1 Introduction

The EENSANE project delivers an open access database of ambient noise cross-correlations and new seismic models of the Eastern European region at multiple scales. This new database was constructed using continuous ground motion data from all available seismic stations in Eastern Europe (Fig. 1) and provides an important basis for a plethora of seismological analysis tools for imaging the 3D subsurface structures beneath the seismically and economically vulnerable countries of Eastern Europe. The new seismic models of the crust and upper mantle expand our knowledge on fundamental geological processes shaping the Eastern European lithosphere, provide insights into earthquake generation mechanisms, and contribute to better seismic hazard estimates.

Fig. 1
figure 1

a Map of Eastern Europe, showing the location of broadband seismic stations (triangles) that are operational or have operated in the past. The colors indicate different seismic networks which operated during our target time interval. Orange triangles mark the CALIXTO temporary network that operated in 1999; yellow triangles mark the PASSEQ and CBP temporary networks that operated between 2005 and 2008; pink triangles are stations from the SCP temporary network between 2009 and 2011; blue triangles mark mostly permanent national seismic networks for which we downloaded data between 1999 and 2020. The inset shows our study area (black polygon) in a global context. b: Inter-station ray paths (pink lines) of empirical Green’s functions (EGF) estimated by cross correlating ambient noise data recorded at synchronous seismic stations in Eastern Europe (red triangles) in 2020. Inset shows a histogram of inter-station EGF path distances. (Color figure online)

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In this paper, we present a review of some of our most important results from the EENSANE project, demonstrating the versatility of the open access database and its usefulness for a wide range of state-of-the-art imaging applications that were initially designed for the sparsely and unevenly distributed earthquake sources. These include both large-scale (East European Craton, Petrescu et al. 2021) and small-scale (the city of Bucharest, Coman and Petrescu 2023) anisotropic seismic models of the crust based on Rayleigh wave dispersion, frequency-dependent attenuation maps of the Carpathian-Pannonian Region, near-surface velocity-depth models of Carpathian sedimentary basins (Petrescu et al. 2023a), and lastly, a realistic simulation of the seismic wavefield radiated by large historical earthquakes which occurred in the Vrancea Seismic Zone (Petrescu et al. 2023b).

2 A new ambient noise cross-correlation database

Inter-station ambient noise cross-correlations are useful data for seismic imaging, earthquake simulation and seismic hazard. By cross-correlating continuous ambient noise simultaneously recorded at broadband seismic stations, one can obtain a cross-correlation function that is theoretically similar to the Green’s function between the two receivers, as if one of them was an impulsive source (Curtis et al. 2006). The implications of obtaining an empirical Green’s function between two coordinates are wide-reaching because the imaging capabilities using such data are vastly superior to using earthquake waveforms, whose sources are unevenly distributed in time and space. Although the kind of frequencies available for ambient noise surface wave imaging were at first restricted to approximately 1–20 s complementing earthquake surface wave bandwidths, theoretically restricting the depth interval to the crust and uppermost mantle (e.g. Ren et al. 2013; Szanyi et al. 2013), more recent research has shown that cross-correlograms can be used to image structures as deep as the mantle transition zone (e.g., Li et al. 2019) or the core-mantle boundary (Retailleau et al. 2020).

Fig. 2
figure 2

Example of ambient seismic noise processing steps. a Raw 1-day long seismic record from station VOIR in Romania. b Resulting seismogram after instrument response correction, removal of mean and trend and bandpass filtering between 0.003 and 2.4 Hz. c The same seismogram from b (black line) and the resulting seismogram after the continuous wavelet transform filter was applied (red line). d The resulting cross-correlation function between station VOIR and station BURAR at a distance of \(\sim\) 222 km away. (Color figure online)

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Since the discovery of the powerful imaging potential of ambient noise Green’s functions, processing steps have evolved over time. Bensen et al. (2007) outlined the basis for ambient noise processing using the tools available at that time. However, several changes were made, including replacing the one-bit-normalization which essentially erases amplitude information from the noise series, with a new Continuous Wavelet Transform method for eliminating transient signals such as earthquakes (Yang et al. 2020), which, in our case, are undesirable because they obscure the background noise. We outline below our methodology step-by-step in which we use one of the most recent algorithms for noise processing.

Our data consist of continuous ground motion records and come from broadband seismic stations that operated in Central, Northern and Eastern Europe between the years 1999 and 2020 (Fig. 1). We downloaded months to years of continuous noise records from all available national permanent networks and temporary deployments out of which 338 stations belong to temporary networks including the CALIXTO seismic experiment in 1999 (Martin et al. 2005), the Carpathians Basins Project which operated in 2005–2007 (CBP, Dando et al. 2011), the PASSEQ experiment from 2006 to 2008 (Wilde-Piorko et al. 2008), and the South Carpathians Project from 2009 to 2011 (SCP, Ren et al. 2012). We downloaded data from permanent stations from national seismic networks whose operation periods overlapped with temporary experiments (1999, 2005–2007, 2009–2011, 2013–2014) and from 2019–2020, archived at EIDA (European Integrated Data Archive) and IRIS DMC (Incorporated Research Institutions for Seismology Data Management Center). Data from seismic stations in Ukraine were provided by the Main Centre of Special Monitoring State Space Agency of Ukraine for the year 2020. More information about data availability and network and station details can be found in the Supplementary Material.

Fig. 3
figure 3

a Inter-station ray paths (light blue lines) between station MLR (red triangle) and other seismic stations in Central and Eastern Europe (blue triangles); b Ambient noise cross-correlograms between MLR and other stations (black) and final de-noised functions (green lines) based on (Petrescu et al. 2024); c Rayleigh wave phase velocity dispersion curves obtained between all available stations (black lines) and mean dispersion curve for Central and Eastern Europe (orange line). (Color figure online)

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We processed these continuous time series using one of the most recent ambient noise techniques to obtain empirical Green’s functions between all possible combinations of simultaneously operating seismic receivers and extracted a number of physical characteristics from these virtual waveforms such as attenuation, dispersion, and the resonance frequency. Data were initially downloaded in 24-h long batches, resampled to 5 sps and quality controlled visually for anomalous recordings and instrumental failure. Metadata and instrument response quality were ensured by seismic network providers. Seismograms were then corrected for instrument response, mean, and trend, and filtered between 0.003 and 2.4 Hz with a two-pole Butterworth bandpass filter (Fig. 2). To extract the ambient noise background and attenuate high-amplitude undesirable transient signals (such as earthquakes or anomalous notches), seismograms were then de-signaled using the Continuous Wavelet Transform (CWT, Yang et al. 2020). At this point, we again ensured that resulting seismic traces were free of anomalous notches or data gaps, before proceeding further. We note, however, that the methodologies for estimating empirical Green’s functions are not unique and the workflow can vary among studies, especially when dealing with transient signals. These can range between complete elimination and one-bit normalization (e.g. Bensen et al. 2007; Molinari et al. 2020), comb filtering (Soergel et al. 2020), or power spectral density normalizationn (Magrini and Boschi 2021). The processed seismograms were then cut in hourly segments and spectral whitening with a waterlevel value of 60 dB relative to the amplitude of the spectrum was applied. Resulting windows were then cross-correlated between simultaneously operating stations, and de-noised using the CWT in reverse, resulting in 75.012 high-quality cross-correlograms from station pairs 32–2901 km apart, comprising high signal-to-noise-ratio Rayleigh waveform packets. Figure 3 shows an example of inter-station ray path coverage for the year 2020 as well as a subset example of cross-correlograms between station MLR located in the South-East Carpathians and other stations from Central and Eastern Europe.

3 Ambient seismic noise tomography

These ambient noise cross-correlations were subsequently processed to obtain a number of seismic parameters of the medium between pairs of stations. We used an automatic Bessel-analogue algorithm for extracting phase velocity dispersion curves of Rayleigh waves from vertical-component Green’s functions (Kästle et al. 2016; Petrescu et al. 2022). The method is based on Aki’s spectral formulation (Ekström et al. 2009) and assumes that the vertical-component ambient-noise cross-correlation spectrum can be described by a Bessel function. Phase velocities are picked from consecutive values where the cross-correlation spectra is zero, while enforcing a range of quality-control criteria described in detail in Kästle et al. (2016). Using this technique, we obtained 21,074 phase velocity dispersion curves between stations as far apart as 2870 km (Fig. 3c).

These inter-station dispersion curves were then inverted into period-dependent gridded phase velocity maps of isotropic and azimuthally anisotropic phase velocities, using the LSQR inversion algorithm with gradient and derivative damping. The total velocity anomaly in each grid cell comprises the contributions from both seismic velocity and anisotropy, according to Eq. 1:

$$\begin{aligned} \delta C = \delta C_{iso} + A_{2\psi } cos\left( 2\psi \right) + B_{2\psi } sin\left( 2\psi \right) + A_{4\psi } cos\left( 4\psi \right) + B_{4\psi } sin\left( 4\psi \right) , \end{aligned}$$
(1)

where \(\psi\) is the horizontal wave-number azimuth and \(\delta\)C is the total phase velocity anomaly at the considered grid knot. This equation is analogous to a Fourier expansion (Deschamps et al. 2008) and the coefficients A and B can be combined to calculate the 2\(\psi\) azimuthal anisotropy amplitude and direction. Seismic attenuation is a complementary information to isotropic and anisotropic seismic velocity, offering crucial constraints to understanding and interpreting seismic models heterogeneities in terms of petrological composition, water content, temperature variations or porosity and permeability. There are several physical properties that affect attenuation more than seismic velocity, so constraining both properties is a crucial key to reducing the interpretation ambiguity.

Using a modified version of the MuRAT2D algorithm (De Siena et al. 2014) originally designed for estimating local earthquake waveform absorption and scattering (e.g Borleanu et al. 2023a, b), we determined inverse quality factors from the coda decay envelopes of Rayleigh waves emerging from ambient noise cross-correlation functions. From a set of 36,634 empirical Green’s functions, we obtained 28,402 inverse coda quality factors of Rayleigh waves (\(Qc^{-1}\)). Figure 4 shows an example of frequency-dependent anisotropic phase velocity anomalies (dC/C,\(\%\)) and attenuation maps expressed as Qc at periods of 5 s and 3–5 s, respectively. Inter-station distance, Rayleigh travel-time, and back-azimuth dependence tests indicate that only coda quality factors obtained from cross-correlation functions between stations 50–250 km apart are most stable (Borleanu et al. 2023b). This restriction results in the removal of many empirical Green’s functions from the starting dataset and reduces the area of the reliable region for attenuation mapping. However, the Carpathian-Pannonian Region is within similar and acceptable resolution limits (150–200 km lateral resolution) in both phase velocity (Petrescu et al. 2024) and attenuation mapping (Borleanu et al. 2023b) and provides excellent ground for joint velocity and attenuation interpretations.

Fig. 4
figure 4

a Rayleigh wave isotropic phase velocity anomaly maps (colours) and azimuthal anisotropy (lines, in percentage) of Central and Eastern Europe after (Petrescu et al. 2024); b attenuation maps from ambient noise Rayleigh waveform coda decay functions (Borleanu et al. 2023b). Green contours show the thickness of Neogene sedimentary basins (after Kováč et al. 2007). The abbreviations are as follows: PB pannonian basin, TB transylvanian basin. (Color figure online)

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The two maps shown in Fig. 4 provide a more integrated view of the upper crustal structure in the Carpathian-Pannonian Region than previous regional seismic tomography models (e.g. Dando et al. 2011; Ren et al. 2013). Joint analysis of both phase velocities and attenuation can offer a more complex view of the buried structures, thermal anomalies, water content or stress states within observed heterogeneities. For example, 5 s period Rayleigh wave phase velocities are widely reduced within the Carpathian Foreland Basin in Romania the Transylvanian and the Pannonian Basins, consistent with thick Neogene sedimentary strata (Fig. 4a). Fast phase velocity polarisations are oblique-to-parallel to the sinuous path of the Carpathian Front in the South Carpathians, aligning along the faults in the sedimentary basin and likely perpendicular to maximum compression (Heidbach et al. 2018), changing to parallel in the Eastern Carpathians at the contact with the Eastern European Platform. Attenuation maps, on the other hand offer a slightly different view of the same basins at similar period intervals. While high attenuation largely corresponds to the known sedimentary basins (Fig. 4b), local heterogeneities showing bands of alternating high and low attenuation are likely connected to the mineralogical water content or fluid-lubricated faults, changes in temperature, or the presence of local microfractures. Changes in attenuation with frequency can relate to the size and nature of the attenuating structures: high-frequency attenuation are sensitive to small-scale scatterers, while low-frequency patterns are more indicative of deep fault extensions, such as the Intra-Moesian Fault (e.g. Borleanu et al. 2023a). Comparing phase velocity with attenuation anomalies in other tectonic units such as the Pannonian Basin, the Trans-European Suture Zone, or the Precambrian-aged platforms of the Eastern European can offer complementary insights into the nature and origin of observed structural heterogeneities, ultimately providing clues on the formation and evolution of the European continent through time (Petrescu et al. 2024).

4 Near-surface geophysics

Ambient seismic noise can also be successfully used to extract the fundamental frequency of resonance beneath seismic stations and to estimate the near-surface velocity models, crucial to understanding the sedimentary structures beneath the station and the depth to the crystalline basement. These are important parameters useful for seismic hazard and risk estimates and may be taken into account when designing buildings in areas with high seismic amplification and sedimentary basin wavefield entrapment.

Fig. 5
figure 5

a Fundamental frequency of resonance estimated using ambient seismic noise recorded at broadband stations in Hungary and Romania (coloured squares, clipped at 9 Hz) from the 23rd of July 2020; b HVSR function at CALIXTO station D17 (coloured square with thick outline) in the South-East Carpathians and intermediate models and their misfit proposed during a Monte Carlo space search; c Best-fit shear and compressional velocity models beneath the station D17

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Using noise data recorded at broadband stations located in the Carpathian-Pannonian Region, we estimated horizontal-to-vertical spectral ratios (HVSR). The peak of HVSR curves is commonly associated with the ellipticity of fundamental mode Rayleigh waves or the resonance frequency of SH waves (Fäh et al. 2003) and can be used to infer the thickness of the underlying sedimentary column (Coman et al. 2020). Figure 5a shows our peak HVSR frequencies estimated from 15 min of 3-component noise recordings from seismic stations belonging to the SCP network (Ren et al. 2012), the CALIXTO experiment (Martin et al. 2005) and the Rmanian Seismic Network (Popa et al. 2015), split in 200 s long time windows. A correlation between topography and frequency are immediately visible from this map: low elevation regions are predominantly characterised by low frequency values (0\(-\)1.5 Hz), with a few outlier exceptions, while high topography regions generally show higher frequencies (4 Hz in orogenic nappes). These results are in line with the expectation of a thick sedimentary layer in areas such as the Pannonian, Transylvanian and Carpathian Foreland Basins, while stations located on thin sedimentary layers or directly on bedrock sites will exhibit high HVSR peak frequencies (Petrescu et al. 2023a).

HVSR curves are sensitive to the high impedance contrast between the sedimentary strata and the crystalline basement, as well as the near-surface seismic velocity structure (García-Jerez et al. 2007). However, HVSR shapes are subject to strong trade-offs between the shear wave velocity and layer thickness (Scherbaum et al. 2003.) Estimating accurate velocity profiles from ambient noise HVSR curves are thus fraught with uncertainty. To reduce this trade-off, Petrescu et al. (2023a) combined ambient noise Rayleigh wave dispersion functions estimated with the Bessel-analogue algorithm (Kästle et al. 2016) with ambient noise HVSR curves, in a joint Monte-Carlo inversion procedure, following García-Jerez et al. (2016), to estimate probabilistic shear wave profiles beneath 81 individual broadband stations down to 20 km (Fig. 5).

5 Reconstructing historical earthquakes from noise

Ambient noise cross-correlations between pairs of seismic stations can be regarded as empirical Green’s functions of the medium between the stations. A seismic wavefield caused by a virtual impulsive source can thus be reconstructed by considering one station as the source and other stations as the receivers. However, these functions do not have the signature of a realistic earthquake, such as the typical P and S wave radiation patterns caused by the theoretical double-couple mechanism, the physical analogue for real earthquakes. The Virtual Earthquake Approach (VEA, Denolle et al. 2013) is a way to transform the Green’s function into a realistic seismogram, given source information such as the moment tensor, source-time function, hypocentral depth, and surface wave dispersion.

Using ambient noise cross-correlations between stations located in the South-East Carpathians and the VEA method, we reconstruct the seismic wavefield that would have been excited by historical devastating earthquakes generated in the Vrancea Seismic Zone, such as the Mw7.4 1977 earthquake, decades after their occurrence (Petrescu et al. 2023b). Firstly, we construct the full Green’s function tensor between the station located closest to the desired historical earthquake epicenter and all available broadband stations surrounding the South-East Carpathians, by cross-correlating between all three components, and rotate it in the direction of the virtual earthquake. We then correct this tensor for radiation patterns, source depth and surface wave dispersion. The latter depends on the velocity structure at the source and is estimated using the Generalized Eigenproblem Spectral Collocation (GESC) method (Denolle et al. 2012). VEA seismograms are calibrated against observed seismograms. However, given the lack of real recordings from some historical earthquakes, we created synthetic seismograms using normal mode summation (Herrmann 2013).

Figure 6 shows VEA waveforms at selected seismic station locations due to the 1977 earthquake, based on its probable source parameters (Radulian et al. 2019), and the peak ground displacement extracted from the calibrated waveforms, in the 15–25 s period interval. Modeled vertical waveforms show striking similarities with synthetic seismograms. However, since the VEA seismograms are based on real ambient noise data, they already contain information on the complex medium between stations, more complex path effects and wave physics that are likely not taken into account in synthetic waveform modeling. Peak ground displacement values are realistic given the high event magnitude: the order of magnitude is 1 m. The displacement pattern is likely related to the radiation pattern based on the given focal mechanism solution, although strong crustal heterogeneities likely play a role in altering the propagation of seismic waves. These results demonstrate that ambient noise provides an excellent opportunity to explore the devastating effects of past earthquakes and improve seismic hazard analysis, even without actual broadband records of historical earthquakes.

Fig. 6
figure 6

Map of peak ground displacement due to the Mw7.4 1977 earthquake (red star) estimated using the VEA method at broadband seismic stations around the South-East Carpathians. The station closest to the earthquake epicenter, SAHR (white triangle), is the virtual source. The inset shows the VEA seismograms (blue) versus purely synthetic seismograms (red). Figure adapted from Petrescu et al. (2023b). (Color figure online)

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6 Conclusions

The EENSANE project provides an open-access database of high-quality ambient noise cross-correlation functions between simultaneously recording broadband seismic stations located predominantly in Eastern Europe and beyond. We have shown that these functions can serve as a useful starting base in a range of seismic imaging applications at multiple scales and seismic wavefield modeling. Cross-correlations, or alternatively called empirical Green’s functions, can be analysed and processed in similar ways to earthquake seismograms. Thus, our database can significantly reduce ambient noise processing time and serve as a basis for seismic imaging tools that would be routinely applied to earthquake data.

Using cross-correlation functions, we estimated Rayleigh wave phase velocity dispersion and attenuation at both local and regional scale, fundamental frequency of resonance and velocity-depth profiles beneath stations. Our results provide new complex information on the internal structure of the East European lithosphere, offering fundamental insights into its formation and evolution. Some techniques were adapted from classical earthquake processing algorithms, showing that ambient noise-derived Green’s functions carry crucial information on wave propagation and the physical parameters of the Earth’s internal structure, in similar ways to earthquake-radiated waves.

Ambient noise-derived Green’s function tensors between pairs of stations can also be used to model seismic wavefields of historical earthquakes that have never been recorded before with modern broadband sensors. Waveforms modeled based on ambient noise cross-correlation intrinsically capture the complexities of wave propagation and medium heterogeneities, providing a more accurate and realistic seismic wavefield than purely synthetic seismograms, and can serve to improve seismic hazard estimates.