Analysis of the primary and secondary microseisms in the wavefield of the ambient noise recorded in northern Poland
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Seasonal changes of the primary and secondary microseisms were analysed in the wavefield of the ambient noise recorded during the entire 2014 at the “13 BB star” array located in northern Poland, composed of thirteen, symmetrically arranged, broadband seismic stations. To that, spectral analysis, seismic interferometry, surface scalar wind speed distribution, and beamforming were used. Spectral analysis allowed to observe that a splitting of the secondary microseism peak was present in winter and autumn, and that the primary microseism peak was visible in spring, summer and autumn. Using seismic interferometry, the long-term characteristics of the noise wavefield were recognized. The seasonal variations of the secondary microseism source were described by means of the analysis of the surface scalar wind speed for each month. The splitting of the secondary peak was attributed to the interaction of a strong wind blowing from the North Sea with a weak wind blowing from the Baltic Sea. The seasonal variations of the primary microseism peak were characterized through the frequency-domain beamforming. The peak was identified during spring, summer and autumn, when the generated wavefield was coming from the Baltic Sea. The velocity of the wavefield was evaluated within the 2.0–5.0 km/s range. The described mechanism of generation of the microseisms, based on the interaction of the nearby winds, was found to be consistent with the models reported in the literature.
KeywordsPrimary and secondary microseisms Ambient noise Broadband seismology Fourier analysis Seismic interferometry Beamforming
The ambient noise is present everywhere and is detected over a wide frequency band. Anthropogenic sources prevailingly cause the wavefield above 1 Hz (Mcnamara and Buland 2004; Lepore et al. 2016). In the 0.1–1 Hz range, the noise wavefield is generated by storms and interactions of wind-driven ocean waves travelling in opposite directions in the shallow (e.g. Schulte-Pelkum et al. 2004; Bromirski et al. 2005; Gerstoft and Tanimoto 2007) or deep water (e.g. Stehly et al. 2006; Kedar et al. 2008; Landès et al. 2010; Obrebski et al. 2012; Bromirski et al. 2013). The produced noise is identified in the literature as the secondary microseism (Longuet-Higgins 1950; Ardhuin et al. 2012; Stutzmann et al. 2012; Bromirski et al. 2005; Gualtieri et al. 2015). Below 0.1 Hz, the wavefield is mainly dominated by the interaction between ocean waves and the seafloor close to the coastlines. In this case, the generated noise is known as the primary microseism (Hasselmann 1963; Bromirski and Duennebier 2002). The primary and secondary microseisms are clearly visible in the ambient noise wavefield when large impulsive sources (mostly earthquakes) are absent (Peterson 1993). The microseisms are distinctly related to atmospheric perturbations and ocean waves: some recent papers linked the pressure variations with the generation of microseisms (Gualtieri et al. 2015; Juretzek and Hadziioannou 2016; Möllhoff and Bean 2016), while others modelled several features of the primary and secondary microseisms (Ardhuin et al. 2011, 2012, 2015; Gualtieri et al. 2013, 2014). The accurate observations of the seasonal variations of the microseisms are the key to understand their physical aspects (Schimmel et al. 2011a).
Seismic interferometry (SI) is used to recognize the long-term characteristics of the ambient noise wavefield. By this technique, new seismic records are created by cross-correlating in time domain the existing ones. Namely, if a record at a random station X is cross-correlated with another one at a station Y, a new record is obtained at Y as generated from a source at X. As for the ambient noise, the Green’s function has been demonstrated to be contained, at least partially, in the cross-correlation (CC) between a pair of two distant stations (Shapiro and Campillo 2004; Sabra et al. 2005a; Wapenaar and Fokkema 2006). Also for diffuse wavefields or isotropic noise source distribution it is possible to retrieve rather well the Green’s function from the CC traces (Derode et al. 2003; Roux et al. 2005). An efficient retrieval of the Green’s function is obtained by summing each CC trace with the consecutive ones and averaged over a long time, assuming the isotropic incidence of noise wavefield between station pairs (Shapiro and Campillo 2004; Sabra et al. 2005b; Campillo 2006). However, it has been shown recently that the distribution of the noise sources is generally neither isotropic nor stationary due to the presence of directional and temporal variations. Consequently, the empirical Green’s function (EGF) is usually retrieved from the CC traces (Stehly et al. 2006; Yang and Ritzwoller 2008; Yao and van der Hilst 2009). Afterwards, surface waves can be extracted from the EGF (Halliday and Curtis 2008; Lepore et al. 2016) and the group velocity of the surface-wave arrivals can be estimated (Shapiro and Campillo 2004; Lepore et al. 2018). As in most situations (e.g. Stehly et al. 2006), the low-frequency band was used for the extraction of the surface waves. More detailed studies on the effects of the variability of the noise wavefield are required at high frequencies (Halliday and Curtis 2008): indeed, only very recently some papers analysed the generation of the high-frequency ambient noise (e.g. Gal et al. 2015; Gimbert and Tsai 2015; Möllhoff and Bean 2016).
The purpose of the present paper is to analyse, by the application of the SI and BF techniques, the seasonal variations of the primary and secondary microseisms generated by the winds blowing from the North Sea and the Baltic Sea and detected in the wavefield related to the ambient noise, recorded during the whole 2014 at the “13 BB star” array located in northern Poland (Fig. 1a). This array, constituted by thirteen stations equipped with broadband seismometers (120–50 Hz), was arranged as shown in Fig. 1b (Grad et al. 2015). The details of the spatial disposition of the array stations are given in Lepore et al. 2016. According to the conservation of the energy flux, the average spectral features of the ambient noise can be extracted by calculating the related wavefield at the central station only (Van Tiggelen 2003). The symmetrical geometry of the array allows to gather the propagation characteristics of the surface waves at low frequencies for any orientation (Grad et al. 2015). The calculation of the beam power is possible at the very low frequencies, where the wavelengths are comparable to the intra-station distances (20–120 km) of the array (Harmon et al. 2008).
To further explore the primary and secondary microseisms in the ambient noise wavefield, we analysed the recorded data in the frequency and time domains. The detected spectrum for each noise record shows a combination of distant and local sources (e.g. Cessaro 1994). At frequencies higher than 1 Hz, the spectrum of the noise wavefield is influenced by the sources located very close to the stations; on the other hand, at frequencies lower than 1 Hz, the distant sources are dominant in the spectrograms (Lin et al. 2010). For our array, the stations were located in the forest or in the glades, allowing the safe retrieval of the spectral content of the noise wavefield (Grad et al. 2015). This wavefield is mainly formed by dispersive surface waves since the noise sources are mostly located on the Earth surface. To allow the extraction of surface waves from the wavefield, they are assumed to propagate without losing energy along the path between two stations (Schimmel et al. 2011b). An accurate knowledge of the spatial and temporal features of the noise wavefield sources is needed to perform a reliable passive seismic monitoring. That means a rather stable wavefield which, however, shows a high variability due to the seasonal distribution of the noise sources (Corela et al. 2017). Seasonal variations, indeed, are usually present in the spatial distribution of those sources: for example, the changes of the azimuth have significant effects on the direction of the wavefields (Zhan et al. 2013).
Before carrying out the evaluation of the ambient noise spectrum and the retrieval of the surface waves from the wavefield, as well as the identification of the variations of the maximum beam power, the continuous noise records were preprocessed for each component, using 0.01 s as data sampling and 0.008–50 Hz as filtering band. At first, the records were cut into windows of 1 h length, from which the seismometer instrumental response, the mean and the linear trends were removed. The undesirable trends were thus eliminated, with the consequent deletion of large distortions that could cause the low-frequency contributions to vanish. Secondly, running-absolute-mean normalization in time domain was employed on each 1-h noise window to remove the effects of huge amplitude events, such as earthquakes, and non-stationary sources. In this way, broadband ambient noise was emphasized by the elimination of all potential effects causing lack of clarity. Thirdly, normalization in frequency domain, founded on spectral whitening, was used in order to reduce the inconsistencies among single-station 1-h windows, conceivably produced by permanent local narrow-band or monochromatic sources (Bensen et al. 2007).
Once the noise records were preprocessed, spectral analysis was performed for identifying the frequency bands suitable to retrieve the surface waves. Given the random nature of the noise wavefield, only the power spectral density (PSD), namely the standard quantity expressing the noise in the frequency domain, can be evaluated (McNamara and Buland 2004). With the purpose of obtaining a thorough view of the noise records, we calculated the PSD as a function of time for the Z, N and E components at the central station of the array. According to Ruigrok et al. (2011) and Lepore et al. (2016), the noise spectrograms were obtained by stacking all the successive PSD curves in time domain for a whole day. Once identified the appropriate frequency band to characterize the primary and secondary microseisms, both were studied for the entire year to show the variations of the PSD amplitude each 5 days along with the seasonal changes.
To extract the surface waves from the noise wavefield using the SI, we calculated the CC between all station pairs along the Z, N and E components for every month of 2014. For each station pair, 1-h windows were selected from the recorded noise, preprocessed as described and cross-correlated in the 0.1–1 Hz frequency range. The processed 1-h CC traces were then evaluated for an entire day and summed together. Finally, the resulting daily CC traces were stacked for each month (Lepore et al. 2016). For each trace, we chose the positive-time lag or the negative-time lag to retrieve the EGF based on the analysis of the dominant direction of the noise wavefield. Specifically, the positive-time lag was chosen when the dominant wavefield direction is from the (virtual) source to the receiver (Wapenaar 2006). Then, the CC traces showing the most proper retrieval of the EGF were selected from the entire collection of the traces; in turn, the group velocity of the surface-wave arrivals was evaluated from the EGF (Romanowicz 2002; Li et al. 2010). The features of the surface waves extracted from the wavefield were related to the seasonal variations of the secondary microseism.
Results and discussion
The spectral analysis, the seismic interferometry and the beamforming were applied to the wavefield of the ambient noise recorded at the “13 BB star” array during 2014 to analyse the seasonal variations of the primary and secondary microseisms caused by the winds blowing from the North Sea and the Baltic Sea.
Variations of the primary and secondary microseisms
The daily spectrograms obtained by the concatenation of the 1-h consecutive PSD curves, evaluated from the noise wavefield at the A0 station, are shown in the middle of Fig. 2 as frequency vs time plots each 50 days for the Z, N and E components. The 2–50 and 0.03–1 Hz frequency ranges represent the two main bands where the noise persists for the whole year. In the high-frequency range (2–50 Hz), the noise wavefield amplitude is the lowest during winter and autumn, while it is the highest in spring and summer. Surface waves in this frequency band are produced by local noise sources not related to the ocean activity, prevalently anthropogenic and less strong during night-time than day-time (Lepore et al. 2016). For each day, a remarkable correlation exists between the duration of the strongest noise and the length of the daylight, measurable from the plots of the sun elevation above the horizon, as shown for the same days at the top of Fig. 2. Moreover, the length of the daylight is shorter in winter and autumn, whereas it is larger in spring and summer. In the low-frequency range (0.03–1 Hz), the surface waves are caused by the interaction of wind-driven ocean waves in shallow or deep water. Two small bands can be observed: the first, coloured in light cyan, goes from 0.03 to ~ 0.1 Hz; the second, coloured in yellow–green, goes from ~ 0.1 to 1 Hz. The first band is rather clear during spring and summer and almost absent during autumn and winter. On the contrary, the second band is well visible during the whole year. The different colours highlight the jump present in the PSD between the two bands. To characterize in detail this jump, the curves of the PSD amplitude as a function of the frequency are shown for the Z, N and E components at the bottom of Fig. 2. In spring and summer, two peaks are observed: the first, within 0.03–0.1 Hz and 10−12–10−13 (m/s)/Hz, corresponds to the primary microseism peak; the second, within 0.1–1 Hz and 10−10–10−12 (m/s)/Hz, corresponds to the secondary microseism peak. The primary microseism peak has a very low amplitude in winter, little higher in autumn, while the highest amplitude is reached in spring and in summer. The secondary microseism peak has the highest amplitude in winter and autumn; at the same time, a splitting into two peaks is observed in the 0.2–0.8 Hz range. In spring and summer, the amplitude is the lowest, and only one peak is observed within the same frequency range.
The variations of the primary and secondary microseisms during the entire 2014 are shown in Fig. 3 by the plots of the PSD amplitude every 5 days as a function of frequency for Z, N and E components at the A0 station. For each of the three plots, the first curve from the bottom (1 January 2014) is in its proper scale, whereas all the other curves are moved up by a Δx shift indicated in the right-bottom corner. The same set of colours (black, cyan, blue, purple, dark blue, fuchsia, red, orange, light green, green) is repeated every ten curves. In the 0.03–0.1 Hz frequency range, significant maxima are observed in several cases (days 21, 26, 61, 76, 81, 101, 131, 136, 146, 151, 166, 186, 201, 206, 226, 236, 246, 261, 266, 281, 311, 321, 326, 341, 355). The PSD amplitude of the primary microseism peak, commonly observed very close to the oceanic coastlines, ranges between 10−12 and 10−15 (m/s)/Hz. In most cases, two maxima are detected in the 0.1–1 Hz frequency range. As reported in the literature (e.g. Koper and Burlacu 2011, 2015), the splitting of the secondary microseism peak implies the simultaneous activation of two wind-driven ocean sources.
To analyse the seasonal changes of the primary and secondary microseisms, five PSD amplitude curves for each season were selected randomly from Fig. 3 for the Z component. These curves, shown in Fig. 4, are gathered in four different plots for winter, spring, summer and autumn. In winter, we observe that the primary microseism peak has the maximum amplitude of ~ 10−13 (m/s)/Hz and the secondary microseism peak is split into two peaks, the first around 0.2 Hz and the second around 0.4 Hz. During spring, the primary peak has the maximum amplitude of ~ 10−12 (m/s)/Hz, while the secondary one presents a single peak either around 0.2 Hz or around 0.4 Hz. In summer, the primary peak has the maximum amplitude of ~ 10−12 (m/s)/Hz, while the secondary one generally presents a main peak around 0.4 Hz. Only for the day 261 another peak around 0.2 Hz is also detectable for the secondary peak. During autumn, the maximum amplitude of primary microseism peak is a bit higher than 10−13 (m/s)/Hz and the splitting of the secondary microseism peak is again evident in the 0.2–0.4 Hz range.
Seasonal changes of the secondary microseism investigated by seismic interferometry
The seasonal variations of the secondary microseism during the whole 2014 are described through the study of surface-wave arrivals on the stacked CC traces for each month. According to the literature (Buffoni et al. 2018; Kimman et al. 2012; Schimmel et al. 2017; Ventosa et al. 2017), only the CC traces along Z component are shown from all the traces calculated along the Z, N and E components.
Sources of noise wavefield for the secondary microseism
Seasonal changes of the primary microseism investigated by beamforming
The seasonal variations of the primary microseism during 2014 are characterized by studying the beam power of the noise wavefield for the Z, N and E components for each month. Before that, the frequency-domain BF technique was validated by the identification of the epicentre azimuths for six selected earthquakes. (Additional data are given in Online Resource 1.)
Features of the wavefield related to the primary microseism
To define more precisely the direction and to calculate the velocity of the wavefield associated with the primary microseism, azimuth and slowness (inverse of velocity) for the dominant beam were extracted from the beam power evaluated each 5 days during the entire 2014.
The study of the seasonal variations of the primary and secondary microseisms was performed on the ambient noise recorded during the whole 2014 at the “13 BB star” array located in northern Poland, by means of spectral analysis, seismic interferometry by cross-correlation, surface scalar wind speed distribution and frequency-domain beamforming.
By applying spectral analysis, the primary and secondary microseisms were recognized in the 0.03–0.1 and 0.1–1 Hz frequency ranges, respectively. The primary microseism peak was well visible in spring and summer, slightly observable in autumn and poorly detectable in winter: its amplitude was relatively low during the whole year. On the contrary, the secondary microseism peak was always well visible: in winter and autumn it was split into two peaks placed in the 0.2–0.4 Hz range.
To outline the seasonal variations of the secondary microseism, the surface-wave arrivals were observed in the empirical Green’s function retrieved from the cross-correlation traces obtained by stacking for each month the daily traces calculated for the Z component in the 0.1–1 Hz frequency band. Two sets of surface-wave arrivals were recognized: the faster showed an average group velocity of ~ 1.5 km/s, while the slower one displayed a velocity of ~ 1.0 km/s. In winter, both the faster and the slower arrivals were well identified. In spring and summer, the faster arrivals were well visible, while the slower ones were poorly observable. In autumn, both the faster and the slower surface-wave arrivals were again detectable.
By analysing the spatial distribution of the surface scalar wind speed within 0–20 m/s for each month from the NCEP-DOE AMIP-II Reanalysis database, two sources of noise wavefield were identified. The stronger wind was located in the North Sea with speed within the range 12–20 m/s, while the weaker wind in the Baltic Sea having speed in the range 2–8 m/s. During autumn and winter, the interaction between the strong and weak winds was observed. During spring and summer, the kinetic energy of the strong wind was much lower than that of the weak wind.
The seasonal variations of the primary microseism were characterized by evaluating the beam power for each month of 2014 in the 0.05–0.1 Hz frequency band for the Z, N and E components. Before the application of the beamforming, the reliability of the method was proved by the evaluation of the epicentre azimuth for six earthquakes in the same frequency band. Only in one case it was observed that the agreement between the azimuth associated with the maximum beam power and the azimuth from known geographic coordinates was not satisfactory: thus, it can be safely concluded that the technique is generally reliable. By analysing the variations of the dominant beam, it was shown that in winter the wavefield generated by the main source of noise was coming from the North Sea, far away from the array, thus making very low the amplitude of the primary microseism peak. For the rest of the year, the wavefield generated by the main source was coming from the Baltic Sea, very close to the array, so as to cause the detection of the primary microseism peak. Evaluating the azimuth of the dominant beam each five days, the two sources of the wavefield were identified within the 30°–90° and 300°–360° regions. Calculating the slowness from the maximum beam power in the same days, we found that the average velocity of the wavefield related to the primary microseism was in the 2.2–3.8 km/s range.
To sum up, the mechanism of generation of the primary and secondary microseisms in northern Poland described in this paper is based on the interaction of the nearby winds blowing from the neighbouring seas. This model is consistent with the models generally accepted in the literature concerning the generation of microseisms, while the observed splitting of the secondary microseism peak has been described up to now only by a few authors.
This work was supported financially by National Science Centre Poland (NCN grant DEC-2011/02/A/ST10/00284). The public domain GMT software (Wessel and Smith 1998) was used to produce array map. We thank Dr. Elmer Ruigrok for the development of the MATLAB codes here used. Surfaces of the Earth in the colour relief images ETOPO2v2 from NOAA/NGDC database were employed for the topographic plans (https://www.ngdc.noaa.gov/mgg/image/2minrelief.html). Wind speeds are obtained from the NCEP-DOE AMIP-II Reanalysis database (https://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis2.html).
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Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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