaling of the attenuation versus magnitude and distance.

2 GMICEs AND SCALING RATIO S

Following Souriau (2006), here we show in more simple terms

that, by assuming the validity of the same functional form for the

C

The Authors 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society. 1765

1766 P. To s i et al.

Tab l e 1 . Coefﬁcients of eq. (1).

I=a1+a2M+a3logRRin km a2a2a3S=–a3/a2

Musson 2005 3.31 1.28 –2.81 2.20

Tos i et al. 2015 2.31 1.03 –2.15 2.09

Souriau 2006 –0.78 2.17 –3.54 1.63

Faccioli & Cauzzi 2006 1.02 1.26 –1.51 1.20

Tab l e 2 . Coefﬁcients of eq. (2).

logPG A =b1+b2M+b3logRPGA in m s–2,Rin km b1b2b3S=–b3/b2

Cauzzi & Faccioli 2008 –1.30 0.56 –1.58 2.80

Souriau 2006 –2.55 1.04 –2.17 2.09

Ambraseys et al. 1996 –0.40 0.27 –0.92 3.47

Marin et al. 2004 –2.93 0.78 –1.5 1.92

Sabetta & Pugliese 1996 –0.85 0.36 –1 2.75

prediction of macroseismic intensity (Musson 2005; Faccioli &

Cauzzi 2006;Tosiet al. 2015)

I=a1+a2M+a3logR,(1)

and logarithm of PGA (Ambraseys et al. 1996; Sabetta & Pugliese

1996;Marinet al. 2004; Cauzzi & Faccioli 2008),

logPG A =b1+b2M+b3logR,(2)

where Iis the macroseismic intensity, Mis the magnitude and Ris

the hypocentral distance, it results that the relationship between I

and PGA must include either the magnitude

I=a1−a3

b3

b1+a3

b3

logPG A +a2−a3

b3

b2M(3)

or the logarithm of distance

I=a1−b1

b2

a2+a2

b2

logPG A +a3−a2

b2

b3logR.(4)

Some authors adopted this last functional form (Murphy &

O’brien 1977; Kaka & Atkinson 2004; Souriau 2006), while others

found a simple linear relationship between I and log PGA (Marin

et al. 2004; Faccioli & Cauzzi 2006; Faenza & Michelini 2010;

Caprio et al. 2015)

I=c1+c2logPG A.(5)

The existence of eq. (5) would mean a relation between the two

quantities that is independent of magnitude and distance. It is worth

noting that the coefﬁcient of magnitude in eq. (3), or symmetrically

the coefﬁcient of log Rin eq. (4)

c3=a3−b3

b2

a2(6)

are equal to 0 only if:

a3

a2

=b3

b2

.(7)

These ratios between the coefﬁcients of logarithm of distance

and magnitude reﬂect the combined role played by magnitude and

distance in attenuations and, with the opposite sign, they express

the slope of the lines of equal log PGA or I, respectively, in eqs (1)

and (2) on a graph log R-M. Here we introduce the variable scaling

ratio (S), formulated as S=–a3/a2(or equally S=–b3/b2). The

values of the coefﬁcients of the relationships having the functional

form of eq. (1) are listed in Tables 1and 2. The corresponding S

values show that there is a speciﬁc pair of functions in which eq.

(7) is true (i.e. Souriau 2006;Tosiet al. 2015), although this is not

the case for other relationships, where the conversion can only be

improved with the addition of a distance term. The distance term

C3in eq. (6) shows that PGA should not be converted directly to in-

tensity, but that certain factors, most likely depending on frequency,

must be included. In fact the magnitude of the event inﬂuences the

frequency content of ground motion and the frequency affects the

attenuation with distance of wave amplitude. A possible approach

consists in making the three coefﬁcients C1,C

2,C

3in eqs (5) and (6)

vary as a function of frequency (Souriau 2006). It is worth noting

that the presence of a term C3=0 would introduce a somehow con-

founding difference in the PGA values at locations with the same

macroseismic intensity but at short and long hypocentral distance,

respectively. For this reason it is important to stress the signiﬁcance

of ﬁnding a relationship between entities with a similar distance-

magnitude scaling, that is with a similar value of S, which would

thus cancel out the C3term and would allow the signiﬁcance of the

simple eq. (5) between I and logPGA without distance and mag-

nitude terms. By using the parameter Sit is possible to compare

attenuation relations for both macroseismic intensity and ground

motion without needing the two types of observations to be col-

lected at the same time and location, thus allowing the use of a

larger data set and improving reliability of results. Moreover Scan

be used to put in evidence different attenuations of effects listed in

macroseismc scales, individually considered.

3 DATA SET OF MACROSEISMIC

EFFECTS

The value of macroseismic intensity is assessed on the basis of the

presence of a speciﬁc set of effects caused by an earthquake. Thus,

an additional source of variation, in the correlation between intensity

and ground motion, could derive from the heterogeneity among the

effects considered, and hence from the different frequency ranges

to which various objects and people are responsive. Towards this

aim, we analysed data collected from macroseismic questionnaires,

particularly suitable to study single effects, since each answer can

be studied independently.

The HSIT system (‘Hai Sentito Il Terremoto’ meaning ‘Did you

Feel The Earthquake’ http://www.haisentitoilterremoto.it/; last ac-

cessed April 2017) of the Istituto Nazionale di Geoﬁsica e Vul-

canologia (INGV) collects the questionnaires ﬁlled in by internet

users reporting the effects caused by earthquakes (Tosi et al. 2015).

The reports are largely provided by registered users who receive

an automatic email inviting them to ﬁll in the questionnaire, fol-

lowing the occurrence of an earthquake potentially perceived, since

Frequency ranges of macroseismic effects 1767

Figure 1. Histogram of the number of selected questionnaires as a function

of magnitude.

it is located within an experimentally determined distance that de-

pends on magnitude (Tosi et al. 2015). For this study we selected

all earthquakes, occurring in Italy or in the neighbouring coun-

tries, from June 2007 to October 2015, at a depth shallower than

35 km and in the magnitude range from 2 to 5.9, which received

more than three responses. We excluded from the data set all earth-

quakes with a potentially wrong attribution of responses, that is the

events immediately following (within 8 hr) or just preceding each

ML≥4.5 earthquake having more than 300 reports. As outcome

we analysed the answers of 251,236 questionnaires, reporting or

excluding the presence of speciﬁc indoor effects (see below) caused

by 7285 earthquakes. Fig. 1shows the histogram of the number

of questionnaires selected as a function of magnitude. In addition,

we included 302,770 reports of not-felt earthquakes only for the

analysis of felt/not-felt.

The great majority of HSIT data regarded low macroseismic in-

tensities; thus we analysed only transient effects of the earthquakes

on people, animals and objects, that is more speciﬁcally the follow-

ing effects: felt/not-felt, fear, dizziness, acoustic effect, disturbed

animals, oscillation of hanging objects or liquids, rattling or move-

ment of china, glasses, small objects, doors, windows, pictures,

vases, books and furniture. In the macroseismic questionnaire all

these effects were mentioned in 12 multiple-answer questions, in

which increasing effect intensities were listed (table S1 in Tosi et al.

2015).

4 ATTENUATION OF EFFECTS

In this work we considered the presence of effect (PE) caused by

earthquakes, which, more speciﬁcally, is the ratio of questionnaires

reporting the presence of a speciﬁc effect (ignoring the differ-

ences of its intensity) over the total number of reports regarding it

(reporting either presence or absence). Each ratio was calculated

summing up data of all earthquakes of the same magnitude within

an exponentially increasing range of hypocentral distance. The lo-

calization and magnitude of earthquakes was provided by Cen-

tro Nazionale Terremoti (http://cnt.rm.ingv.it/; last accessed April

2017). In Fig. 2we show the variation of PE, calculated on each

distance-magnitude bin, for each effect considered, as a function of

hypocentral distance and magnitude. Each PEvalue was calculated

from at least 3 questionnaires, although the majority of PEvalues

was calculated from more than 100 feedbacks. The minimum num-

ber of questionnaires has been set to only 3 in order to have at least

some PEvalues inside the windows characterized by very short dis-

tance ranges, mainly located in the depopulated upper left portion

of the graphs. The pixels located at the bottom right of each graph

(Fig. 2) were plotted in more faded tones since located beyond the

range of the automatic email inviting to ﬁll in the questionnaire. For

this reason, less information is available at these distances, since it

was derived largely by voluntary occasional compilers, and the cor-

responding PEfrequently suffered from a high content of random

error.

The lowering of PEat increasing distances and smaller magni-

tudes, excluding the areas of values saturated near 0 or 1, was quite

regular and consistent even when the lowest magnitudes were con-

sidered. Each trend was approximated to a ﬁrst degree polynomial

on the magnitude-log distance representation of the same functional

form of eq. (1):

PE=a1+a2M+a3logR.(8)

We chose this simple functional form because it was previously

used in intensity prediction equations and because it has the advan-

tage of allowing a direct comparison, simpliﬁed by the use of the

parameter S, with the ground motion prediction equations of same

form.

For each effect, we excluded all the values located at the bottom

right of each plot, which, as already mentioned, were not obtained

from registered users. In addition, we also excluded the values PE

<0.1 and PE>0.9 because, besides the experimental error affect-

ing PEvalues near 0 and 1, each effect is responsive to a limited

range of energy, thus there are magnitude and distance ranges in

which the values of PEare constant despite the variation of seis-

mic solicitation. We applied the least-square ﬁtting to the remaining

values (all pixels plotted in full colour in Fig. 2), thus obtaining the

values of the empirical coefﬁcients of eq. (8) with the corresponding

Svalues (Table 3). All correlations had Pearson coefﬁcients greater

than 0.5 and, due to the high number of samples, they pointed to a

signiﬁcance level better than 0.0001 according to both F-Fisher and

t-Student tests. We are aware that the application of least-squares

multiple regression analysis on ground motion data is usually not

recommended because of the strong correlation between distance

and magnitude (Joyner & Boore 1981) ampliﬁed by the stacking of

multiple earthquakes. In fact, being the maximum distance of data

proportional to the magnitude and being the number of earthquakes

related to magnitude, the stacking causes a strong concentration

of data points on the upper left portion of the distance-magnitude

graph and, in particular, on the set of maximum distances reached

by the shaking of earthquakes. Our case, however, was different in

that each distance-magnitude bin corresponded to a single value

given by all earthquakes so that the problematic effect of the corre-

lation between independent variables was reduced. Anyway follow-

ing Fukushima & Tanaka (1990), in order to quantify the possible

miscalculation of the coefﬁcients, we separately applied the single

regression in two steps: for the same magnitude and for the same

distance. Results showed that the averages of coefﬁcients were very

near to the coefﬁcients found with the multiple regression applied

on all data. We estimated the standard error σSof Sratio through the

errors of coefﬁcients a3and a2of eq. (8), obtained with least square

ﬁtting, and their propagation. All Svalues (Table 3), except for those

corresponding to disturbed animals and acoustic effect, had σSless

than 0.1, showing a limited range of variation. The ﬁrst degree

polynomials are depicted as black isolines in each plot (Fig. 2).

Searching for a possible explanation behind the different be-

haviours of the effects considered as a function of distance and

magnitude, we operated a simpliﬁcation excluding some factors

linked to speciﬁc situations: site responses, source mechanisms,

propagation paths, behaviour of furniture and buildings (Sbarra

1768 P. To s i et al.

Figure 2. Value of the presence of each effect (PE), listed in the HSIT macroseismic questionnaire, plotted in ﬁlled squares, as a function of hypocentral

distance and earthquake magnitude ML, each pixel represents the bin width. The regression of eq. (8), calculated for each effect with all values plotted in full

tones, is drawn in black contour lines (0.2, 0.4, 0.6, 0.8) for each plot (a colour version of this ﬁgure is available in the online version).

et al. 2015), individual response to vibration (Sbarra et al. 2014).

Searching for a relation with the variation of ground motion in terms

of frequency, we were conﬁdent on the statistical approach and on

the heterogeneity of situations covered by our data set regarding the

whole Italian region. In the context of the magnitude and distance

scaling of attenuation, we searched for a correspondence between

the presence of effects and the ground motion prediction equations

(GMPE). To this aim, we examined three cases of response spectra

prediction equations, regarding acceleration, velocity and displace-

ment, that have the functional form of eq. (1) and (2) when ignoring

Frequency ranges of macroseismic effects 1769

Tab l e 3 . Coefﬁcients of eq. (8), scaling ratios S, standard errors σ, number of data N, Pearson correlation coefﬁcients r.

Effect a1σa1 a2σa2 a3σa3 S=–a3/a2σSNr

Earthquake felt 0.49 0.017 0.43 0.010 –0.99 0.021 2.32 0.072 990 0.83

Fear 0.28 0.012 0.20 0.004 –0.45 0.009 2.26 0.061 1587 0.82

Dizziness –0.13 0.014 0.16 0.004 –0.20 0.008 1.25 0.060 1353 0.75

Animals 0.16 0.012 0.11 0.004 –0.22 0.009 1.97 0.105 1460 0.62

Hanging objects –0.17 0.014 0.26 0.005 –0.22 0.011 0.84 0.044 1272 0.84

Liquids 0.06 0.015 0.20 0.005 –0.22 0.012 1.10 0.066 1325 0.76

China and glasses 0.13 0.013 0.25 0.004 –0.48 0.010 1.92 0.052 1500 0.84

Small objects –0.14 0.024 0.26 0.008 –0.47 0.016 1.83 0.083 874 0.76

Doors and windows 0.43 0.012 0.18 0.004 –0.42 0.009 2.33 0.073 1545 0.78

Pictures vases books –0.2 0.032 0.26 0.010 –0.47 0.019 1.80 0.097 694 0.74

Furniture 0.04 0.013 0.18 0.004 –0.33 0.009 1.78 0.064 1465 0.77

Acoustic effect 1.03 0.014 0.10 0.004 –0.63 0.011 6.21 0.293 1462 0.85

ground categories. The GMPEs considered were: the 5 per cent

damped horizontal acceleration response spectrum by Ambraseys

et al. (1996), the 5 per cent damped horizontal pseudo velocity

response spectrum by Sabetta & Pugliese (1996) and the 5 per

cent damped horizontal displacement response spectrum (CF08) by

Cauzzi & Faccioli (2008). The CF08 model in particular, which is

based on several active shallow crustal data sets and is valid for

magnitude ranging from 5 to 7.2 and for hypocentral distances up

to 150 km, has one of the best forecasting performances on Italian

data (Roselli et al. 2016) as well as being one of the best-ﬁtting

models for weak motions (Beauval et al. 2012). In order to com-

pare the coefﬁcients of the effect empirical equations eq. (8) with

their corresponding of GMPEs, we used Sthat,asaratio,isinde-

pendent from any unknown factor of proportionality between the

logarithm of ground motion and the presence of effects (PE). It can

be used even to compare displacement, velocity and acceleration,

because, under the assumption of the theoretical transformation of

each spectral value into the other through the multiplication by T

2π,

the coefﬁcients a3and a2as well as their ratio Sshould not change.

Fig. 3shows the Svalues of GMPEs for periods (T) in the range

0.05–11 s, together with the Svalues (horizontal lines) obtained

for the presence of the effects (Table 3). The periods of GMPEs

corresponding to the Svalues of effects should give an indication of

the frequencies that dominate in each group of effects. Going into

more detail, Fig. 3shows that the majority of effects (earthquake

felt, feeling of fear, disturbed animals, vibration of doors, china,

glasses, small objects, furniture, pictures, vases and books) were

grouped and corresponded, accordingly to all three GMPEs, to the

period range 0.5–2 s. In particular, the corresponding period of

0.4 s for the ability to recognize the occurrence of an earthquake,

was in accordance with Trifunac & Brady (1975), who showed

that the human perception of body vibration is more efﬁcient in

the period range 0.1–0.5 s. Liquid oscillation and dizziness, this

last probably caused by body oscillation, pointed to a period range

4–5 s according to CF08 and, although Svalues of GMPEs never

went under 0.88 even at T>10 s, the low Svalue corresponding

to the oscillation of hanging objects pointed to periods quite long

and in particular longer than the natural period (T=1.8 s) of a

common 0.8 m chandelier calculated using the simple pendulum

formula, suggesting that complex interactions with other variables

were acting in this case.

In contrast, the Svalue of acoustic effect was very high and

in fact out of range of the considered GMPEs. Acoustic effect

is related to a speciﬁc frequency range, being conditioned by the

human hearing range that commonly begins from 20 Hz. This effect

is thus inﬂuenced by very short periods, regarding ground motion

extent, and it is worth noting that its Svalue, experimentally derived

Figure 3. Values of the Sratio computed for 5 per cent damped horizontal

response spectra of: displacement (Cauzzi & Faccioli 2008, black dots),

pseudo velocity (Sabetta & Pugliese 1996, triangles) and acceleration (Am-

braseys et al. 1996, crosses). Horizontal lines mark Sratio experimental

values found for the speciﬁed macroseismic effects (a colour version of this

ﬁgure is available in the online version).

with questionnaire data, did not contradict the comparison with

GMPEs.

5 DISCUSSION AND CONCLUDING

REMARKS

The method here presented investigated the correlation between

ground motion and macroseismic records overcoming the problem

of the collection of the two types of observations at the same time

and location, thus allowing the use of a much larger data set and

making the result more stable.

This study adds but a piece in the puzzle of GMICE. In fact, our

data are based on weak macroseismic effects, so that our consider-

ations may not be applicable to high macroseismic intensities and

associated damage. Additionally, our study only considered sim-

ple prediction equations among the several different formulations

present in the literature that include more terms (e.g. a quadratic

1770 P. To s i et al.

dependence from magnitude aM2, an anelastic attenuation term aR

or a magnitude-distance coupled term aMR), and we excluded the

duration of ground motion, which probably has an inﬂuence even

on transient effects. On the other hand, the choice of studying transi-

tory effects has allowed the analysis of a great quantity of data even

for minor earthquakes. Furthermore, the use of equations having

the simple functional form of eq. (1) has allowed the direct com-

parison of scaling terms, while the addition of other coefﬁcients to

the empirical equation, involving distance and magnitude, would

have modiﬁed the a2and a3values because of the trade-off be-

tween the terms (Souriau 2006). The relationship between pseudo

spectral acceleration and certain macroseismic effects (grouped in

four parameters: personal feelings, object vibration, object displace-

ment, acoustic noise) has already been investigated by Lesueur et al.

(2013), who found a higher correlation coefﬁcient in the period

range 0.1–2 s, with small differences among effects. The approach

here presented, based on the analysis of single effects, has allowed

a clearer distinction of the periods involved and the separation of

acoustic noise behaviour from other macroseismic parameters, in

agreement with theoretical expectation.

In our data set, PEvalues showed a variation, versus magnitude

and distance, which could be represented with the same simple

functional form adopted in ground motion prediction equations.

The introduction of the new parameter Sand the differences among

effects found in distance and magnitude scaling brought to the iden-

tiﬁcation of the involvedfrequency ranges and to the clear separation

of three of the effects of the macroseismic scale related with slow

oscillations (dizziness, oscillation of hanging objects and liquids)

from the behaviour common to the other effects. In accordance

with other authors (Brazee 1979; Vannucci et al. 2015), our results,

which were also based on quantitative analysis although using dif-

ferent methods, suggest a revision of the grouping of effects in the

macroseismic scales (Sbarra, Tosi & De Rubeis, The contribution of

each diagnostic effect to the assessment of macroseismic intensity,

submitted).

It is important to stress that, for the assessment of macroseismic

intensity, one should only use the effects showing similar Svalues in

order to improve the correlation between macroseismic intensity and

ground motion. Moreover, the ground motion should be considered

at speciﬁc frequencies. This concept is in agreement with Faenza

& Michelini (2011), who analysed the regression between intensity

and spectral acceleration (SA) at 0.3, 1.0 and 2.0 s. In particular,

they suggested to derive low (I≤4), moderate (4 <I≤6) and

high (I>6) intensities from SA 0.3 s, SA 1.0 s and SA 2.0 s,

respectively. We suspect that this difference could actually be due to

the effects used in intensity assessment. In fact, in the macroseismic

scales I=4 is assessed using effects that are associated to periods

T<1 s (i.e. felt/not-felt and vibration of china, glasses, doors,

windows, Fig. 1), while for I=5 the description involves also effects

associated to longer periods (oscillation of hanging objects and

liquids).

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