the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Jun 2026
Seasonal Seismic Velocity Variations in the Western Bohemian Massif Using Ambient-Noise Cross-Correlation
Abstract. Changes in surface and near-surface loads, such as temperature and precipitation, can perturb crustal stress and generate measurable responses, including triggered seismicity, transient strain, and seismic velocity changes. Quantifying these responses provides a means to track the spatiotemporal evolution of stress and its coupling to fault slip and subsurface fluid processes. Traditional approaches, relying on recurring earthquakes or controlled sources, are limited by poor repeatability and high operational cost. Ambient-noise–based imaging avoids these constraints by using fixed receivers and continuous records to enable near-continuous monitoring. Here, we investigate relative seismic velocity variations (δv/v) in the western Bohemian massif using four years of ambient-noise recordings from 20 stations. We estimate δv/v in the 0.1–0.5 Hz band across three coda windows and evaluate potential environmental drivers using cross-correlation. The strongest seasonal δv/v signal is observed for station pairs with interstation distances shorter than 20 km and azimuths of 600-1200, indicating that path geometry and ambient-noise illumination strongly influence the stability of the measurements. Correlation estimates suggest that, δv/v is primarily associated with thermoelastic strain driven by atmospheric temperature variations, while groundwater-level fluctuations may contribute a weaker secondary hydrological signal whose mechanism remains ambiguous.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-3274', Anonymous Referee #1, 19 Aug 2026
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RC2: 'Comment on egusphere-2026-3274', Anonymous Referee #2, 12 Oct 2026
Review of “Seasonal Seismic Velocity Variations in the Western Bohemian Massif Using Ambient-Noise Cross-Correlation”
This paper presents a thorough analysis of seismic velocity variations derived from ambient-noise cross-correlations in the Western Bohemian Massif. The manuscript is well written, clear, and logically structured, and I enjoyed reading it. I particularly appreciated the systematic investigation of factors that may influence the observed velocity variations, including changes in the noise-source distribution. The manuscript is already in good shape. I have several comments and suggestions that should be addressed before publication.
- Introduction
Line 35: I could not find Kramer et al. (2025) in the reference list. Please add the missing reference. Although the spatial and temporal scales may differ, it would also be useful to briefly summarize the main findings of Kramer et al., particularly if this is the only previous study of dV/V in the study area. This would give the reader more context.
- Methodology and Data Processing
I appreciated the comparison of different processing methods designed to reduce irregularities and improve the signal-to-noise ratio of the cross-correlations. However, I suggest showing the differences between the three approaches in an additional supplementary figure. This would better illustrate why Method 3 was selected and make the reasoning easier to follow.
Line 64: You state that one-bit normalization artificially modifies the noise spectrum and that this is problematic. However, spectral whitening also intentionally modifies the spectrum. The goal of these methods is to somewhat modify the noise spectrum. Please clarify.
The order of the processing steps is also somewhat difficult to follow, please make clearer which processing step follows which.
Around line 85: It may be worth noting that later coda lapse times can provide broader or more effective spatial sensitivity, but may also contain more incoherent noise.
- Results
3.1. Observed velocity variations
Line 103: The observed seasonal relationship—lower dV/V during winter and higher dV/V during summer—should be placed in context by citing studies that have observed similar seasonal variations in other regions.
Line 108: This repeats the seasonal winter/summer trend already described in lines 102–103 and could be removed.
Line 110: It is unclear what is meant by a “strong seasonal signal.” The entire time series appears to show a clear seasonal pattern. Are you referring specifically to larger amplitudes? The amplitudes in 2018 and 2019 appear somewhat larger than in previous years, but not obviously anomalous. If the intended point is that selecting stations based on the noise-source distribution increases the other seasonal peaks and thereby reduces the relative prominence of the 2018–2019 amplitudes, please state this more explicitly.
3.2. Spectral content
Figure 4: Several of the annotated secondary peaks at periods shorter than one year, do not stand out clearly from the variability in the spectra. It is unclear whether all of these peaks are sufficiently robust to warrant physical interpretation. If the secondary peaks are discussed as meaningful subannual cycles, please provide some assessment of their robustness or significance. Alternatively, since the discussion focuses primarily on the annual signals, consider reducing the number of annotated peaks to improve the readability of the figure. Please also provide units for the PSD y-axis.
Line 149: Please explain more clearly what physical mechanism would generate harmonics in the dV/V time series.
- Environmental source mechanisms
Please reference Figure 5 in the text before Figure 6 is introduced.
Figure 5: It is unclear which meteorological stations were used and how the environmental data were processed. Given the size of the study area, difference in lithology and the presence of multiple stations, this information is important, particularly because variables such as groundwater level can vary substantially over relatively short distances. Are measurements averaged across stations, or is one station selected for each variable? Please describe the processing and station selection more clearly.
It would also be useful to clarify how the environmental variables are cross-correlated with dVV. Are the time series demeaned, standardized, or otherwise normalized beforehand, and is the quantity shown in Figure 6 a normalized cross-correlation coefficient? Please provide sufficient methodological detail to make this analysis reproducible. I also suggest showing the individual meteorological time series from the different stations in the Supplementary Information to illustrate their spatial variability.
Figure 6: For clarity, consider marking one year (365 days) with a vertical line so that the annual periodicity is immediately apparent. The main lag times discussed in the text, such as the approximately four-month groundwater lag, could also be annotated.
It would also be helpful to plot the dV/V time series alongside the environmental variables to facilitate direct comparison. For example, Figures 3 and 5 could potentially be combined.
Comparing Figures 3 and 5, there appears to be a (seasonal) relationship between precipitation and velocity changes, particularly in 2016 and 2017. This relationship deserves further investigation, or a more convincing demonstration that the apparent correlation is not significant. The relatively weak correlation amplitude in Figure 6b may partly reflect the behavior in 2018 and 2019, when the correspondence appears weaker.
Line 240: Could groundwater infiltration also increase seismic velocity through fluid saturation of previously air-filled pore space, thereby increasing elastic moduli relative to density (without opening of cracks)? The response of seismic velocity to water input should depend strongly on lithology and rock properties, e.g., porosity. Is a negative relationship specifically expected for the lithologies present in the study area? Please discuss this more explicitly.
Line 274: Please provide some information on the relevant lithology of the Western Bohemian Massif and, if possible, specify the thermal diffusivity assumed in the analysis and the corresponding estimated delay time.
Line 290: A brief explanation of how the method works would help readers understand the analysis and interpretation.
Line 296: Please clarify what is meant by “the dominant peak azimuth is unchanged in W1.” The figure shows W1, W2, and W3, so it is unclear what comparison is being made.
Line 299: Are you referring to B(theta) here, or to the seasonal variations in the dV/V estimates? Please clarify.
- Discussion
The observed lag between groundwater level and velocity changes is interesting. I wonder whether additional insight could be gained by calculating velocity changes separately from the causal and acausal parts of the cross-correlations. In theory, both sides should provide consistent results, and I understand the motivation for averaging them to stabilize the measurements. However, researchers often see differences between causal and acausal measurements, attributed to - for example - the noise source distribution. Examining the two sides separately could therefore help assess the robustness of the observed lag.
Line 331: It is unclear what is meant by “the cross-correlations are coherent.” Does this mean that they have a high signal-to-noise ratio, or that they are consistent across the three time windows? Please clarify.
Code and Data Availability
Line 411: Please provide, if possible, a reference for DISBA.
Citation: https://doi.org/10.5194/egusphere-2026-3274-RC2
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- 1
Review of “Seasonal Seismic Velocity Variations in theWestern Bohemian Massif Using Ambient-Noise Cross-Correlation » by Mandal et al
general comments:
This article reports on observations of relative seismic velocity changes (dv/v) derived from ambient seismic noise in the Western Bohemian Massif, Central Europe. The processing involved data optimization by selecting station pairs with limited aperture (distance) and a preferential NW-SE orientation. The results show that seasonal dv/v variations are primarily controlled by thermoelasticity, with additional contributions from hydraulic loading. The dataset and observations are valuable, the data processing is performed correctly, and the paper is well written. The article deserves publication but requests major corrections, including analyzing the data in a wider frequency band to locate the changes at depth, and performing a 2D surface wave horizontal tomography to identify the regions were changes are more significant.
specific comments:
1) Introduction: Solar radiation (radiative heat transfer) is at least as important as air temperature (convective heat transfer). Therefore, air temperature cannot be the sole source or mechanism driving ground temperature changes.
2) End of the Introduction: References to previous work using ambient seismic noise in the Bohemian Massif should be cited. Examples include (but are not limited to):
3) Section 2: Whitening should be performed before amplitude normalization, not after—especially for highly non-linear processing such as 1-bit normalization or clipping.
4) Lines 105–106: Structural changes and damage are more likely monitored by cross-correlation (CC) than by dv/v. See, for example:
A. Obermann et al., Imaging pre- and co-eruptive structural changes of a volcano with ambient seismic noise, J. Geophys. Res., 118, 6285–6294 (2013).
5) Figure 3: A larger frequency band analysis is needed. Additionally, surface wave inversion would be useful to better locate changes at depth. A horizontal 2D surface wave tomography could then be performed to identify the regions of most significant changes.
6) Line 115: A theoretical model describing the decrease of SNR with longer inter-station distance is proposed in:
E. Larose et al., Fluctuations of correlations and Green’s function reconstruction: role of scattering, J. Appl. Phys., 103, 114907 (2008).
7) Line 172: “Mostly sensitive” does not imply that the observed changes originate from that depth. A full frequency analysis, including higher frequencies, is necessary to confirm the depth sensitivity.
8) Line 175: Clarification is needed: “later in the coda” means (to a lesser extent) deeper probing, but (mostly) broader horizontal 2D probing. Given the dominance of surface waves, regions outside the network may exhibit less dv/v. A 2D surface wave dv/v tomography would be highly beneficial.
9) Line 371: 2D surface sensitivity kernels average over horizontally larger surfaces/volumes, but not necessarily deeper ones. The conclusions remain valid: the larger the volume, the smaller the fluctuations—assuming the fluctuations are local.
technical corrections:
L23-24: literature is missing
Figure 2: color lines brackets are hardly visible
L263: here we assume that the continuous solid material propagates stress, which is not 100% the case for cracked rocks and/or granular materials, and even lesss evident in soils. This assumption/limitation could be clearly stated.
L338: “short period” generally relates to the seismic spectrum (<10s), improper or missleading here