Since the original research of Bertelli (1872), many investigations have confirmed a close connection between microseisms and disturbed ocean weather conditions (Longuet-Higgins, 1950). The primary microseism peak (around 0.07 Hz) is generated when ocean waves reach shallow water near the coast and interact with the sloping seafloor (Hasselmann, 1963). The secondary peak of microseisms (between 0.1 and 0.2 Hz) is generated by the interaction of ocean waves of similar frequencies traveling in opposite directions (Longuet-Higgins, 1950). Longuet-Higgins' theory explains how counter-propagating ocean waves can generate propagating acoustic waves and create secondary microseisms by exciting the sea floor. Hasselmann (1963, 1966) generalized Longuet-Higgins' theory to random waves by investigating non-linear forcing of acoustic waves.

Microseism modeling was introduced by Kedar et al. (2008). The good correlation between the observed microseism amplitudes and their predicted values was shown (Shapiro, 2005; Shapiro and Campillo, 2004; Stehly et al., 2006; Stutzmann et al., 2012; Weaver, 2005). The different patterns between microseismic body and surface waves, resulting from the amplification of ocean wave-induced pressure perturbation and seismic attenuation, have been studied with implications for seismic imaging and climate studies (Obrebski et al., 2013). Coastal reflections also play an important role in the generation of microseisms, but modeling ocean wave reflections off the coast still remains a major source of model uncertainty (Ardhuin et al., 2013a). Ardhuin and Herbers (2013b) developed a numerical model based on Longuet-Higgins–Hasselmann's theory for the generation of Rayleigh waves, by considering an equivalent pressure source at the undisturbed ocean surface.

Inaudible low-frequency sound, known as infrasound waves, propagates through the atmosphere for distances of thousands of kilometers without substantial loss of energy. Below 1 Hz, infrasound has been observed since the early nineteenth century at different locations distributed around the globe. Gutenberg (1953) first pointed out the relation between microseisms, meteorological conditions, ocean waves, and microbaroms. Donn and Naini (1973) suggested a common source mechanism of microbaroms and microseisms from the same ocean storms demonstrating that the only mechanism capable of transmitting energy into both the atmosphere and the sea bottom is associated with surface wave propagation.

There is a significant difference between microseisms and microbaroms. While propagation paths for microseisms can be either along the Earth's surface as Rayleigh waves, or through the Earth as body waves (Gerstoft et al., 2008), microbarom observations are typically along propagation paths that have undergone multiple bounces on the Earth's surface. As for microseisms, microbaroms are not impulsive signals but quasi-monochromatic sequences of permanent waves (Olson and Szuberla, 2005); therefore, it is not possible to detect their onset and identify their propagation paths. However, these signals are well detected using standard array processing techniques, such as beam-forming methods (Capon, 1972; Haubrich and McCamy, 1969; Toksöz and Lacoss, 1968). Several studies demonstrated the efficiency of beam-forming approaches (e.g., Evers and Haak, 2001), or correlation-based methods (e.g., Garcès, 2004; Landès et al., 2012), to detect and characterize microbarom signals globally. Posmentier (1967) started developing a theory of microbaroms based on the Longuet-Higgins' theory. A microbarom source model was first developed by Brekhovskikh (1960), later extended by Waxler and Gilbert (2006), Waxler et al. (2007), and more recently extended by de Carlo (2020).

Losses along the propagation path control the ability to observe microbaroms. Thus, in order to accurately assess the microbarom source intensity, it is necessary to take into account a realistic description of the middle atmosphere. Several studies have been conducted to characterize the ambient infrasound noise. Smets et al. (2014) compared microbarom observations with predicted values to study the life cycle of sudden stratospheric warming (SSW). Landès et al. (2014) compared the modeled source region with microbarom observations at operational stations of the International Monitoring System (IMS). A first-order agreement between the observed and modeled trends of microbarom back-azimuth was shown. Le Pichon et al. (2015) compared observations and modeling over a 7-month period to assess middle atmospheric wind and temperature models distributed by the European Centre for Medium-Range Weather Forecasts (ECMWF). It was shown that infrasound measurements can provide additional integrated information about the structure of the stratosphere where data coverage is sparse. More recently, Hupe at al. (2018) showed a first-order agreement between the modeled and observed microbarom back-azimuth and amplitude in the North Atlantic.

In this paper, we develop a synergetic approach to better constrain microbarom source regions and evaluate propagation effects. To this end, we apply the method developed by Hupe et al. (2018) to the dense Kazakhstani seismo-acoustic network. The considered network is operated by the Institute of Geophysical Research (IGR) of the National Nuclear Centre of the Republic of Kazakhstan. It includes both seismic and infrasound arrays. Since the pioneering work of Donn and Naini (1973), to our knowledge, this study is the first multi-year comparisons between observed and modeled ambient noise at collocated seismo-acoustic arrays. In the first part, we have presented the observation network and the methods used. In the second part, the processing and modeling results of microseism and microbarom signals recorded by the IGR seismo-acoustic network from 2014 to 2017 are shown. In the last part, comparisons between the observed and modeled microbaroms and microseism are discussed.

Where previous studies analyzed microbarom signals at a single station (Hupe et al., 2018), further investigations are conducted here by considering a multi-year dataset of continuous records collected by the IGR network. Regional features of both microbaroms and microseisms are highlighted. Figure D1a–n in Appendix D show the azimuthal distribution of infrasound detections with maximum amplitudes. Figure D2a–d show similar histograms for seismic stations. One can distinguish seasonal trends for both infrasonic and seismic observations. In winter, microbaroms and microseisms are detected from the northern and northwestern directions. In summer, southern, southwestern, and southeastern directions dominate; signals from the northwestern direction are also recorded at ABKAR, KKAR, and MKAR. Azimuths differ from one station to another depending on the strongest microbarom and microseism source regions relative to the station locations. Observations and simulations show large temporal variations in the dominating microbarom source regions explained by the seasonal reversals of the prevailing stratospheric winds, which in turn cause the migration of the storm activity area to the winter hemisphere. The histograms of the azimuthal distribution of microbaroms (Fig. D1) clearly show the dominating direction of arrivals in winter with prevailing directions ranging from 270 to 350∘. The predicted azimuths are in good agreement with the observed ones as shown by Figs. 2c, g, and k and D1 and Table 2. In winter, microseism observations exhibit a similar pattern with a larger spread (250–360∘), and an additional peak (0–20∘) at KKAR and MKAR (Fig. D1d–f). These peaks are explained by North Pacific microseism source regions.

In winter, microseisms exhibit similar trends with some differences as shown by Fig. 3c, g, k, and o. The dominant directions are comparable with a larger spreading: from 250 to 360∘ and from 0 to 20∘. At KKAR and MKAR, two peaks are noted in the histograms, with a second peak at 0–20∘. These peaks are explained by North Pacific microseisms. In summer, microbaroms are predicted mainly from the southern direction (180–200∘). Such a peak is observed only at IS31 and MKIAR (Fig. D1c), although there is a large spreading in the predictions (45–225∘). The closest peak observed at KURIS and MKIAR is shifted northwards by ∼ 50∘. The dominant back-azimuths are close to 90∘. In winter, signals from ocean storms in the North Atlantic dominate at all stations. This is supported by microbarom and microseism simulations. Microbarom sources recorded by the Kazakh network in summer are not fully characterized. The cross-bearing location considering detections at IS31, KURIS, and MKIAR yields a hotspot located southwest of South America (Fig. C2). Since the localization does not include the crosswind effect, the true location may differ significantly from the preliminary estimation. Furthermore, the fact that a signal should pass a considerable portion of the way upwind would prejudice the likelihood of its registration. However, this preliminary location is consistent with the relatively low amplitude values and larger periods in summer than in winter (Fig. C1). Additional studies using more realistic propagation modeling are required to confirm this hypothesis. In this study, the method used to predict the attenuation assumes a range independent atmosphere along the propagation paths. Such an approach cannot be applied to situations involving long propagation ranges where significant along-path variability of wind and temperature profiles may occur (especially when sources and network are located in different hemispheres). Using historical IGR datasets, the spatiotemporal variability of microbarom signals due to changes in the source location and the structure of the atmospheric waveguides can be studied. There is a clear seasonal trend in both directions and amplitudes of microbaroms and microseisms (Fig. 2). Moreover, microseism amplitudes synchronously vary at all stations (Fig. 4). A good agreement between observations and simulations is found for the azimuths. The bathymetry effect plays an important role when calculating the microseism source intensity. As already shown by Evers and Siegmund (2009) and Smets and Evers (2014), SSW events can be inferred from the observed spatiotemporal variations of microbarom parameters. Such observations are noted at IS31 where microbaroms in early and late February 2017 are shifted to easterly directions (∼ 40∘), which is consistent with the simulated source regions in the North Pacific (Fig. 2a, c). As noted at IS31, KURIS also recorded signals with back-azimuths of ∼ 40∘ in late January 2017 (Fig. 2e, g). Similarly, signals from ∼ 100∘ were also recorded during the 2017 SSW event at MKIAR. However, the observed back-azimuths differ from the predicted ones (∼ 60∘). It is likely that this station recorded signals from other regions over the Pacific Ocean, which are not described by the ocean wave model used. These findings are consistent with comparisons between the observed and modeled microbaroms carried out by Landès et al. (2014) at IS31. This study shows that modeling well describes microbarom sources in the North Atlantic in winter, while signals in summer are poorly explained.

Comparing microbaroms and microseisms at collocated sites highlights similar features. Figure 5a–d present the observed back-azimuths and signal amplitudes from 1 January 2014 to 31 December 2017 at ABKAR and IS31, located 230 km apart. Figure 5e–h show the detection results for the collocated Kurchatov Cross and KURIS arrays. The comparison of the bulletins in Fig. 5 shows similar seasonal patterns:

North Atlantic microseisms and microbaroms prevail in winter. Back-azimuths of 300–360∘ are clearly visible in Fig. 5a, b, e, and g.

This study aims at characterizing the oceanic ambient noise using infrasound and seismic methods. The results show that exploiting the synergy between seismic and infrasound ambient noise observations is valuable to (i) better constrain the source strength using seismic records as microseisms propagate through the static structure of the Earth, while microbaroms travel through a highly variable atmosphere both in space in time, (ii) improve the detectability of ocean–wave interaction and location accuracy as microbarom wave parameters are less affected by heterogeneities in the propagation medium, and (iii) improve the physical description of seismo-acoustic energy partitioning at the ocean–atmosphere interface. While dominant features of microseisms and microbaroms are successfully recovered, some limitations of the proposed approach are identified. One limitation is the inability of the PMCC method to detect signals from several sources overlapping in the same frequency band. Another methodological shortcoming is the range-independent atmosphere considered for propagation simulations. Such an approach cannot be applied to situations involving long propagation ranges where significant along-path variability of wind and temperature profiles may occur; especially when sources and network are located in different hemispheres. Additional studies are also required to further evaluate whether the bathymetry effect could explain discrepancies between the observed microbarom and microseism signals (Longuet-Higgins, 1950; Stutzmann et al., 2012; De Carlo, 2020).

The IGR seismo-acoustic network is much denser than the global IMS infrasound network. Analyzing multi-year archives of continuous recordings provides a detailed picture of the spatial and temporal variability of the seismic and infrasound ambient noise originating from two hemispheres. In winter, the most intense oceanic storms are modeled in the North Atlantic, and their signature prevails on infrasound and seismic records. During minor SSW events, bi-directional conditions may occur which may have strong impacts on the retrieved microbarom signals (Assink et al., 2014). Simulated and observed microbarom parameters are consistent, as shown by moderate correlation coefficients. In summer, the location of microbarom signals using detections at IS31, KURIS, and MKIAR is found southwest of South America, at a distance larger than 15 000 km, near the peri-Antarctic belt where strong ocean storms circulate. This location is consistent with the relatively low amplitude and frequency of the recorded signals.

Further numerical investigations are needed to define the most suitable detection parameters in terms of missed events and the false alarm rate and estimate wave parameter uncertainties accounting for the response functions at all arrays. In this study, the discrepancies between observations and predictions motivate the use of high-resolution detection methods to identify multiple propagation paths from which microbarom energy can reach the array (e.g., Assink et al., 2014). Exploring the capability of high-resolution detection processing techniques to extract multi-directional overlapping coherent energy would be valuable to provide a more realistic picture of the recorded ocean ambient noise (e.g., den Ouden et al., 2020).

For such long propagation ranges, more realistic numerical simulations could reduce the differences between the observed and modeled amplitude; additional studies are thus required to explore time- and range-dependent full-wave propagation techniques while still maintaining computational efficiency (e.g., Waxler and Assink, 2019). Finally, including additional data from other seismo-acoustic networks worldwide would help constrain the microbarom source location, validating long-range propagation modeling, and better characterize station-specific ambient noise signatures, which is important for a successful verification of the CTBT using the IMS.