Ground-motion scenarios on Mt. Etna inferred from empirical relations and synthetic simulations

Abstract

Ground motion scenarios for Mt. Etna are created using synthetic simulations with the program EXSIM. A large data set of weak motion records is exploited to identify important input parameters which govern the modeling of wave propagation effects, such as Q-values, high frequency cut-off and geometrical spreading. These parameters are used in the simulation of ground motion for earthquakes causing severe damage in the area. Two seismotectonic regimes are distinguished. Volcano-tectonic events, though being of limited magnitude (M_max ca. 5), cause strong ground shaking for their shallow foci. Being rather frequent, these events represent a considerable threat to cities and villages on the flanks of the volcano. A second regime is related to earthquakes with foci in the crust, at depths of 10–30 km, and magnitudes ranging from 6 to 7. In our synthetic scenarios, we chose two examples of volcano-tectonic events, i.e. the October 29, 2002, Bongiardo event (I = VIII) and the May 8, 1914, Linera earthquake (I = IX–X). A further scenario regards the February 20, 1818 event, considered representative for stronger earthquakes with foci in the crust. We were able to reproduce the essential features of the macroseismic field, in particular accounting for the possibility of strong site effects. We learned that stress drop estimated for weak motion events is probably too low to explain the intensity of ground motion during stronger earthquakes. This corresponds to findings reported in the literature claiming an increase of stress drop with earthquake size.

Appendix: Parameter study

1.1 Shallow events

In order to identify suitable input parameters for the simulations with the EXSIM code (Motazedian and Atkinson 2005), we tested a number of sets with the aim of matching the empirical GMPEs published by Tusa and Langer (2015) for data recorded on Mt. Etna. For a shallow event we have tested the parameters given in Table 6.

Table 6 Input parameters related to frequency dependent absorption

In Giampiccolo et al. (2007) a frequency dependent Q value is reported with Q₀ = 30 (at 1 Hz) and an increase f^0.5 for higher frequencies. F _max of 15 Hz is a standard value that is widely used in stochastic simulation (see for instance Boore 1983, 2009) and is commonly used for sources whose foci are situated in a crystalline-type basement. It is still debatable whether this high frequency cut-off F _max is an effect of wave propagation or a characteristic of the source. In any case, the ω²-source model, which is at the basis of the EXSIM code, requires this band limitation for the law of energy conservation.

As mentioned in the main text, the use of the Giampiccolo et al. (2007) attenuation law together with F _max  = 15 Hz PGA and PGV are somewhat overestimated at close distances, whereas an underestimation of both PGA and PGV is encountered at distances >20–30 km. Greater distances were not considered by these authors for the lack of available data. Using a higher Q₀ value (90 instead of 30, and applying the same exponent for frequency dependence), we find a considerable overestimation of PGA and PGV, particularly at distances less than ca. 30 km. One way to resolve the problem is the choice of a lower value for F _max . From a physical viewpoint, we may justify a low F _max by the fact that the foci of shallow events on Mt. Etna are hosted by layers of sedimentary material—often shales or marnes. This may limit the radiation of high frequencies from such sources. Strong heterogeneities such as faults that are present on the flanks of the volcano, may further limit the propagation of high frequency energy. Choosing F _max  = 5 Hz the simulated PGA and PGV fit values obtained from Tusa and Langer (see their Table 3) fairly well (Fig. 16).

Fig. 16

a Simulated and empirically predicted PGA, b simulated and empirically predicted PGV. The legends refer to the combinations mentioned in Table 6, for example “q30_f05” represents the simulations carried out using Q ₀ = 30, and F _max  = 5 Hz. The source and other parameters correspond to those reported in Table 1. The size of the diamonds (empirically predicted ground motion parameters) is about 0.4 units, corresponding to the RMS-error reported in Tusa and Langer (2015)

The simulations carried out for the parameter couple Q₀ = 90/F_max = 15, and Q₀ = 30/F_max = 5 show that—considering the whole range of distances—a tradeoff between Q and F _max can be ruled out. The choice of F _max affects the peak GMPs (PGA and PGV) at close distances (say less than ca. 20–30 km), whereas the choice of Q is critical for GMPs at greater distances.

As the effects of F _max are most evident for peak ground motion values at small epicenter distance, we examine whether there may be the risk of confusion with other simulation parameters, in particular the stress parameter. In a further sequence of simulations, we used the parameter combination shown in Table 7.

Table 7 Model parameters varying F _max and stress

It can be seen from Fig. 17a, b that more or less all combinations yield a reasonable fit of the empirical relations by Tusa and Langer (2015). The combination F _max  = 5 Hz, stress = 5 bar best fits PGA near the source, whereas the combination F _max  = 3 Hz, stress = 10 bar performs slightly better than the others for PGA at greater distances. The empirical relation for PGV is matched best by the choice F _max  = 10 Hz, stress = 3 bar. Note that the stress drop reported by Giampiccolo et al. (2007), is found at ca. 5–10 bars. In the end, we adopted the combination stress = 5 bar, F_max = 5 Hz as a suitable compromise between the various options in our parameter study and the results of Giampiccolo et al. (2007).

Fig. 17

a Simulated and empirically predicted PGA, b simulated and empirically predicted PGV. “f5_s5” stand for the combination F _max  = 5 Hz, stress = 5 bar, in the same way “f3_s10” stands for F _max  = 3 Hz, stress = 10 bar, and “f10_s3” for F _max  = 10 Hz, stress = 3 bar. The source parameters correspond to those reported in Table 1. The size of the diamonds is about 0.4 units, corresponding to the RMS-error reported in Tusa and Langer (2015)

1.2 Deep events

For deep events we have used F _max  = 15 Hz, which is the standard value frequently used in stochastic ground motion simulation. Since the sources are situated in the crystalline-type basement, we have no specific reason to use a different value to the standard. The role of the stress parameter is discussed in the framework of the simulation of the 1818 earthquake (Sect. 5.2). Here we focus on the choice of Q, comparing values of 50, 90 and 150 for Q₀, and an exponent of 0.5 for the frequency dependent increase (see Fig. 18). Compared to the empirical relations of Tusa and Langer (2015), the choice Q₀ = 90 yields a good match of PGA for small and intermediate distances (<50 km), and a somewhat greater discrepancy at larger distances. PGV is slightly overestimated for small distances and fits better at larger distances. The choice Q₀ = 150 tends to overestimate all values at all distances, whereas using Q₀ = 50 peak the simulated ground motion values underestimate predictions of Tusa and Langer (2015). This holds specifically for intermediate and greater distances. The choice with Q₀ = 90 and frequency dependent increase (f^0.5) proves a reasonable compromise for fitting PGA and PGV in the distance range of interest.

Fig. 18

a Simulated and empirically predicted PGA, b simulated and empirically predicted PGV. The source parameters correspond to those reported in Table 1. The size of the diamonds is about 0.4 units, corresponding to the RMS error reported in Tusa and Langer (2015)