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Map of the main active structural elements of Mt Etna. White arrows represent the horizontal displacement vectors as measured by Bonforte et al. (2008) between 2005 July and 2006 June. The upper panel shows Mt Etna in the seismotectonic framework of the central Mediterranean area (redrawn after Monaco et al. 2005).
Source publication
The Pernicana Fault (PF) is the main structural element of Mt Etna and
the northern boundary of a section sliding to the southeast. Observed
ground motion records in the damage zone of the PF show strong
variations of directional resonance in the horizontal plane. The
observed resonance directions exhibit an abrupt rotation of azimuth by
about 30°...
Contexts in source publication
Context 1
... papers ( Rigano et al. 2008;Di Giulio et al. 2009). The PF is the major tectonic element of the Mt Etna volcano, extending from the volcanic crater to the coastline along 18 km, with an average strike of N110 • , and kinematics varying from oblique to purely left-lateral strike-slip. The PF structure borders to the North a large sector of Mt Etna (Fig. 1), which is charac- terized by flank instability in the southeastern part of the volcanic edifice (Acocella & Neri 2005). This instability produced a lateral movement with horizontal displacements (Bonforte et al. 2008) up to a ten of centimetres in a year during the 2005-2006 activity. Di Giulio et al. (2009) performed a detailed ...
Context 2
... Etna is located along the Ionian coast of Sicily (Fig. 1), at the front of the Apennine-Maghrebian Chain (Lanzafame et al. 1997;Monaco et al. 2005, and references therein). It is the largest ac- tive volcano in Europe with an elliptical base of 38-45 km and a height of 3320 m through the accumulation of basaltic lava flows and pyroclastic eruptive episodes during its 170 kyr of activity ...
Context 3
... and pyroclastic eruptive episodes during its 170 kyr of activity (Romano 1982;Calvari et al. 1994;Corsaro et al. 2002;and references therein). Volcanic activity occurs in the present at the four summit craters and along flank fissures, mainly concentrated in three 'rift zones' (Garduño et al. 1997;Behncke & Neri 2003) at northwest, south and west (Fig. ...
Context 4
... models have been proposed to explain the complexity of the tectonic environment where Mt Etna has formed. The pre- dominant role can be deduced from field observations of faults, fractures, dikes and scoriae cones. The PF represents the most pro- nounced tectonic lineament of the Mt Etna structure (Fig. 1). Fault evidence extends eastward from the NE Rift (around 1850 m a.s.l.) to the coastline, for a total length of 18 km ( Neri et al. 2004). Its morphology is represented by a scarp (up to 80 m high) at elevations between 950 and 1530 m; the lack of a clear morphological signa- ture in the other zones has been related to the most ...
Context 5
... to the West by the N-S trending Ragalna fault system, with a predominant dextral-normal motion (Rust & Neri 1996;Acocella & Neri 2005) and to the South by the Trecastagni- Mascalucia-Tremestieri fault system (Froger et al. 2001). Geodetic surveys indicate an E to ESE relative movement of the sliding sector as indicated by the white arrows in Fig. 1 (Bonforte et al. 2008;Alparone et al. 2011). The relation between the PF and the sliding is evident from the relative downthrown of the southern sector that prevails on the movement of the ...
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The anelasticity and anisotropy widely exist in real subsurface media. Strong anelasticity will lead to phase dispersion and amplitude attenuation during seismic wave propagation. Anisotropy cause seismic waves to have obviously different kinematic characteristics from that of isotropy. For seismic migration, ignoring the anelasticity and anisotrop...
Citations
... They both show a near-orthogonal relation (∼88° in the northern sector and ∼83° to the south) with the azimuth of the observed directional resonance ( Figure 4C). Therefore, as in previous sections, even [79] concluded that the direction of the largest resonance motions is sensitive to and has a transversal relationship with the dominant fracture orientation ( Figure 4D). ...
... The seismically-active Mattinata fault (MF) outcrops for over 40 km in the Gargano Promontory, Puglia region of southern Italy. It shows an undulated trajectory that is char- Therefore, as in previous sections, even [79] concluded that the direction of the largest resonance motions is sensitive to and has a transversal relationship with the dominant fracture orientation ( Figure 4D). ...
... The Pernicana fault, at Piano Pernicana, Mt. Etna (Italy), redrawn after[79]. (A) Map of the PF[77]. White arrows indicate the horizontal displacement vectors as measured by[77] between 2005 and 2006. ...
Site effects refer to the modification of ground shaking caused by the local geological conditions that can result in the strong amplification of ground motion. The best-known cause for site effects is the presence of superficial soft soil deposits, which are considered in seismic design codes of many countries through the use of scaling factors. Rock sites are assumed to show no local site amplification. However, even at rock sites, seismic waves can be locally amplified at frequencies of engineering interest, with larger motion along one site-specific azimuth on the horizontal plane (the so called “directional site resonance or amplification”). These effects have been related to the presence of large-scale open cracks or microcracks in different geological environments (faults, landslides, volcanic areas) everywhere with a common signature: maximum amplification occurs transverse to the predominant fracture strike. In this paper, we summarize our main results obtained in the last decade with regard to several fault zones with different kinematics, where ground motion is polarized (and amplified) perpendicularly to the predominant fracture field as an effect of the stiffness anisotropy. In order to give a further constraint, we also show some cases where the directional amplification effects were compared with the S-wave splitting analysis method.
... Directional distributions characterize randomness to unit vectors (directions). Spherical data sets appear in a wide range of problems arising from Earth sciences [102], biology [91], and material science [33]. Directional data are important in cosmology and astrophysics, for instance, in results of the Laser Interferometer Gravitational- [85]. ...
Abstract
Entropy is one of the most basic and significant descriptors of a probability distribution.
It is still a commonly used measure of uncertainty and randomness in information
theory and mathematical statistics. We study statistical inference for Shannon
and Renyi’s entropy-related functionals of multivariate Gaussian and Student-t distributions.
This thesis investigates three themes. First, we provide a non-parametric
test of goodness-of-fit for a class of multivariate generalized Gaussian distributions
based on maximum entropy principle via using the k-th nearest neighbour (NN) distance
estimator of the Shannon entropy. Its asymptotic unbiasedness and consistency
are demonstrated. Second, we show a class of estimators of the Renyi entropy based
on an independent identical distribution sample drawn from an unknown distribution
f on R^m. We focus on the maximum R nyi entropy principle for multivariate
Student-t and Pearson type II distributions. We also consider the entropy-based test
for multivariate Student-t distribution using the k-th NN distances estimator of entropy
and employ the properties of entropy estimators derived from NN distances.
Third, we introduce a new classes of unimodal rotational invariant directional distributions,
which generalize von Mises-Fisher distribution. We propose three types of
distributions in which one of them represents the axial data. We provide all of the
formula together with a short computational study of parameter estimators for each
new type via the method of moments and method of maximum likelihood. We also
offer the goodness-of-fit test to detect that the sample entries follow one of the introduced
generalized von Mises-Fisher distribution based on the maximum entropy
principle using the k-th NN distances estimator of Shannon entropy and to prove its
L^2-consistence.
... This polarization pattern coincides well with the direct surface displacement field measured with GNSS between May and November 2018, that is in the period of the seismic array measurement. Such alignment of the wavefield polarization perpendicular to dominant fracture systems could be observed in field and synthetic data acquired on other rock instabilities and around tectonic faults before (Burjánek et al. 2010Pischiutta et al. 2012Pischiutta et al. , 2013Häusler et al. 2019). Since all stations are resonating in-phase, these findings support our interpretation that this frequency band is sensitive to one large unstable volume. ...
... The wavefield polarizes perpendicular to the fracture network and changes its orientation towards northeast as well. Pischiutta et al. (2013) showed in numerical models that the stress field, orientation of extension fractures and polarization of ambient vibrations are closely related. Polarization monitoring of frequency band B at Brinzauls showed that the counter-clockwise rotation was already in process in July 2018 (by 5 • until March 2019), thus, before a rotation was visible in surface displacement vectors. ...
... Polarization monitoring of frequency band B at Brinzauls showed that the counter-clockwise rotation was already in process in July 2018 (by 5 • until March 2019), thus, before a rotation was visible in surface displacement vectors. Following the interpretations by Pischiutta et al. (2013), we suggest that this early rotation was an effect of changing stress conditions, which was followed by changing landslide kinematics in spring 2019. However, while wavefield polarization could be used as an immediate proxy for the orientation of the dominating fracture network and thus for the anticipated surface deformation vector field in extensional regimes, there is no direct causality between displacement and polarization. ...
Seismic measurements on unstable rock slopes are a complementary tool to surface displacement surveys to characterize and monitor landslides. A key parameter is seismic amplification, which tends to scale with the degree of rock mass degradation. Amplification also provides a direct measure of how the wavefield is intensified during seismic loading, eventually leading to coseismic failure. Here we present the dynamic response of the fast-moving Brienz/Brinzauls rock slope instability in Switzerland (10 $ \times $ 106 to 25 $ \times $ 106 m3), which threatens settlements and infrastructure in the area. The rockslide shows strong seismic amplification at two resonant frequencies with factors of up to 11 and wavefield polarization influenced by the local fracture network orientation. We monitored the dynamic response over a period of 30 months using ambient vibrations and regional earthquake recordings. We observed a change in wavefield polarization of up to 50°, coinciding with a rotation of the relative surface displacement vector field measured by geodetic systems, highlighting the linkage between wavefield polarization and stress field (i.e. rock mass kinematics). For the analysis of secondary, relative surface displacements, we propose a singular value filtering of the displacement field to remove the principal component of landslide motion. In addition, we found increased seismic amplification values after periods of strong precipitation, providing empirical field evidence that the local precipitation history is a key parameter for assessing the hazard of earthquake-induced slope failure.
... Directional distributions characterize randomness in unit vectors (directions). Spherical data sets appear in a wide range of problems arising from Earth sci-ences [44], biology [39], and material science [16]. Directional data are important in cosmology and astrophysics, for instance, in results of the Laser Interferometer Gravitational-Wave Observatory [1] and the Alpha Magnetic Spectrometer on the International Space Station [2]. ...
We introduce some new classes of unimodal rotational invariant directional distributions, which generalize von Mises–Fisher distribution. We propose three types of distributions, one of which represents axial data. For each new type we provide formulae and short computational study of parameter estimators by the method of moments and the method of maximum likelihood. The main goal of the paper is to develop the goodness of fit test to detect that sample entries follow one of the introduced generalized von Mises–Fisher distribution based on the maximum entropy principle. We use kth nearest neighbour distances estimator of Shannon entropy and prove its L^2-consistency. We examine the behaviour of the test statistics, find critical values and compute power of the test on simulated samples. We apply the goodness of fit test to local fiber directions in a glass fibre reinforced composite material and detect the samples which follow axial generalized von Mises–Fisher distribution.
... Although the earthquake recordings and the SSR calculation is the most suitable method to obtain information on the amplification, there are difficulties linked to set up of seismic stations for several months. For this reason, horizontal-tovertical spectral ratio (HVSR) of ambient vibrations was tested as alternative technique for site effects investigation in fault zones in several places around the world (Rigano et al., 2008;Di Giulio et al., 2009;Pischiutta et al., 2012Pischiutta et al., , 2013Pischiutta et al., , 2015Pischiutta et al., , 2017Panzera et al., 2014Panzera et al., , 2016aPanzera et al., , 2016bPanzera et al., , 2017aPanzera et al., , 2017b. The authors observed a good agreement between outcomes coming from earthquake data and ambient vibration recordings and a systematic directional amplification perpendicular to the fault strike in normal faults and at about 60 • from the strike-slip faults direction. ...
Mt. Etna, in eastern Sicily, is a composite active volcano whose eastern flank is affected by several normal and strike-slip active faults. In this study geological-structural field survey and ambient vibration measurements are performed in the lower eastern flank of Mt. Etna in order to define the role of the tectono-stratigraphic setting on the seismic site response. The sites of measurements are mainly distributed inside the few hundreds of meters long S. Caterina Graben, which is located between two main seismogenic active faults of this volcano sector, the Acireale and the Fiandaca faults. Our study aims at defining the contribution of the fault related active deformation in determining the local ground motion amplification, also providing a subsoil geological model based on the integration of geological and geophysical investigation. Therefore, structural measurements were made in seven sites, revealing coseismic and aseismic extensional fractures mainly striking NNW. The seismic site response was studied processing the ambient vibration measurements through Horizontal-to-vertical spectral ratio. The measured fundamental frequency fall in the range 1.0–4.0 Hz, that we linked to the presence of a velocity contrast at depth of 80–200 m by calibrating a frequency depth function. Moreover, the seismic site effect is due to the stratigraphic setting and is markedly directional, showing maximum amplification along the direction orthogonal to the strike of the observed isooriented extensional fracture field produced by the activity of the S. Caterina Graben. It is noteworthy that, far from the graben on sites of measurements located near the Fiandaca Fault, we observed directional effects parallel to the direction of maximum extension inferred for this tectonic lineament. Our results suggest a linkage between directional site effects and local stress tensors and fractures field orientation.
... Directional distributions characterize randomness in unit vectors (directions). Spherical data sets appear in a wide range of problems arising from Earth sciences (Pischiutta et al., 2013), oceanography (Wyatt et al., 1997;Shabani et al., 2016), biology (Mouritsen & Mouritsen, 2000), physics (Torrance et al., 1966), material science (Dresvyanskiy et al., 2020). ...
We introduce some new classes of unimodal rotational invariant directional distributions, which generalize von Mises-Fisher distribution. We propose three types of distributions, one of which represents axial data. For each new type we provide formulae and short computational study of parameter estimators by the method of moments and the method of maximum likelihood. The main goal of the paper is to develop the goodness of fit test to detect that sample entries follow one of the introduced generalized von Mises--Fisher distribution based on the maximum entropy principle. We use $k$th nearest neighbour distances estimator of Shannon entropy and prove its $L^2$-consistency. We examine the behaviour of the test statistics, find critical values and compute power of the test on simulated samples. We apply the goodness of fit test to local fiber directions in a glass fibre reinforced composite material and detect the samples which follow axial generalized von Mises--Fisher distribution.
... For this reason, non-reference techniques, such as horizontal to vertical spectral ratios (HVSR), have received an increasing attention and it is usually adopted for estimation of the fundamental resonance frequency at sedimentary sites (Lermo and Chavez-Garcia, 1993;Bard and Riepl-Thomas, 2000). Recently, the HVSR technique, both on earthquakes and microtremors, has been applied also for the evaluation of topographic effects (Chavez-Garcia et al., 1996;Chávez-García et al., 1997;Zaslavsky and Shapira, 2000), showing encouraging results also at complex structures and fractured rock sites and allowing to catch the preferential polarization of the amplification and the resonance frequency of the relief (Martino et al., 2006;Pagliaroli et al., 2007Pagliaroli et al., , 2015Lovati et al., 2011;Marzorati et al., 2011;Pischiutta et al., 2013Pischiutta et al., , 2017Panzera et al., 2014;Hailemikael et al., 2016;Di Naccio et al., 2017). ...
This work deals with the experimental and numerical evaluation of the local seismic response of Arquata del Tronto area (Marche Region, central Italy), severely struck by the Mw 6.0 August 24th, 2016 earthquake. Arquata main village rises on elongated WNW-ESE-trending ridge of the central Apennines thrust-belt (central Italy), at elevations about 170 m higher than the underlying alluvial valleys where Borgo and San Francesco hamlets are built on. Despite their proximity (less than 500 m), Arquata del Tronto, Borgo and San Francesco reported a different damage distribution after the August 2016 mainshock, suggesting that the seismic response of the area may be controlled by site effects. In order to explore this hypothesis, we evaluated the 2D numerical local seismic response along four representative geological cross-sections passing through Arquata del Tronto, San Francesco and Borgo. Additional 1D analyses were carried out at strategic points along the cross-sections in order to explore the 2D physical phenomena governing the local response. The satisfactory agreement between numerical amplification functions in linear range and experimental amplification functions obtained by the Generalized Inversion Technique (GIT) applied to a large number of aftershocks confirms the substantial reliability of the subsoil models. Numerical analyses representative of the 2016 mainshock were carried out and processed in terms of peak and key ground motion parameters. A comparison with the damage induced by the 2016 mainshock was finally undertaken substantially justifying the observed pattern. This study provides general implications about site response and seismic microzonation in sites characterized by similar complex geological and morphological settings.
... The results of these analyses indicate that the average HVSR receives more contribution from one of two horizontal components, and the direction in which it operates. Several studies [9,45] have shown that microseismic noise and seismic signals in fault zones are polarized across a horizontal plane with a preferred orientation that is comparable with the directions of fault zones near these locations. ...
The city of Ivanec is located between valley of the Bednja River and Mt. Ivanščica and this area can be prone to significant seismic site amplification due to local site characteristics. This study presents the first assessment of seismic site amplification for the city of Ivanec by the microtremor horizontal-to-vertical-spectral-ratio (HVSR) method and the equivalent-linear (EQL) site response analysis. Based on microtremor measurements and HVSR analysis, fundamental soil frequency and HVSR peak amplitude maps indicate potentially seismic danger zones. The 1-D EQL site response analysis was performed using multiple suites of earthquake ground motions scaled to the 95- and 475-year return periods of peak ground accelerations. Site amplification maps at the predominant peak frequency and ground surface indicate two microzones, one with high amplification in the central part of the city due to soft soil characteristics, and the other with small amplification in the transitional zone from alluvial basin towards the foothills of Mt. Ivanščica. HVSR peak amplitudes and site response peak amplifications showed similar spatial distributions with similar predominant peak frequencies but with different amplitude levels. Site amplification maps provided significant information about potential resonance effects for structures of certain heights that can be correlated with the local ground shaking characteristics.
... Cochran, Vidale and Li (2003) and Griffith, Sanz and Pollard (2009) connected the directional amplifications in fault zones to the stiffness anisotropy of the fractured rock mass, where the predominant seismic motion is expected to be normal to the fractures orientation. Pischiutta et al. (2013) interpreted the directional resonance observed at PFS in terms of changes in the kinematic and deformation fields on the opposite sides of the fault. Following these authors, the northern side is primarily affected by eastwards strike-slip movement, whereas the southern side, also subject to sliding, is under a dominant extensional stress regime. ...
... volcanoes or fault zones by recent numerical and experimental papers (Shelley et al. 2014;Pischiutta et al. 2015;Li and Peng 2017;Vignaroli et al. 2018). In fault zones, the estimation of the elastic properties within the subsoil model is therefore a key issue to solve with the aid of experimental data Pischiutta et al. 2013) with seismic stations (circle symbols) installed for noise measurements by Di Giulio et al. (2009) along two main north-south transects nearby the Pernicana fault (grey segments). The trace of PFS is shown as a thick grey line. ...
... The active source was at 10 m distance from the closest station. For the polarization analysis, we focused on the 5 Hz signal produced by the MiniVIB because this frequency is the closest we could excite near the 'naturally polarized' frequency of 1 Hz, as observed in past studies (Di Giulio et al. 2009;Pischiutta et al. 2013). The 5 Hz frequency was excited several times during the experiment and was recorded with a high signal-to-noise ratio by all the stations of the two lines. ...
The paper presents the results of a controlled‐source seismic experiment performed using a vibratory source capable of producing harmonic vibrations. The survey aimed at investigating the horizontal directional amplification mechanism observed at the Pernicana fault (Mt. Etna in Sicily, Italy) along a N150°/N330° orientation. With the vibratory source (a shaker truck) working in shear‐wave mode in the frequency range 5–40 Hz, we recorded seismic data using both three‐component velocimeters and 4.5 Hz geophones. These two types of receivers were arranged in linear configuration along two orthogonal orientations; radial and transversal to the direction of the main polarization observed within the fault zone. The two lines of seismic stations allowed us to investigate the polarization evolution as a function of the distance from the source. Results show that when the shear excitation induced by the source is parallel to the direction of observed polarization of the ground motion, the seismic signal propagates efficiently, maintaining the same horizontal polarization induced by the active source. This polarization is well recorded up to distances as large as 300 m from the source. On the contrary, when the shear excitation is orthogonal to the predominant site polarization, the ground excitation loses its initial polarization in less than 50 m away from the source position. At larger distances, the transmitted energy propagates with the natural site polarization independently from the original source polarization. The observations in terms of polarization were combined to a surface‐wave analysis, aimed at investigating the dispersion characteristics of the wavefield on the geophone lines. The data suggest that the experimental Rayleigh‐wave dispersion spectra show a more coherent signal over frequency along the same orientation of the observed site polarization, supporting a preferential direction in the propagation of surface waves. By inversion of the Rayleigh dispersion curves, we inferred the shear‐wave velocities (Vs) in the range of 120–450 m/s in the first 30 m deep of Quaternary volcanic sediments. The dispersion curves are not constant along the transversal and radial direction, suggesting the presence of fracture‐induced seismic anisotropy in the near surface.
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... On the other hand, Cultrera et al. [38], Calderoni et al. [37], and Pischiutta et al. [46] observed evidence of ground-motion amplification in the fault-zone environments and strong directional effects with high angle to the fault strike, therefore indicating a mechanism different than trapped waves. Similar studies, performed by Cara et al. [47], Imposa et al. [2], Lombardo and Rigano [48], Rigano et al. [49], Di Giulio et al. [50], Pischiutta et al. [46,51,52], and Panzera et al. [4,5,23,53], documented the presence, besides amplification effects, of a systematic horizontal ground-motion polarization near faults. These directional effects, never coincident with the strike of the tectonic structures, were observed both during local and regional earthquakes and using ambient vibration measurements, therefore suggesting the use of microtremors for investigating ground-motion polarization properties along and across the main tectonic structures. ...
... They also used frequency-wave-number techniques, applied to array data, in order to investigate the nature of ambient vibrations and verified that the observed polarizations were not affected by features of local sources, such as the volcanic tremor. By analyzing several faults, Pischiutta et al. [46,52] found a near orthogonal relation between the horizontal polarization and the orientation of the main fracture field produced by the fault kinematics. They modeled the expected brittle deformation pattern in the fault damage zone using a combination of numeric and analytic tools and interpreted the directional amplification as produced by stiffness anisotropy, with higher stiffness parallel to the dominant sets of fractures. ...
