Investigating Rayleigh Wave Dispersion Across the Carpathian Orogen in Romania

Abstract

The Carpathian orogen represents a natural laboratory for the study of geodynamic interactions between lithospheres of different ages. The ancient Archean Cratons, such as the East European Craton, and Proterozoic platforms like the Scythian and Moesian platforms collided with the younger Tisza and Dacia mega-units, resulting in the formation of the current architecture of the Carpathian Mountains. To better understand how the lithospheric structure on Romanian territory changes from the East European Craton to younger European microplates, we use earthquake data recorded at the permanent broadband seismic stations of the Romanian National Seismic Network (RSN). Applying the multiple filter technique, we examine the dispersion of Rayleigh wave group velocities for earthquakes located within a 4000 km radius of the epicenter. Travel time tomography, conducted through fast marching surface tomography, helps us to construct group velocity maps for periods between 30 and 80 s. Our findings highlight a low-velocity body in front of the Vrancea slab, indicating asthenospheric upwelling due to slab verticalization.

1. Introduction

The present-day configuration of the Carpathians (Figure 1) is evidence of a plate convergence process that began in the Late Cretaceous and continued through the Tertiary and Quaternary [1,2]. The tectonic units of the Carpathian orogen are part of the Alpine–Carpathian–Dinaric orogenic system, with a complex geometry and tectonic evolution. In the Late Jurassic (ca. 156 Ma), the new Alpine Tethys opened, and its branches led to the separation of the Alpine–Carpathian Pannonian (ALCAPA), Tisa, and Dacia mega-units from the European continent. The Ceahlau–Severin Ocean in the Eastern Carpathians is a distinct segment of the Alpine Tethys that stretches towards the east but does not connect to the ancient Meliata–Maliac Ocean crust, which dates back to the Triassic period [1,3].

The compressional regime began in the Cretaceous and led to the closure of these ancient oceans and the consumption of the oceanic lithosphere and thinned continental lithosphere. In the later stages of this compressional process, the formation of fold–thrust belts and the emergence of Neogene volcanism occurred [4,5]. The Neogene–Quaternary magmatism associated with the subduction process along the Carpathian orogen displays unique features within the inner part of the Carpathian curvature. The observed characteristics indicate a shift in the composition and structure of the lithosphere, which has significant implications for the geodynamic process of subduction in this region [6]. Seismic tomography is very useful in visualizing the actual tectonic configuration at depth, providing valuable information about the geodynamic evolution of the Carpathian orogen.

The study of Rayleigh wave propagation in orogenic belts is important in understanding the structure and evolution of continental lithospheres. Surface waves are long-period waves often used to image seismic velocities in the crust and upper mantle [7,8,9,10,11,12,13]. Surface wave tomography models are obtained from Rayleigh and/or Love wave dispersion measurements and are valuable indirect imaging tools available to accurately estimate absolute velocities at depth.

Several tomographic studies have been conducted in our study area, with a predominant focus on the Vrancea seismic zone. These studies have utilized body wave data [14,15], combinations of body and shear wave data [16], and full-waveform tomography [17]. While body wave tomography offers useful, detailed information about the crustal and upper mantle seismic velocity structure, it suffers from the limited vertical resolution inherent to the data or technique, which can hinder the interpretation of fine-scale lithospheric features. Surface wave tomography, as applied in this study, is particularly sensitive to shear wave velocity variations in the crust and upper mantle, making it well suited for the imaging of lithospheric and upper mantle structures. The velocity models derived from surface waves can place meaningful constraints on the tectonic architecture, thermal regimes, and compositional variations, offering a clearer view of the lithospheric configuration and the geodynamic processes shaping the Carpathian orogen.

These seismic velocity structures are essential in interpreting slab dynamics and understanding the mechanisms of intermediate-depth seismicity (60–180 km) in the region. For instance, SKS anisotropy studies [18] show that the mantle flow directions change from being initially perpendicular to the slab to parallel, consistent with recent slab rollback and retreat. Such observations, when evaluated alongside shear wave velocity anomalies from surface wave tomography, can help to delineate the slab geometry, deformation zones, and the evolution of mantle flow. Moreover, intermediate-depth earthquakes in Vrancea exhibit atypical mechanisms not solely attributable to brittle failure. Instead, they likely involve ductile deformation [19,20] and may be influenced by mineralogical phase changes or dehydration embrittlement at depth [21,22]. A decreasing stress ratio with increasing earthquake magnitudes [23] suggests that, while smaller events are dominated by thrust faulting with vertical elongation, larger events are linked to more complex failure processes. By resolving the velocity structure with surface waves, our tomographic model contributes to identifying these zones of mechanical instability and provides a structural framework within which these dynamic processes can be better understood.

This study aims to investigate the lithospheric structure beneath Romania by analyzing Rayleigh wave group velocities in order to understand the geodynamic interactions and transitions between the ancient East European Craton, Proterozoic platforms, and younger European microplates. Using seismic data such as teleseismic signals, which create dispersion curves at long periods, we aim to identify deep structural anomalies like asthenospheric upwelling associated with the subduction process. Unlike ambient noise [24], Rayleigh wave dispersions obtained from distant earthquakes allow us to penetrate deeper into the Earth’s interior, providing better insights into these deep structures.

2. Data and Methods

2.1. Earthquake Data and Seismic Stations

In this study, we analyzed the dispersion of Rayleigh waves generated by earthquakes with epicentral distances of less than 4000 km and magnitudes (Mb) greater than 4.5. Seismic data were recorded by 23 broadband stations from the Romanian Seismic Network (RSN) between 2011 and 2018. The waveforms were truncated by 3000 s after the origin time of the earthquake to ensure the capture of the events depicted in Figure 1. To reduce the file size and boost the data processing, the waveforms were decimated at a sampling rate of 0.5 s, which did not affect the signal generated by our target surface waves, whose periods ranged between 20 and 150 s. The earthquakes that generated high-quality surface waves from which dispersion could be extracted are represented in Figure 2. Seismic sources originate in the Mediterranean Sea, mostly concentrated in the Hellenic subduction zone and Iran predominantly, as well as in the North Atlantic region. The intersection of these rays is essential for high-resolution tomography without numerical artifacts caused by a lack of coverage.

2.2. Rayleigh Wave Dispersion

Before running the dispersion analysis, the data were prepared following several steps. Seismograms were downloaded from the NIEP server in MiniSEED format and then converted to SAC files, and earthquake information was added to the SAC headers. The instrument response was removed, and, to enhance the visualization of Rayleigh waves, the seismograms were rotated from the ENZ to the RTZ coordinate system. Using dedicated scripts, thousands of seismograms were filtered and windowed by extracting 1000 s before and after the surface wave packet, and they were subsequently prepared for the dispersion analysis program.

Accurate measurements of the group and phase velocities of surface waves, such as Rayleigh waves, are essential inputs in surface wave tomography. Surface waves are, by nature, dispersive, meaning that their velocities vary with the frequency because each frequency component samples a different depth. As a result, dispersion curves provide valuable information about the vertical variations in wave velocity within the Earth’s lithosphere. To analyze Rayleigh wave group velocity dispersion, we used the Computer Codes for Seismology (CPS) software (Version 3.0) [24]. We applied the multiple filter technique (MFT) to isolate group velocities as a function of the period. Data processing involves applying multiple filters to the seismogram and enables interactive data visualization, allowing the user to select the maximum amplitude for each frequency/period of the fundamental mode of Rayleigh or Love waves. The method uses a Gaussian filter (Hω), described by Equation (1), to filter the dispersed signal mode of surface waves, as expressed by Equation (2). In Equation (1), α represents a resolution-testing parameter, ω₀ represents the central frequency (peak of Gaussian function), and ω_n is a parameter that determines the width of the function. Equation (2) illustrates the dispersion of a surface wave, with ϴ representing the phase of the source, k representing the wave number, and r representing the distance of the seismic signal.

$$H_{\left(\omega \right)}=\left[exp-{\displaystyle \frac{\alpha {\left(\omega -{\omega }_0\right)}^2}{{\omega }_n^2}}\right]$$

(1)

$$g\left(t\right)={\displaystyle \frac{1}{2\pi }} {{\displaystyle \int }}_{-\infty }^{+\infty }A\left(\omega \right)H\left(\omega \right)e^{i\left(\omega t-kr+\varnothing \right)}d\omega$$

(2)

The choice of the filtering parameter α is important, and it should be selected based on the epicentral distances of seismic sources, with higher values of α for seismic events with greater epicentral distances. Since the maximum epicentral distance was below 4000 km, α was set to be less than 100 s.

The extraction of fundamental mode dispersion curves was performed interactively, by selecting peak amplitudes of the signal at discrete periods. We successfully selected nearly 400 high-quality dispersion measurements. Figure 3 shows an example of the interactive CPS program output for the recovery of Rayleigh wave group velocities.

2.3. Seismic Tomography: The Fast Marching Method

To map the distribution of group velocities across the Carpathian orogen, we used the fast marching surface tomography (FMST) method [25]. FMST performs travel time tomography using iterative non-linear inversion in spherical coordinates. The arrival times of surface waves were calculated initially using a fast marching algorithm, where a data gridding method is used to solve the eikonal equations governing wave propagation. To solve the inverse problem, a gradient-based method is employed that iteratively minimizes an objective function containing a residual data term and two regularization terms (ɛ, η). At each iteration, the model is perturbed and updated according to Equation (3):

$${\delta }_m=-A{\left[A^T\left(G^T{C}_d^{-1}G+\epsilon C_m^{-1}+\eta D^{T}D\right)A\right]}_A^{-1}T\gamma$$

(3)

where A represents the subspace matrix, G is the matrix of group arrival time gradients from the model m, Cm is the covariance matrix of the a priori model, and $\epsilon$ is a damping operator and represents the difference between the observed and synthetic data at the current iteration. The damping factor serves the purpose of restricting the deviation of the solution model from the initial model, effectively keeping it within a reasonable range, while the smoothing factor ($\eta )$ constrains the smoothness of the solution model. D represents the discrete Laplacian operator, which enforces smoothness by penalizing the model’s curvature. The damping and smoothing parameters were chosen empirically based on multiple test inversions. We evaluated the trade-off between data misfit and model roughness by visually inspecting the stability and resolution of the recovered structures for a damping range of 6–500 and a smoothing range of 10–1000, respectively. Our chosen values (30 and 100) were also close to those in previous, similarly scaled studies [23]. The model was parametrized on a 0.2° × 0.2° grid with velocity nodes in spherical shell coordinates.

To map the distribution of group velocities on the gridded model, we first computed initial travel time values between source and receiver locations based on the estimated dispersion curves at each period. The travel time field was estimated using the fast marching method by forward-modeling the eikonal equation on the gridded model. This initial model served as input for the subsequent iterative inversion that accounted for ray bending [24]. The velocities in each grid cell and ray paths were then adjusted iteratively using the fast marching method and a subspace inversion scheme that satisfied the observed data and regularization constraints [26]. The selected high-quality travel time data were assigned appropriate uncertainty estimates from the CPS program. Additionally, the tomographic inversion process in FMST incorporates an effective secondary layer of filtering. Observations are weighted based on their associated uncertainties, and the iterative inversion minimizes residuals while applying smoothing and damping constraints. This naturally suppresses the influence of any remaining inconsistent data, ensuring that the resulting model is primarily informed by coherent, reliable input.

3. Results and Discussion

Using the multiple filter technique, we obtained 396 Rayleigh wave group velocity dispersion curves (Figure 2) with a period range of 20 s to 160 s (Figure 4) from earthquakes with epicentral distances ranging from 568 km to 3327 km. The coverage with Love waves was not sufficient for preliminary tomography and it requires data processing over a longer period of time, encompassing earthquakes with higher signal-to-noise ratios. Using similar methods but employing ambient noise [23] instead of teleseismic earthquakes, a previous study succeeded in obtaining Rayleigh wave group velocity maps for periods of 6, 10, 15, 20, 25, and 30 s in a regional study covering the Pannonian Basin and all of Romania. The Vrancea region is known for its intermediate-depth seismicity, and, while the velocity maps derived from the dispersion of Rayleigh waves with periods of up to 30 s offer valuable lithological information, they unfortunately only cover depths above the Vrancea intermediate-depth earthquakes. To overcome this limitation and explore deeper parts of the lithosphere, we used teleseismic earthquake signals, which make it possible to generate dispersion curves at longer periods and investigate deeper structures, including the seismically active Vrancea zone.

In Figure 4, the dispersion curves estimated at the VLDR seismic station are presented, which are color-coded based on the earthquake azimuth. We observed higher group velocities for earthquakes originating from the southwest of Europe (yellow lines) compared to the group velocities from earthquakes in the south–southeast direction (orange lines).

In the upper mantle, minerals like olivine have a tendency to align themselves in the same direction as the applied stress, and this preferential orientation leads to anisotropic behavior in the propagation of surface waves [27,28]. At lower depths, a similar phenomenon occurs, where feldspar, being the most abundant mineral in the Earth’s crust, maintains its brittle behavior. Meanwhile, quartz and mica exhibit plastic deformation primarily through dislocation creep, resulting in the development of feldspar microboudinage [29]. According to the European active tectonic strain–stress map shown in [30], the higher group velocities for the seismic sources produced in the Mediterranean Sea (south–west) could have been caused by the crystallographic preferred orientation. Another plausible explanation relates to the differing propagation paths: waves arriving from the south travel through the complex Hellenic Subduction Zone and its surrounding mantle, while those coming from the west propagate through Central Europe. In general, subduction zones such as the Hellenic Subduction Zone are cold and fast seismic regions, tending to produce high seismic velocities [31].

Rayleigh wave dispersion analysis has proven to be a powerful tool in investigating the Earth’s deep interior [32,33]. Waveforms with periods shorter than 30 s are generally more sensitive to shallow subsurface features, while those with periods longer than 30 s primarily reflect structural variations within the upper mantle. This frequency-dependent sensitivity enables the use of surface waves to probe different depths, offering valuable insights into the vertical layering of the Earth.

Data from the Rayleigh wave group velocity dispersion curves were then integrated into the FMST tomography routine, which converged successfully (Figure 5A) to construct group velocity maps at discrete periods between 30 and 80 s. The residual travel times shown in Figure 5A are distributed around zero, indicating the good convergence of the inversion.

The reliability of the tomographic inversion was assessed by performing resolution tests. In Figure 6, the first panel shows the input synthetic checkerboard model. This model consists of alternating velocity anomaly spikes of ±1 km/s, spaced every 0.6 degrees, and demonstrates that the inversion method is capable of resolving anomalous structures as small as 60 km in the studied area. The subsequent panels display the recovered models obtained after six iterations of tomographic inversion. Figure 6 shows the retrieved velocity from checkerboards for periods of 40, 50, 60, 70, and 80 s and shows that our inversion demonstrates adequate reliability. The displayed values represent absolute velocities corresponding to each depth interval, based on the synthetic reference model used in the analysis. These synthetic models use a constant propagation velocity for the preset depth range. For example, for periods of 30 s, the preset model uses a velocity of 3.28 km/s, while, for periods of 80 s, the velocity is 3.72 km/s.

The correspondence between the period and the depth interval to which surface waves are sensitive is not straightforward and changes with the depth and the considered seismic velocity model. Using the local seismic model [34], we forward-modeled the sensitivity kernels for the Rayleigh wave group velocities, which helped us to interpret the frequency-dependent maps. Figure 5B shows that surface wave depth sensitivity decreases inversely with the period. The sensitivity depth interval also widens as the wave period increases, leading to greater uncertainty in estimating heterogeneities at greater depths.

At relatively short periods (around 30 s), the group velocity maps (Figure 7) reveal low seismic velocities consistent with overthrust Carpathian fold structures, which are mainly composed of sedimentary rocks. Although the sensitivity kernels at this period peak near a 40 km depth, corresponding to the lower crust and uppermost mantle, the sensitivity is distributed over a range of depths, including shallower layers. Therefore, the observed slow velocities likely reflect a combination of effects from both the deep crust/mantle structure and the overlying one. The Rayleigh waves with a period of 50 s propagate through an interval of 50–80 km (Figure 5B). The group velocity maps generated from these dispersions highlight the Scythian Platform and parts of Moesia and the EEC as regions characterized by high velocities.

The platform units or Craton-type units are characterized by greater thicknesses, older ages, and faster seismic velocities. The map generated using the dispersions with 60 s periods best highlights the separation of platform-type units located outside the Carpathian arc from the younger and slower seismic units located above the Transylvanian and Pannonian basins. Additionally, in the same period, we observe an artifact in the northeastern part, generated by the inversion model due to the lack of ray path intersections in this area. This lack is primarily due to the absence of seismic sources in the northeastern part of the study area and not the weak distribution of receivers/broadband seismic stations.

At periods longer than 40 s (Figure 7), the 2D group velocity maps indicate a region of reduced group velocities located in front of the Vrancea lithospheric slab (adjacent to the seismogenic body to the northwest). This observation supports the hypothesis of an asthenospheric upwelling cell, as previously suggested in [35,36,37,38,39].

In the context of collisional processes, these upwelling cells can be observed in subduction zones, where two tectonic plates converge and one plate is forced beneath the other. As the denser oceanic lithosphere sinks into the underlying mantle, it exerts a downward force on the overriding plate.

This process can also impact the behavior of the asthenosphere, potentially leading to the development of asthenospheric upwelling cells [40,41,42]. The change in the volcanism’s composition in front of the Vrancea seismic zone, as well its propagation direction, has been attributed to the toroidal flow of the asthenosphere accompanying the gradual subduction of the Vrancea lithospheric fragment [6].

4. Conclusions

In this study, we analyzed the group velocity dispersion of Rayleigh waves generated by regional earthquakes with an epicentral distance of less than 4000 km and a magnitude Mb > 4.5. The data studied consisted of records from 23 RSN broadband stations covering the period between 2011 and 2018. We further used the fast marching method and an iterative subspace inversion scheme to construct frequency-dependent maps of the Rayleigh wave group velocities across the Carpathian orogen.

Our new results confirm the presence of slow velocities in the overthrusting Carpathian folds at short periods (30 s). For periods longer than 50 s, the group velocity maps show locally high seismic velocity amplitudes in the East European Craton, the Scythian, and the Moesian platforms.

The 2D maps indicate a low-velocity anomaly in front of the Vrancea slab, likely associated with the subduction process. An analysis of the Rayleigh wave group velocities shows that this low-velocity region is located at depths between approximately 50 and 90 km. This anomaly may represent the seismic signature of the asthenospheric upwelling of hot material. Such upwelling is commonly linked to the subduction process, where the sinking slab induces mantle flow and causes hotter asthenospheric material to ascend near to the slab.