1 Introduction

Ground motion simulation in volcanic areas is a difficult task due to the complexity of seismic source, heterogeneity of the propagation medium and surface geomorphological features. In regions where large earthquake data are not available we can use the ground motion produced by small size earthquakes to simulate the ground shaking likely associated with larger events. This is the case of Campi Flegrei caldera, an active volcanic area located in southern Italy, west of Naples. Two caldera collapses [Campanian Ignimbrite, 39 ka; Neapolitan Yellow Tuff (NYT), 15 ka] have contributed to define the present structural setting of Campi Flegrei (Selva et al. 2011). In the past 15 ka, volcanic activity has been concentrated within NYT caldera; the last eruption occurred in 1538 (Mt. Nuovo eruption) after a long period (LP) of quiescence. During the last century the two major unrest episodes occurred in 1969–1972 and 1982–1984. During the latter episode, when a ground uplift of 2 m occurred, more than 16,000 shallow earthquakes were recorded, the most of which were located in Pozzuoli-Solfatara area (central sector of the volcanic area). The maximum duration magnitude was 4.2 (Aster et al. 1992), while the maximum macroseismic intensity was VI/VII degree (Branno et al. 1984). Minor swarms of volcano tectonic (VT) seismicity occurred in 2000 (maximum MD = 2.2, Saccorotti et al. 2001) and 2006 (maximum MD = 1.4, Saccorotti et al. 2007), while a large swarm of LP events was recorded in 2006. Focal mechanisms evaluated for 2006 VT events show a predominance of normal faults, with stress drop values between 1 and 10 bar (Saccorotti et al. 2007). Several studies were performed to investigate source features (e.g. Del Pezzo et al. 1987), propagation characteristics (e.g. Petrosino et al. 2008) and site effects (e.g. Tramelli et al. 2010). The present structural setting of the caldera is dominated by faults, fractures and morpho-structural elements related with the volcanic history of the area. Fault main trends are NE–SW and NW–SE, while only a few are around N–S and E–W fault alignments are observed. A detailed description of historical volcanism and structural setting can be found in the work of Selva et al. (2011).

Some efforts have been done to assess ground motion parameters peak ground velocity (PGV), peak ground acceleration (PGA) and peak spectral acceleration (PSA) based on empirical observations and stochastic simulation of the source (e.g. De Natale et al. 1988; Galluzzo et al. 2004; Douglas et al. 2013), or probabilistic approach (e.g. Convertito and Zollo 2011). The present study is part of a European project (UPStrat_MAFA: Urban disaster Prevention Strategies using MAcroseismic Fields and FAult Sources) in which several volcanic areas were studied. In the present paper we adopted a simulation procedure to calculate ground motion scenarios associated with large earthquakes that can potentially strike the area of Campi Flegrei. Before applying a stochastic procedure to simulate strong ground motion, all parameters and physical quantities must be tuned by comparing simulated and observed PGV and response spectra. To achieve this goal we adopted the finite fault stochastic method by Motazedian and Atkinson (2005). First we evaluated ground motion prediction equation (GMPE) for small local earthquakes of Campi Flegrei and later we compared observed and simulated ground motion to asses a set of input parameters representative of the true ground motion. The last step consisted in the evaluation of moderate-to-large earthquake scenarios based on historical parametric data. The data set used in the present study is composed of twenty well located earthquakes (MD∈[−0.3, 2.2], maximum hypocentral distance R = 12 km) recorded in the Campi Flegrei caldera in the period 2000–2012 (Tables 1, 2; Fig. 1). The five earthquakes with the best signal-to-noise ratio recorded by the largest number of stations were used to compare observed and simulated ground motion in order to calibrate input parameters for simulations, as explained in the next section. Figure 2 shows the seismograms of horizontal components for one of selected earthquakes recorded at seven stations (earthquake 20120907 0734, Mw2.2).

Table 1 Hypocenters and magnitude of earthquakes considered in this work
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Table 2 Coordinates of the seismic stations used in this work
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Fig. 1
figure 1

Epicenters of analyzed earthquakes (red stars) and seismic stations (blue triangles) in the Campi Flegrei area. The size of star symbol is proportional to the earthquake magnitude. The yellow square in the inset map of Italy shows the position of Campi Flegrei

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Fig. 2
figure 2

Horizontal components of ground velocity (E–W on the left, N–S on the right) produced by the earthquake 20120907 0734, Mw2.2, recorded at six seismic stations. The waveforms are plotted with epicentral distance (1–4 km) increasing from top to bottom, as indicated inside the figure

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2 Method of analysis

We started our analysis by computing GMPE on twenty local earthquakes. The general formulation of GMPE equation is:

$$ {\text{F}}\left( {\text{Y}} \right) = {\text{ a f}}_{1} \left( {\text{M}} \right) + {\text{ b f}}_{2} \left( {\text{R}} \right) \, + {\text{ c }} +\upsigma, $$
(1)

where F(Y) is a function of ground acceleration or velocity, f1(M) and f2(R) are functions of magnitude M and distance R respectively. Taking into account the small ranges of magnitudes, focal depths and epicentral distances, we assumed F(Y) equal to log10(PGV), f1(M) as a linear function of moment magnitude and f2(R) equal to log(R). Consequently GMPE was evaluated by fitting the PGV values with a non linear model given by the equation:

$$ \log_{10} \left( {\text{PGV}} \right) = {\text{ a }} + {\text{b M}}_{\text{w}} + {\text{ c log}}_{10} {\text{R }} +\upsigma_{\text{LogY}} , $$
(2)

where PGV (cm/s) indicates the PGV on horizontal (or vertical) components of motion, Mw is the moment magnitude and R (km) is the hypocentral distance. PGV on horizontal components was set by considering the maximum value between the N–S and E–W components.

Following Havskov and Ottemoller (2010), preliminary Mw was evaluated from the seismic moment M0 (Hanks and Kanamori 1979), computing the low frequency spectral amplitude averaged on all available stations. The seismic moment M0 was calculated by considering the relationship (Lay and Wallace 1995):

$$ M_{0} = \frac{{4\pi \rho v_{s}^{3} R\Omega_{0} }}{{FY_{\theta \varphi } }} $$
(3)

where ρ is the density of the medium, vs is the shear wave velocity at source, R the hypocentral distance, Ω0 the low-frequency level of the source displacement spectrum, F the free surface operator (F = 2) and Yθ,φ the radiation pattern term. Attenuation parameters, density, and shear wave velocity model were taken from the papers of Petrosino et al. (2008), Aster et al. (1992) and Aster and Meyer (1988) respectively. For seismic moment evaluation, geometrical spreading was set to 1/R and radiation pattern term was set to the average value of 0.55.

The attenuation terms were deconvolved from the displacement spectra (evaluated on 1 s window starting 0.2 s before S wave arrival and averaged on the horizontal component of motion), before evaluating low frequency spectral level of seismic source. Low frequency spectral amplitude was evaluated in the frequency range between 2 and 6 Hz. Mw was calculated from M0 at each site and averaged over all the available stations. The average can reduce the effect of local amplification at a single site. By considering the previous procedure we obtain an error of 0.3–0.4 on the estimate of Mw.

After the estimation of GMPE we have calibrated input ground motion parameters for stochastic simulation (magnitude, fault size and subdivision, stress drop, and attenuation features). Hence, the second step was to select five local earthquakes characterized by the largest number of recording sites. We have used the finite fault stochastic approach by Motazedian and Atkinson (2005) coded in the software EXSIM. The basic principle of finite fault stochastic approach is based on the assumption that, considered a target fault subdivided in subfaults, the ground motion acceleration (the same occurs for velocity) a(t) is obtained by summing with a proper delay time all the contributions from each subfaults as:

$$ {a\left( t \right) = \sum\limits_{i = 1}^{nl} {\sum\limits_{j = 1}^{nw} {a_{ij} } } \left( {t + \varDelta t_{ij} } \right)}, $$
(4)

where nl and nw are the number of subfaults along the fault length and width, and Δtij is the radiation delay time from the ij-th subfault to the observation point. Each time series a ij (t) is stochastically generated by assuming that the corresponding spectrum A ij (f) can be modeled by an ω-squared shape (Boore 1983) as:

$$ {A_{ij} (f) = \frac{1}{{R_{ij} }}\frac{{CM_{0ij} (2\pi \pi)}}{{1 + \left( {f_{0ij} } \right)^{2} }}^{2} \exp ( - \pi f\kappa ) \cdot \exp \left( {\frac{{ - \pi fR_{ij} }}{Q\beta }} \right)}, $$
(5)

where M0ij, f0ij and Rij are the ij-th subfault seismic moment, corner frequency and distance from the observation point, respectively. The constant C includes radiation pattern, free surface amplification, horizontal components partition factor, density and shear wave velocity at the source. The term exp(−πfk) is relative to high frequency fall off decay (Anderson and Hough 1984) and can be alternatively modeled by fmax filter. The term 1/Rij and the quality factor Q(f) are related to geometrical spreading and elastic attenuation, respectively. The seismic moment M0ij associated to each subfault is obtained by dividing the seismic moment M0 associated to the entire fault by the number N of total subfaults, being N = nl × nw. In case the slip on the entire fault is not uniform, M0ij is obtained by considering a specific weight associated to the relative slip of the ij-th subfault. In the present study, the simulated PGV and response spectra (5 % of damping) were obtained by averaging among 50 simulations. To check the validity of the simulation parameters retrieved from other studies we compared PGV and spectral response spectra of observed and simulated ground motion through a quantitative fit method as explained in the next section. Finally, with the well-tuned set of parameters, we have simulated the ground motion produced by strong earthquakes occurred in the past centuries, known from historical seismicity and parametric catalog.

3 Results

Before the evaluation of empirical relationship for PGV, the seismic moment M0 (and hence Mw) was calculated for the 20 selected earthquakes. The obtained range of magnitude is Mw∈[0.8, 2.4] (corresponding to MD∈[−0.3, 2.2]). PGV was measured on the vertical and horizontal components of motion for all selected earthquakes. The peak velocity versus hypocentral distance is shown in Fig. 3 for different ranges of magnitude. By fitting the data shown in Fig. 3 with Eq. (2) we obtained the corresponding parameters for GMPE relationship (for vertical and horizontal components of motion), as shown in Table 3. This GMPE relationship is valid in the overall range of magnitude Mw∈[0.8, 2.4]. For such a low magnitude range, that has no direct application for seismic hazard, very few GMPEs are found in literature. In Fig. 4 we compare the GMPE found in this work with GMPEs evaluated for the volcanic area of Etna (Langer et al. 2015) and Irpinia (Bobbio et al. 2009), a tectonic active area about 90 km East of Campi Flegrei. Although we compare Mw with ML scale (in the case of Mw1.6), it is noteworthy that the attenuation of peak velocity for Campi Flegrei (black line) is stronger than that of the other two areas (magenta and cyan lines).

Fig. 3
figure 3

Peak ground velocities a vertical PGV, b horizontal PGV observed for 20 local earthquakes occurred in Campi Flegrei area between 2000 and 2012

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Table 3 Regression coefficients and associated standard errors for PGV (horizontal and vertical) relationship in Eq. (1)
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Fig. 4
figure 4

Campi Flegrei GMPE for Mw1.6 ± sigma (black continuous line and dotted lines) compared with Irpinia GMPE ML1.6 (cyan continuous line, Bobbio et al. 2009) and Etna GMPE ML1.6 shallow earthquakes (magenta continuous line)

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The evaluated GMPE was used to calibrate the set of parameters for the stochastic simulation. The calibrated set of parameters was fixed by comparing simulated and observed ground motion. The synthetic seismograms closest to the observed ones were set by a trial and error procedure performing a grid search of the best solution on various input parameters retrieved from other studies. The best solution was chosen on the base of GOF test (Good Of Fitness based on normalized root mean square error) between observed and simulated PGV. The simulations were performed for shear waves, therefore the comparison was done with the horizontal components of ground motion. The set of input parameters for the finite fault stochastic procedure is shown in Table 4 with the respective references. The comparison between observed and simulated ground motion was carried out on 5 selected earthquakes. In Fig. 5 we show the cases of three earthquakes (20120907 0734 Mw2.2, 20111004 1211 Mw1.8, 20110519 0039 Mw1.5), in terms of PGV trend for horizontal components of motion. The source parameters used for the simulations shown in Fig. 5 are resumed in Table 4. The hypocenters were assumed to be located at the fault center and random slip distribution was set. Fault size and stress drop were set on the base of source scaling analysis (Del Pezzo et al. 1987), while focal mechanisms were evaluated through the FOCMEC code (Snoke 2003). As an example, in Fig. 5d we show the GOF test for different values of stress drop: the best fit is obtained for Δσ = 5 bar. The simulated values of PGV reproduce the GMPE trend, even though sometimes the observed values are much higher than predicted ones. The high variability of the peak amplitude and the shape of waveforms is typical of Campi Flegrei area. This is clearly seen in Fig. 2, where the signals of the earthquake 20120907 0734 (Table 5) are shown with epicentral distance increasing from top to bottom. This observation can be explained by the local site effects in the area; Tramelli et al. (2010) showed that for some sites there are relative amplifications of a factor 3 or 4 in the frequency band 1-20 Hz. The comparison between observed and simulated response spectra for the 20120907 0734 earthquake is shown in Fig. 6 at four sites. The simulated response spectra are quite similar to those observed on the horizontal component of motion.

Table 4 Input parameters for the generation of synthetic ground motion in Campi Flegrei area using the program EXSIM
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Fig. 5
figure 5

Comparison between PGV values observed on horizontal components (gray full squares and diamonds), GMPE evaluated for Campi Flegrei (dotted line) and simulated PGV (circles with error bars). Results are shown for three specific earthquakes of magnitude Mw2.2 (a), Mw1.8 (b) and Mw1.5 (c). d Mw1.5 GOF test obtained for different values of stress drop

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Table 5 Source parameters, seismic stations and epicentral distance of local earthquakes used for the calibration procedure
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Fig. 6
figure 6

Observed (red and blue lines for E–W and N–S components respectively) and simulated response spectra (black line; 5 % of damping averaged on 50 simulations) for the earthquake 20120907 07:34, Mw2.2, at four stations

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Once the calibrated parameters were tuned, we performed two simulations for the moderate-to-large earthquake scenarios. To define the possible moderate-to-large earthquake that could occur in the area, we considered the following results from literature: the largest magnitude earthquake occurred during the 1982–1984 bradyseismic episode (M = 4.2, Aster et al. 1992); the maximum expected magnitude M = 4.3 (Galluzzo et al. 2004), and the largest earthquake from the historical parametric catalog CPTI11 (M = 5.4 occurred in 1582, Rovida et al. 2011). For the sake of simplicity hereafter we refer to the previous magnitude scales as moment magnitude Mw. We have performed two simulations, one for Mw = 4.2 and another for Mw = 5.4. Chosen an arbitrary epicenter, we have generated PGV along radial distance by averaging over all directions. By using the calibrated parameters shown in Table 4, the stochastic simulation for the two earthquake scenarios have been performed. For Mw4.2 we have adopted the source depth at 2.7 km b.s.l, stress drop values equal to 5, 10, 20 and 30 bar and fault size of 2 km × 1 km. In the case of Mw5.4 we set arbitrarily the depth at 4 km b.s.l., stress drop values equal to the Mw4.2 case and fault size of 6 km × 5 km, considering the results of Konstantinou (Konstantinou 2014) obtained for the Mediterranean region. The results are shown in Figs. 7 and 8 for Mw4.2 and Mw5.4 respectively. Superimposed to PGV trend in the case of Mw4.2, we plotted, in Fig. 7, the GMPEs from Langer et al. (2015) obtained in the volcanic area of Mt Etna for superficial events in the magnitude range ML[3,4.8].

Fig. 7
figure 7

Comparison of simulated ground motion PGV for Mw4.2 (black line) with hypocenter at 2.7 km depth for different values of stress drop (5, 10, 20 and 30 bar), and ML4.2 GMPE for Mt Etna Superifical Events (from Langer et al. 2015, magenta line)

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Fig. 8
figure 8

Simulated ground motion PGV for Mw5.4 (black line) with hypocenter at 4.0 km depth for different values of stress drop

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4 Discussion and conclusions

The observations about low magnitude local earthquakes (MD[−0.3, 2.2]; Mw[0.8, 2.4]) occurred in Campi Flegrei area show high variability among the different sites in terms of PGV, waveform shape and spectral content. The use of a stochastic simulation procedure allowed us to calibrate source (fault size, stress drop) and propagation (attenuation Q) parameters by comparing observations and simulated waveforms, which are averaged over the selected set of earthquakes and over the area of study. This analysis has been performed for the five well recorded earthquakes and has shown the following features: fault size of 200/300 m, stress drop of about 5 bar, and Q attenuation factor (Qs = 25·f0.4) very close to values described in literature. Both GMPE trend and Qs have revealed a considerable attenuation which characterizes the investigated area, as confirmed by the comparison with other volcanic and tectonic environments. It is not simple to quantify the influence of site effect on simulated results. Simulated PGV and response spectra were obtained by averaging the results over 50 simulations but in some cases the observed PGV are quite larger than the simulated ones. The difference between observed and simulated trend (most of them 3–4 times greater than the simulated PGV) indicates the presence of site effects in the area.

The tuned parameters and simulation method allowed us to simulate ground motion scenario for large earthquakes that could strike the area. In the specific case we have selected, on the base of published works and catalogs, the Mw4.2 and Mw5.4 earthquakes to perform ground motion simulation. In synthesis, for Campi Flegrei the main results of this study are:

  • Large variability of peak velocity in the area due to local site effects;

  • Strong attenuation that affects the amplitude trend far from epicenter;

  • The simulated PGV takes a maximum value of 4 cm/s for Mw4.2 (depth = 2.7 km, Δσ = 30 bar), and 7 cm/s for Mw5.4 (depth = 4.0 km, Δσ = 30 bar) simulated amplitude;

  • The simulated PGV for Mw4.2 shows similar values to PGV obtained for Mt Etna (ML = 4.2) for a stress drop of 30 bar. Taking into account the difference between ML and Mw scale (Mw − ML = 0.3 as deduced from Azzaro et al. 2011) we are confident that the two curves show similar results in a stress drop range of 10–30 bar. Imcs intensities calculated from PGV (Faenza and Michelini 2010) are equal to 6–7 (in the range 10–30 bar) and are similar to the values found by Branno et al. (1984);

  • The simulated PGV for Mw5.4 gives Imcs value equal to 7, and only in some cases, for stress drop of 30 bar, equal to 8. These values are in agreement with the value (7–8) reported by Rovida et al. (2011).

The stochastic approach has revealed an useful tool to investigate source, path and site effect features in heterogeneous environment as volcanic areas, characterized by low magnitude seismicity. More efforts should be addressed to understand the influence of site amplification on the GMPE evaluation and on stochastic simulations. However, the stochastic finite fault approach coded in EXSIM has been an useful tool to simulate strong ground motion scenario although, for low magnitude local seismicity, fault size of hundreds of meters represents a lower limit for the application of the method which has been implemented for larger earthquakes.