In this study, we determine spectral characteristics and amplitude decays of
wind turbine induced seismic signals in the far field of a wind farm (WF)
close to Uettingen, Germany. Average power spectral densities (PSDs) are
calculated from 10 min time segments extracted from (up to) 6 months of
continuous recordings at 19 seismic stations, positioned along an 8 km
profile starting from the WF. We identify seven distinct PSD peaks in the
frequency range between 1 and 8 Hz that can be observed to at least 4 km
distance; lower-frequency peaks are detectable up to the end of the profile.
At distances between 300 m and 4 km the PSD amplitude decay can be described by a power law with exponent

In recent years, debates on the emission of seismic waves produced by wind turbines (WTs) and its potential effects on the quality of seismological recordings have led to increased research efforts on this topic. The main objectives are the characterization of WT-induced seismic signals, the definition of protection radii around seismological stations, and the modeling-based prediction of WT effects on seismological recordings in advance of the installation of WTs. Styles et al. (2005) reported about discrete frequency peaks in seismic noise spectra that increase with wind speed and the rotation rate of a nearby WT and assigned the observed peaks to vibration modes of the WT tower and rotor rotation. Zieger and Ritter (2018) and Stammler and Ceranna (2016) confirmed discrete frequency peaks between 1 and 10 Hz and analyzed signal amplitude decays with distance to the WTs described by a power law. Saccorotti et al. (2011) observed seismic signals with a frequency of about 1.7 Hz that were associated with WTs at distances of up to 11 km. Friedrich et al. (2018) used a migration analysis to identify seismic signals from nearby wind farms (WFs) and were able to distinguish
between various WFs based on differences in frequency content. Polarization
analyses was used by Westwood and Styles (2017) to show that Rayleigh waves
dominate the wave field emitted from WTs. This observation was confirmed by
numerical simulations (Gortsas et al., 2017). The increase of the noise
amplitude with the square root of the number of WTs (

Approaches to model the seismic radiation from WTs are rare and focus mostly on modeling the ground vibration of a single WT (Gortsas et al., 2017) or its operational components only (e.g., Zieger et al., 2020) but not on wave field propagation considering superimposed wave fields and amplitude decay with distance to multiple WTs simultaneously. However, Saccorotti et al. (2011) used an analytical approach to model the observed amplitude decays by summing up the calculated noise amplitudes produced by several WTs, including an intrinsic attenuation law, but they did not study possible effects of multiple WTs on the interference of the emitted wave fields.

In this paper, we present an analytical approach to model frequency-dependent seismic radiation and amplitude decays with distance in comparison to robust long-term observed decay curves, measured at a WF in Uettingen (Bavaria, Germany). In a first step, we derive distance-dependent noise spectra from recordings of up to 6 months in duration and characterize the relation between signal frequency and amplitude decay. We face the challenge of handling phase differences between multiple source signals that have strong effects on the seismic radiation due to significant changes in interference pattern of the superimposed wave fields. We apply the phase shift elimination method (PSE method) to generate representative source signals as an input for the analytical modeling of the observed amplitude decays. The comparison between modeled and observed amplitude decays also allows the constraining of the parameters of a simple two-layer model of the subsurface. We further show how it is possible to generalize the approach to predict radiation patterns for arbitrary WF geometries.

Our surveys were conducted in the neighborhood of a WF in Uettingen, about 9 km west of Würzburg in Bavaria. The WF consists of three WTs positioned in a NW–SE line with a spacing of 350 m and 450 m, respectively. The Nordex N117 type WTs have 2400 kW rated power and a tower height of 141 m. Their maximum rotation rate is about 12 rpm (rotations per minute). To measure the amplitude decay of the seismic WT signals we deployed 19 seismic stations along a profile of 8.3 km length, starting at the easternmost of the three WTs and running in NE direction approximately perpendicular to the geometrical layout of the WF (Fig. 1). Additionally, we placed three stations in the WT basements in order to record the seismic source signal of each WT. The instruments were installed between July and November 2019, and data recording will extend until August 2021. All stations are equipped with Trillium Compact posthole sensors (20 s) and Centaur data loggers (Nanometrics) recording continuously at a sampling frequency of 200 Hz. To improve the signal and noise conditions the sensors of the profile stations were placed in shallow boreholes of 1–2 m depth.

Location of the wind farm in Uettingen (red crosses) and seismic profile stations F01 to F19 (blue triangles). Three additional seismic stations are positioned in the WT cellars (I01, I02, I03). Wind farms A and B (dashed boxes) are not targeted by our experiment but are located in the area.

The local near-surface geology is defined by Triassic sedimentary rocks. Beneath a thin soil layer, limestones of the Muschelkalk are situated over clastic sediments of the Buntsandstein, mainly terrestrial quartzite, sandstone, and claystone layers. Geologic cross sections suggest that the lower Muschelkalk under the topographic surface reaches a thickness of up to several tens of meters (Bayerisches Geologisches Landesamt, 1978). However, at some seismic stations the Muschelkalk–Buntsandstein boundary is only a few meters below the surface. In topographic depressions the Muschelkalk can be completely missing, i.e., thin quaternary soft sediments directly cover Upper Buntsandstein rocks.

We analyzed a continuous dataset between September 2019 and March 2020, covering a range of 159 to 207 d depending on the exact station installation date. We associate the measured amplitudes in the seismic waveform data with the corresponding WT parameter (in this case “rotor speed”) at a resolution of 10 min. For this reason, the recordings of each profile station were split into 10 min segments that were transformed to power spectral density spectra using the method of Welch (1967). Each of these spectra were then sorted according to the respective rotor speed into bins of 1 rpm width. With this procedure we generated close to 10 000 single PSDs within the bin of maximal rotor speed (11–12 rpm) called “full power” status for each station, and about 2000 single PSDs for the “zero power” status of the WT (0–1 rpm). In order to reliably remove outliers and reduce the impact of local transient noise (e.g., traffic on nearby roads), we excluded 75 % of the largest PSD amplitudes and used only 25 % of the single PSDs to calculate the final average PSD spectra. This seems to be a relatively strong limitation of the dataset. However, due to the long observation period there are still enough data left to calculate robust average spectra. We think that this approach provides a reliable and conservative estimate of the spectral WT amplitudes with a minimized influence of interfering transient signals. Figure S1 in the Supplement illustrates the influence of different percentiles on the calculated average PSD at station F01.

Figures 2 and 3 show the resulting average PSDs (25 % percentile) for the
full power and the zero power WT status, respectively. Besides the
strong microseismic peak at about 0.2 Hz, we identified nine peaks of
significant energy centered at 1.14, 1.7, 2.3, 3.5, 4.8, 6.0, 7.6, 10.5, and 17.2 Hz. All of them show a systematic amplitude
decrease with increasing station distance, indicating that their origin is
located at the WT. For peaks 1 to 7 we fitted the observed amplitude decay
with a power law model (see next section). Because of the rapid amplitude
decay at frequencies

Average PSD spectra at full power status (11–12 rpm), calculated at profile stations F01 to F16 in the time range from September 2019 to March 2020. The distance of each station to the WT is color coded and indicated in the figure legend. In total, nine energy peaks are identified between 1.14 and 17.2 Hz, all of which show a systematic amplitude decrease with increasing station distance. The amplitude decays of peaks 1 to 7 have been measured and fitted by a power law.

Average PSD spectra at zero power status (0–1 rpm), calculated at profile stations F01 to F16 in the time range from September 2019 to March 2020. The identified peaks at full power (Fig. 2) have disappeared. The remaining sharp peaks show no systematic decrease with increasing distance, indicating that they have a different origin.

To quantify the PSD amplitude decay, the respective peak maxima of the
full power PSDs (Fig. 2) were picked at each station. Figure 4 shows the
resulting attenuation curves for peak 1 (1.14 Hz) to peak 7 (7.6 Hz) using a double-logarithmic representation, i.e., the logarithm of peak amplitude is
shown versus the logarithm of the station distance. If the PSD amplitude
decay corresponds to a power law, which is the basic assumption, there should be a linear correlation between log(amplitude) and log(distance). The attenuation factor,

Double logarithmic representation of PSD amplitude decay
at seven different peak frequencies. Blue circles mark the measured
amplitudes from station F01 (194 m) to station F19 (8413 m) at full
power status of the WT. Filled symbols denote data points that were used
for power law fitting (red lines) between station F02 (301 m) and F12 (3944 m) with attenuation factor

For these reasons we decided to restrict the analysis of the amplitude decay
to the distance range between 300 and 4000 m and to estimate the
attenuation factor,

Frequency dependence of

The

Calculated

Each WT can be considered a seismic source. By analyzing the seismograms
measured simultaneously in the three WTs (I01, I02, and I03) of the WF
Uettingen, we observe phase shifts between the individual wave forms (Fig. 6a). As an example, three time series (vertical component), each recorded in one of the WT cellars during a rotation rate of about 11.5 rpm, are filtered to a narrow bandwidth around frequency peak 1 with 1.14 Hz (1.10–1.18 Hz) and are compared within a time window of 22 s. In the first 2 s, the signal phase of seismic station I03 is shifted by

In the following section, we model the observed amplitude decays and set up a mathematical formulation that includes a source function, attenuation factors, geological properties, and the superposition of multiple wave fields (produced by multiple WTs). In view of the observation that the source signals of neighboring WTs are not in phase, we study the influence of possible signal phase differences on the amplitude decay and propose a solution as to how to account for or “eliminate” this effect in the calculation.

Previous research suggests that mainly vertically polarized Rayleigh waves
are emitted from WTs and that they dominate the WT-induced seismic noise (Westwood and
Styles, 2017; Neuffer and Kremers, 2017; Gortsas et al., 2017). However,
recent studies indicate that both Rayleigh and Love waves are emitted from
WTs (see Lerbs et al., 2020; Neuffer et al., 2021). In our models, we assume that
surface wave amplitudes decay proportionally to

Geometrical spreading is independent of wave frequency. In addition, attenuation due to intrinsic absorption reduces the wave amplitude with
distance to its source

Assuming a homogeneous half-space, the wave amplitude can be calculated for
any distance

Schematic figure of the analytical modeling approach.
Amplitudes as functions of time are calculated at points (

By modeling the interference wave field as a function of time, this approach
allows to derive root-mean-square amplitudes (rms amplitudes) at any point
at the surface. For the calculation, the amplitude calibration factor

Since we observe significant changes of the phase shifts between signals
measured at the three WTs (Sect. 2.3), we aim to study its effect on the
wave field that is emitted by the three WTs in Uettingen. Hence, three wave
fields are calculated using three different source phase compositions
assuming a 1.14 Hz source signal frequency, 1500 m s

Calculated amplitude decay curves (in the direction of the magenta line) for three scenarios with different source signal phase compositions using

In this section we propose a method of how to handle the observed time-varying
source signal phases and their effect on the seismic radiation using the
assumption of a random appearance of signal phase constellation of multiple
WTs, especially regarding long time periods. To define representative source
signals, we developed a phase shift elimination method (PSE method). Within
this PSE method, 500 radiation patterns (i.e., wave fields) are calculated
using random signal phases

Calculated and observed data are fitted by a

Description of the fitting process to find the best model parameters from the comparison of calculated and observed amplitudes.

Moreover, the normalized root-mean-square error (NRMSE) is obtained to
quantify the fitting quality. To determine the NRMSE, each RMSE is divided
by the range (maximum value

To fit modeled and observed amplitudes we performed a separate grid-search
for both the group with high-frequency signals and with low-frequency signals.
During each individual fitting process, the PSE method was applied to ensure
results that are independent of source signals phases. Regarding the group
of low-frequency signals (

Best model parameters (

Distribution of the NRMSE of the fit between modeled and observed amplitude decays obtained by a

Two-layer model derived by fitting observed and modeled amplitude decays. The best model parameters (

Averaged modeled radiation patterns (right) and averaged amplitude decays (left, black line) along the profile (magenta line) by averaging 500 wave fields and decay curves (gray lines), based on random

Averaged modeled radiation patterns (right) and averaged amplitude decays (left, black line) along the profile (magenta line) found by averaging 500 wave fields and decay curves (gray lines) based on random

The aim of this study is to present reliable amplitude decays of seismological signals produced by multiple WTs and to model these amplitude
decays with an analytical approach. The propagation of WT-induced seismic
signals has been the subject of numerous studies. Many authors found that
the amplitude decay with increasing distance (

In terms of modeling approaches, most of the recent publications focus on modeling the seismic signals that are emitted by one single WT (e.g., Gortsas et al., 2017) or the whole WF is considered as one emitting source. Since we observe time-varying phase differences between the signals that are measured directly at the three individual WTs of the WF Uettingen, we propose that this effect must be included in the modeling of WFs. Our observations confirm the significance of phase differences between the seismic signals from the WTs of a wind farm and that the signal phase of a single WT is not stable over time. Hence, we expect that phase differences between source signals vary randomly, which was already presumed by Saccorotti et al. (2011). Superimposed wave fields lead to constructive and destructive interferences (which depend on, e.g., signal phases) and affect the spatial amplitude decay, as we can show in this study (Fig. 8). Similar to our approach, Saccorotti et al. (2011) modeled amplitude decays on the basis of superimposed wave fields and attenuation laws but did not include phase shift variations between signals of the WTs. However, they noticed that the increase of noise depends on WT number, which was later shown by Neuffer et al. (2019). Saccorotti et al. (2011) suggest that more accurate results can be derived by considering WTs that are not vibrating in phase. Here, we can prove the randomness of these phase differences between WTs and propose a solution by applying the PSE method to the modeling. Only with this consideration we can reproduce the observed amplitude decay. The PSE-method (averaging 500 wave fields calculated with random signal phases) is generally difficult to apply if full wave form propagation simulation is needed (e.g., FEM, finite element methods), since the required computation time would increase rapidly. Within our modeling approach, the source amplitude is chosen to be uniform for the three WTs. Previous studies (e.g., Lerbs et al., 2020) showed that WTs emit signals with time-varying amplitude and azimuths. In terms of modeling radiation patterns for very short time periods, this should be considered when choosing representative source characteristics. To model radiation patterns that represent long time periods (quasi-static processes), a uniform source amplitude should be sufficient, provided that the WTs are of the same type.

For the Uettingen WF the discrepancy between observed and simulated amplitude decays for 1.14 Hz in distances larger than 2000 m to the WTs are likely due to the other nearby WFs A and B (Fig. 1). We assume that the low-frequency signals of these WFs travel farther compared to higher-frequency signals and are measured in addition to the signals from the targeted three WTs in Uettingen (Fig. 1). This could lead to an overestimation of the signal amplitudes, especially in the far field of the WF Uettingen. However, since we observe peaks at identical frequencies in the near and far field of the WF, it is reasonable to assign these signals mainly to the wave field produced by the WTs in Uettingen. Signals from various WFs can generally be distinguished using, e.g., a migration approach (Friedrich et al., 2018). However, detailed analysis of the effect of additional WFs around Uettingen is beyond the scope of this study, but their impact should be considered in future analysis. Interestingly, the sensitivity to source signal phases (gray lines in Figs. 12 and 13) is significantly higher for 1.14 Hz signals than 7.6 Hz and is generally decreasing with increasing frequency. This indicates that the signal phases are not as important for higher frequencies than for lower frequencies (e.g., 1.14 Hz). It should be noted that some of the individual input source signal phase compositions led to decay curves that could not fit the observation data at all. This is solved using the PSE method.

Lerbs et al. (2020) proposed a solution that describes the wave attenuation
with distance using an attenuation model solely based on a power law
assumption (

To demonstrate the capability and possible application of the modeling
approach used in this study, we modeled the radiation pattern of the
original WF in Uettingen for 1.14 and 7.6 Hz signals and compared the
results with the case where three imaginary WTs are arbitrarily added to the
existing WF (Fig. 14). Model parameters are

Estimated seismic radiation pattern (red showing high amplitudes) of

We recorded the seismic signals emitted from a three-turbine WF in Uettingen, Bavaria, over a period of 6 months and analyzed the spectral characteristics and spatial amplitude decays. During the full power operation mode of the WTs we identify seven prominent spectral peaks in the frequency range from 1.14 to 7.6 Hz. The attenuation of the peak amplitudes with respect to the WT distances can be described by a power law with exponent

An analytical approach was developed to model the seismic radiation of the
WF. From measurements we observe that WTs are not vibrating in phase and
that the phase differences vary randomly over time. Furthermore, the results
of the simulation show a strong influence of phase differences between
single WT source signals on the radiation pattern and hence on the spatial
amplitude decays. We applied a phase shift elimination method (PSE method)
to eliminate this effect with the aim of deriving a representative seismic
wave field. Modeling results were compared to the observed
frequency-dependent amplitude decays to derive model parameters (

The code and data used in this research are currently restricted.

The supplement related to this article is available online at:

FL and ML performed the field work and data analysis. FL set up the modeling approach and performed model calculations. GR participated in data interpretation and model development and supervised the article outline. HD and GR initiated the project and provided the computational framework. FL, ML, GR, and HD edited the article.

The authors declare that they have no conflict of interest.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We would like to thank ESWE Versorgungs AG for providing access to the wind farm facilities in Uettingen and their operational data, and we would especially like to thank Ulrich Schneider for his support in initiating the project. We appreciate the support of the mayors of Uettingen, Greußenheim, Remlingen, and Leinach as well as their respective municipal administrations. Special thanks are given to Wolfgang Reinhart, Joachim Palm, and Ana Costa for their help during fieldwork and station maintenance and to Gabriele Schmidt (ESWE), who was our contact person regarding technical matters of the WF Uettingen.

This research is part of the project KWISS and has been supported by the German Federal Ministry for Economic Affairs and Energy (FKZ no. 0324360) and ESWE Innovations und Klimaschutzfonds.This open-access publication was funded by the Goethe University Frankfurt.

This paper was edited by Charlotte Krawczyk and reviewed by Joachim Ritter and Hortencia Flores Estrella.