Reduction of windturbine generated seismic noise with structural measures

Reducing wind turbine noise recorded at seismological stations promises to lower the conflict between renewable energy producers and seismologists. Seismic noise generated by the movement of wind turbines has been shown to travel large distances, affecting seismological stations used for seismic monitoring and/or the detection of seismic events. In this study, we use advanced 3D numerical techniques to study the possibility of using structural changes in the ground on the wave-path between the wind turbine and the seismic station in order to reduce or mitigate the noise generated by the wind turbine. Testing 5 a range of structural changes around the foundation of the wind turbine, such as open and filled cavities, we show that we are able to considerably reduce the seismic noise recorded by placing empty circular trenches approx. 10 meters away from the wind turbines. We show the expected effects of filling the trenches with water. In addition, we study how relatively simple topographic elevations influence the propagation of the seismic energy generated by wind turbines and find that topography does help to reduce wind turbine induced seismic noise. 10

Results for the vertical (Z) component of seismometers located behind the metamaterials given in Fig. 1-a is presented in Fig.   2. We can observe that for the Ricker wavelet source with a dominant frequency of 5 Hz the seismic energy is not attenuated, on the contrary it is increased. This is likely due to interference of scattered waves from the different cross-shaped cavity walls.

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In addition, the waveforms change, also due to superposition of waves scattered from the cavity sides. Similar amplification results are obtained when shifting the individual cross-shaped unit cells (see Fig. 1-b,c and d). The shift of every second row with respect to the first seems to have little to no effect on the seismic waveforms, also for different distances. One needs to take into account that the wavelength of the propagated wavelet at the surface is about 1500(m/s)/5(Hz) = 300 m, almost half the total length of our models. Also, the location of the source is about 40 m away form the first unit cell cavity. It thus 105 seems that these kind of cross-shaped large-scale seismic metamaterials are not able to reduce seismic energy for our 5 Hz wavelet, but when we tested source wavelets with higher frequencies (15 to 25 Hz) the energy was attenuated. However, our target frequencies for the attenuation of WT noise is in the range of [1-10] Hz, thus this size and type of metamaterial is not of practical use for our purposes, because they would have to have very large dimension for attenuating waves with frequencies below 10 Hz thereby increasing costs and environmental impact.

Half circular trenches
We now consider simpler models compared to the cross-shaped metamaterials presented by Miniaci et al. (2016). To do so, we create a total of eighteen models with half circular trenches, nine of them empty and nine filled with water. We included varying depths of 20, 15 10 and 5 m and included two different widths of 3 and 5 m (see Fig. 3). Again we numerically model a frequency range of seismic energy between [1-10] Hz with a Ricker wavelet centered at 5 Hz as a source time function. The 115 point source is placed 10 m in front of the trenches while the stations are placed at a range of distances behind the trenches. We use a numerical model with dimensions of 400 × 400 × 200 m (length/width/depth) discretized with more than one hundred million of global points (see Fig. 3). At the edges and bottom of the model we consider absorbing boundaries and at the top the free surface condition. The structural models are assumed to have constant velocities v p = 1500 m/s and v s = 900 m/s and density ρ = 2300 kg/m 3 . The reason for using constant velocities for this scenario is the fact that adding material to the 120 trenches is computationally difficult to implement due to the creation of the meshes and we therefore resort to a simpler case for filled and empty trenches so that the difference in the seismic recordings is only due to the filling material for a better comparison.
Results for the vertical (Z) component seismic recordings for the model with empty trenches are presented in Fig. 4-a. We can observe that all models attenuate the seismic energy in a similar way and only for 5 m deep trenches the attenuation is less attenuation results but it is not the best scenario. At larger distances (355 m) all models, excluding those with 5 m depth, behave virtually equal and at shorter distances (28 m) the best models are those with the deepest trenches.
Results for the models with trenches filled with water show a more complex behavior compared with empty trenches (see  Fig. 4-b). This indicates that filling the circular trenches with water, or indeed other material, may have the opposite effect to the desired attenuation of seismic energy, since amplification effects similar to those that occur in sedimentary basins can be expected (Olsen, 2000;Wirth et al., 2019). We tried models of trenches filled with other material, i.e., material with a different velocity and attenuation, however, the effect was the same as filling them with water. Modeling porous small-scale material was not possible due to the size of possible meshes in combination 140 with our frequencies and model sizes.
The results obtained in this section are, however, encouraging since we can observe a reduction of WT generated noise by placing half circular trenches between the WTs and seismic stations. These constructions lower the financial and environmental  impacts compared to results presented by Miniaci et al. (2016). Note that the above models were generated only for short distances between WT and stations, however, most seismic stations are more than 100 m away from WTs and we will explore 145 a more realistic scenario in the next section.

Empty half circular trenches at larger distances
Encouraged by the results obtained in the previous section, we investigate how empty trenches can attenuate the seismic energy at large distances and in presence of structural changes in the soil (i.e., trenches) and with a more realistic sources.
We create a total of eight modes with empty half-circular trenches within a model with dimensions of 2500 × 400 × 1000 m 150 (length/width/depth) discretized with more than one hundred million global points (see Fig. 3-b) with boundary conditions as above. The velocities in the model increase with depth as in the first scenario, with v p = 1200 − 3200 m/s and v s = 900 − 2400 m/s and a constant density of ρ = 2300 kg/m 3 (see Fig. 3 b) -c)). Using this model allows to properly take into account the generation of surface waves at larger distances compared to the previous experiments, where we had to use a homogeneous velocity due to the complexity of the models with water-filled trenches.

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Different to the experiments above, for this case we use source time functions that are taken from seismic noise measurements made by Neuffer (2020) and re-inject these at the place of the WT as a point sources for the three spatial coordinates. The seismic measurements by Neuffer (2020)   Results for the vertical (Z) component are presented in Fig. 5 as frequency spectra. Here we show spectra over waveforms due to the complex nature of the source and to be able to detect whether any frequencies are attenuated or increased compared with the model without structural changes (trenches) that is shown by the black line. In addition, previous studies also display spectra rather than waveforms (e.g. Stammler and Ceranna, 2016;Neuffer and Kremers, 2017;Neuffer et al., 2019;Zieger and Ritter, 2018) and we aim for a better comparison with those studies. In our results in Fig. 5, we can observe the overall 175 reduction of noise amplitudes for all frequencies when placing circular trenches between the WT and the seismic stations. The models that most effectively reduce the seismic energy are those that are deepest (purple lines) with the wider trenches (dashed lines) reducing the energy slightly better than narrower trenches (solid lines). Our half-circular trenches act as barrier to seismic energy but for shallower trenches the energy of waveforms can still travel below the structure therefore the reduction of energy is less pronounced here.

Topographic effects
As a last numerical experiment we change our model to include topographic variations at the surface. It is well known that topographic variations have an effect on noise waveform amplitudes (Lacanna et al., 2014;Köhler et al., 2012) and it will be instructive to see how WT noise is affected by simple topography since many WT are placed at the top of hills. We model this scenario using the source measurements made by Neuffer (2020) as source input as described above. The model dimensions 185 are 2500 × 1000 × 1000 m (length/width/depth) and we create topography in the shape of mounds with varying height of 33.5, 67, 100, 153 and 200 m (see Fig. 6-a). The velocity model for the bulk model domain (i.e., the box) is the same as above with velocities increasing with depth. Inside the tomographic mounds we change the velocity, including higher and lower velocities with and without random scattering media (see Fig. 6-b). All these models in Fig. 6-a and -b have the same topographic horizontal extension and velocity variations, which guaranties that the differences observed in the simulations are only due to 190 the topographic elevations. The WTs are placed at the top of the mounds.
As mentioned before, in our numerical simulations, we consider that the topographic elevation may have a different velocity perturbation compared with top layer of the bulk of the model domain, i.e., at zero elevation (see Fig. 6-g). This will introduce an impedance (velocity x density) contrast at the bottom of the topography for the case of lower or higher velocities both with and without scatterers. Therefore we expect changes in waveform and energy also due to these impedance contrasts.

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Looking at different scenarios, we find that mounds with the same velocity as the top layer of the box reduces the recorded seismic energy for most frequencies for all topographic heights, and including scattering into these models emphasizes the effects. Higher mounds reduce the energy more efficiently than smaller mounds. If we use a velocity decrease inside the mound compared with the top layer of the box, we find instead increased energy for all frequencies and including scattering in that model increases the energy even more. This can be explained in analogy to sedimentary basins where the trapped energy 200 in the basin increases due to wave interference and depending on the structural geometry of the basin (Shumway, 1960;Olsen, 2000;Wirth et al., 2019). If, however, the velocity is faster in the mounds compared with the top layer of the box, the seismic energy recorded at the seismic station is reduced, and even further reduced is scattering is included (Fig. 7). As above, the reduction of the energy correlates with the height of the hills with larger hills reducing the energy more efficient. Because the modeling of attenuation within the topographic region remains outside the capabilities of our numerical models, we instead 205 included intrinsic attenuation in the entire numerical models and general observations remain virtually unchanged. The mounds modeled here are very simple topography and one can expect that the amplification or reduction of the energy is dependent on the morphology of the topographic elevations. For evaluating how complex topographic variations affect the seismic noise recorded at stations behind the topographic variations, we consider two additional models given in Fig. 6 c-d.
Both scenarios variations have an elevation of 200 m and the topographic elevation has a random velocity perturbation of 210 scatterers in a velocity model that is the same as the top layer of the box (i.e., at zero elevation). Results are presented in Fig. 8, where we compare to the simplified hill presented in Fig. 6 with the same height of 200 m as the top of the complex topography.
We can observe that the complex topographies reduce the energy for some frequencies, for others increase the energy. This is true also for different distances of stations from the WT but it is not necessarily the same frequency for which the energy is enhanced or reduced. We can observe that in general the amplitude/reduction of seismic energy will depend on the complex 215 topography and will affect differently each particular frequency.

Discussion and conclusion
The demand of renewable energy systems increases every year around the world. In particular, the expansion of wind energy is expected to help renewable electricity generation to rise and it is expected to increase the most in absolute generation terms among all renewables (Tabassum-Abbasi et al., 2014). This increase in the number of wind turbines conflicts with seismic 220 stations since the noise generated by wind turbines is recorded at seismic stations (e.g. Neuffer et al., 2021Neuffer et al., , 2019