Interaction of Air Pressure and Groundwater as Main Cause of Sub‐Daily Relative Seismic Velocity Changes

Our study investigates variations of seismic velocity that occur over short time scales of hours. We use coda wave interferometry to inspect 5 months of continuous data from a seismological array in southern Germany. This results in relative seismic velocities (dv/v) that show temporal variations on the order of 10−4. Spectra of the velocity time series contain strong daily and sub‐daily behavior indicating that the daily and sub‐daily changes in the seismic velocity are primarily caused by atmospheric tides. We also note the influence of temperature changes on daily variations, but as a second‐order effect. The explanatory model focuses on depth variations of the groundwater table, linking atmospheric pressure (loading and de‐loading the Earth's surface) to variations in seismic velocity. Our results highlight an important environmental influence on seismic velocity that needs to be considered before seismic velocity variations can be used for inspecting fluid and stress variations in situ.

periodicity which may be forced by the repetitive loading and unloading of the Earth's surface due to the atmospheric pressure changes and thermal effects. This coupling of atmospheric pressure and seismic velocity provides insight into the behavior of aquifers in the near-surface region, and it might give rise to a range of new seismic applications for groundwater purposes.

GERES Array
We use seismic data from the GERES (German Experimental Seismic System) array (Harjes, 1990). GERES is part of the global network of seismic stations for the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO), providing a long continuous data set over several years. The GERES array is located in the Bavarian Forest in South East Bavaria, close to the borders with the Czech Republic and Austria (see Figure 1a). It consists of 25 vertical short-period seismometers (GS-13 seismometers, typically 1 Hz corner frequency, 40 Hz sampling frequency). The seismometers are installed in 3-5 m depth holes on four concentric circles around the center station A0 (see Figure 1b). The circles' minimum and maximum radii are 200 and 1,988 m, respectively, which corresponds to a maximum aperture of around 4 km. Due to the emplacement in holes, the seismometers are directly coupled to the granitic bedrock (Haidmühler granite). This type of emplacement ensures that the seismometers are not directly affected by environmental effects, for example, wind and air pressure changes. GERES is thus one of the most sensitive seismic arrays in central Europe (Harjes, 1990), with particularly high data quality. Beside this, GERES is located in a low-noise area, in a forest far away from particular noise sources, such as coastal lines, lakes or big cities. We use the GERES array to perform a monitoring of the subsurface properties with high temporal (hourly) sampling, for frequencies up to 10 Hz. For our investigation, we used 5 months of continuous data from January to June 2014. As additional data sets, we use the meteorological measurements from the close-by infrasound array I26DE, which provides temperature and atmospheric pressure measurements.

Monitoring Seismic Velocity
Our seismic monitoring is based on ambient seismic noise, from which we estimate the Green's function by calculating the cross-correlation function of the noise recorded at two stations (Shapiro & Campillo, 2004). The Green's function represents the seismic impulse response of a medium to a point source at one station, recorded at the other. To monitor changes in the subsurface, we then use the technique of coda wave interferometry (Snieder et al., 2002). This concept, based on scattered coda waves, shows its advantage in capturing small changes in the probed medium's elastic properties (Poupinet et al., 1984). The technique can be seen as probing a given volume in the subsurface repeatedly over time (Snieder et al., 2002). We use this to calculate differences in the coda waves' arrival time (dt/t) over the investigation period and transform this into a relative seismic velocity change (dv/v). Our workflow starts with a continuous record of ambient seismic noise cut into hourly segments to gain a high temporal resolution. Afterward, we apply spectral whitening and estimate Green's function for every possible station pair using MSNoise (Lecocq et al., 2014). We use a Wiener Filter similar to Mao et al. (2019) to increase the signal-to-noise ratio. This 2D filter is applied with the same filter length of 3 in both dimensions (vertical: hour [h]; horizontal: lag time [s]), which helps to reduce incoherent noise. From the filtered traces, we calculate a reference stack for every month and station pair to remove seasonal trends and increase the focus on the daily behavior of the subsurface. To determine the differences in the arrival time (dt/t), we use the Moving Window Cross Spectral Analysis (MWCS; Clarke et al., 2011;Ratdomopurbo & Poupinet, 1995). The underlying assumption is that the velocity perturbation is constant within the whole medium. This perturbation leads to a linear proportionality between the lapse time and the delay time (Poupinet et al., 1984). By estimating the slope of this proportionality, we get the relative arrival time changes (dt/t) which corresponds to the negative relative velocity change (dt/t = −dv/v). Using the MWCS analysis, we measure phase changes in coda waves to rule out or avoid potential influences of changes in the noise spectrum (Zhan et al., 2013). In addition to other studies on daily behavior, we calculate the relative seismic velocity changes in different frequency bands (3-7, 4-8, 5-9, 6-10 Hz) to investigate their depth dependency (after Herrmann, 2013, Figure S1 in Supporting Information S1).

Relative Seismic Velocity Changes
The result of the MWCS-Analysis in the 4-8 Hz frequency band is shown in Figure 2a. To decrease errors of individual station pair dv/v measurements, we calculate the mean over 300 station pairs. The other time series of dv/v can be found in Figure S2 in Supporting Information S1. We observe dv/v perturbations of the order of 10 −4 , which is in good agreement with other studies (Mao et al., 2019;Schönfelder & Eulenfeld, 2019). Our results show short-term (daily) variations and long-term (monthly) trends. The driving force for the long-term behavior is likely precipitation (Nakata & Snieder, 2012;Schönfelder & Wegler, 2006), including snowfall and the resulting load of the snow (Guillemot et al., 2021;Mordret et al., 2016), as well as barometric pressure (Gradon et al., 2021;Niu et al., 2008). Comparing the results of the other frequency bands shows that all significant longterm features are observable in the different bands (see Figure S2 in Supporting Information S1), for example, the linear decrease of the seismic velocities around Julian day 110. This study rather focuses on daily and sub-daily features which are more accessible via spectral analysis as presented in the following.

Spectral Analysis
To reveal the periodicity of dv/v throughout the days we have calculated the Fourier transform. For that, we split the dv/v time series into chunks of 7 days and padded them with zero to get more frequency bins. The overall process works in a sliding window with a step of 2 days. We do that to increase the number of individual spectra to increase the signal-to-noise ratio of the final stack. The resulting 2D spectrogram in Figure 2b shows consistent strong amplitudes around one and two cycles per day (called in the following simply S 1 and S 2 ). They are also often called the diurnal and semidiurnal terms. Some weaker amplitudes are observable at three, four, and five cycles per day. This trend manifests itself, when we increase the length of the sliding window. Even with a high resolution in the frequency domain the main peaks occur at S 1 and S 2 . We do not observe a strong peak at 1.93 cycles per day, which we might have expected from solid-Earth tides (M2). The stack along the time axis (see Figure 2c) verifies the observation and reveals the strong peaks and their ratios. The spectrograms and stacks for the different frequency bands show some differences (Figures S3 and S4 in Supporting Information S1). For the highest frequencies S 1 is dominant. The lower the frequencies the stronger the S 2 peak is. The band in between shows the background trend, which is an increase of the S 2 peak. For the three-and four-cycles-per-day peaks, a decrease in strength is observed as well.

Possible Environmental Effects Causing Seismic Velocity Variation
High-temporal-resolution monitoring has received more attention in recent years (Mao et al., 2019;Oakley et al., 2021;Schönfelder & Eulenfeld, 2019). The interest is to observe small changes in subsurface properties, and to eventually relate them to changes in stressing conditions and/or fluid content. There are more factors the observations are sensitive to, and we need to consider several environmental effects and their potential influence on the behavior of seismic velocities.
We can distinguish between periodic and non-periodic influences. Precipitation is a non-periodic effect, which affects the long-term behavior of seismic velocities (Andajani et al., 2020;Nakata & Snieder, 2012;Schönfelder & Wegler, 2006;Wang et al., 2017). If water is added or removed from the medium, the seismic velocity changes. The slow diffusion of water toward greater depth can be a reason for a long-term trend (Roeloffs, 1996). On the same timescale, atmospheric pressure influences velocities (Gradon et al., 2021). A particular case of precipitation is snowfall, which is a coupled effect that not only changes the water content. It adds a load to the medium, which changes the elastic properties (Guillemot et al., 2021;Mordret et al., 2016).
In this paper, we focus primarily on periodic effects. Temperature and atmospheric pressure are largely, but not strictly periodic; we investigate their influence on a daily time-scale only. Figure 3 shows a combined plot of the spectra of these effects together with the spectrum of the velocity time series. We can see that all of them have daily and sub-daily components.
The deformation of the Earth's subsurface due to solid-Earth tides is widely discussed (Schönfelder & Eulenfeld, 2019). Due to gravitational forces, the elastic rocks are deformed, which leads to variation of the seismic velocities (Yamamura et al., 2003). The spectrum of the tides (Figure 3 inset) shows a one (S 1 ), two (S 2 ), and 1.93 (M 2 ) cycles per day behavior. The first two are called diurnal and semi-diurnal term. The M2 component is the one with the highest amplitude. Since the dv/v observations show no such component, the influence of solid-Earth tides is clearly much weaker than that of other effects.
The temperature spectrum shows a strong one-cycle-per-day (S 1 ) and a weak two-cycles-per-day (S 2 ) peak. This suggests that temperature contributes to the S 1 peak but not significantly to the S 2 behavior. The influence of temperature on the dv/v measurements is not as straightforward as the one of precipitation or tides. On one hand, the direct influence of temperature changes applies to the top meters of the subsurface. On the other hand, heating and cooling throughout the day caused changes in the strain in the subsurface. From Ben-Zion and Leary (1986) or Berger (1975), we know that the impact of this thermoelastic strain can be much deeper than the few meters influence of temperature.
Since atmospheric pressure shows a strong S 1 and S 2 behavior, similar to the dv/v, we suggest it as the dominating force of the daily behavior of the dv/v. Gradon et al. (2021) already emphasized a strong correlation between longer-term atmospheric pressure changes and dv/v measurements over certain time scales. In the following section, we suggest a model of how the strong influence on daily behavior can be explained.

Interaction of Aquifers With Atmospheric Pressure
Spectral analysis of the dv/v time series shows a dominant peak around one and two cycles per day (S 1 and S 2 ). The comparison with potential periodic effects has suggested that the dominant driving force for this behavior is the atmospheric pressure changes. The atmospheric pressure has strong diurnal and semi-diurnal variations. This phenomenon is called atmospheric tides. It is a globally observed phenomenon mainly caused by solar radiation and thermodynamic effects related to ozone and water vapor (Chapman, 1951;Palumbo, 1998). In contrast to the solid or ocean Earth tides, the gravitational effects play a minor role in the generation of atmospheric tides. The diurnal component (S 1 ) is directly related to the heating and cooling of air due to solar radiation during the day. The origin of the semi-diurnal component (S 2 ) is still under discussion. It is most likely due to an interplay between thermodynamic mechanisms with a one cycle per day component (Palumbo, 1998). A quantitative analysis of both cycles shows that the S 2 is much stronger than the S 1 component (Chapman & Malin, 1970). This is also visible in the spectrum of atmospheric pressure measured at the GERES array (see Figure 3). The question arises, why the atmospheric pressure has such a strong imprint on the dv/v measurements while solid Earth tides do not. In the following, we will discuss possible mechanisms related to seismic velocity changes and air pressure variations.
The direct effect of air pressure changes is the loading and unloading of mass at the Earth's surface. An increase of pressure is associated with the mass which acts on the surface. This load results in a compression of the material in the subsurface. On a microscopic scale, this would mean that cracks are closing (Silver et al., 2007). This yields an increase of seismic velocity. During an episode of unloading cracks open up again and seismic velocity decrease. In saturated conditions, another mechanism must be considered. When cracks are closed, the fluid within is pushed to the pores. This leads to an overall increase of the pore pressure and a decrease of seismic velocity (Andajani et al., 2020). To quantify the effect we assume that a change of 1 kPa induces 10 −9 elastic strain in the Earth's crust (Rabbel & Zschau, 1985). We observe daily changes of 600 Pa, so this will result in 6 × 10 −10 . A comparison with Mao et al. (2019) shows that this strain will lead to a relative velocity change of about 6 × 10 −6 . This effect is too small to explain the observed velocity changes of 10 −4 .
The second mechanism which one has to take into consideration is the displacement of the water table due to changes in atmospheric pressure. Hydrological measurements, for example, McMillan et al. (2019), show a strong correlation between atmospheric pressure changes and groundwater level. The effect of groundwater level changes on long-term dv/v measurements has already been discussed in the literature (Clements & Denolle, 2018;Voisin et al., 2017). More importantly, we can observe these changes on a daily and sub-daily basis. If the pressure increases the water table is pushed into deeper parts.
During a period of low pressure, the water migrates toward the surface (see Figure 4). The reaction of the groundwater table to the pressure changes is lagging and thus phase shifted up to several hours (for example, Rasmussen & Crawford, 1997), due to the propagation time of the pressure wave to the aquifer and water diffusion towards greater depth. This will influence the subsurface in several ways. Tsai (2011) proposed two mechanisms that come along with the change of groundwater table depth. The first one is the poroelastic effect which describes the reaction of a saturated material to a strain. It is characterized by the hyd raulic properties of the media. The second mechanism is the direct elastic effect due to the additional mass of water. According to Tsai (2011), the two effects have the same order of magnitude, but the model is not fully suitable for our observations. The model is constrained for the media below the groundwater table. We expect that our method is most sensitive around the groundwater table. This leads to a minor influence of the two described effects. We therefore want to introduce another mechanism that would lead to the observed velocity changes. If the atmospheric pressure changes the depth of the groundwater table some parts of the subsurface will change their saturation degree. According to multiple laboratory measurements, for example, Mavko et al. (2009), Dong andLu (2016) as well as modeling studies like Solazzi et al. (2021) a different saturation would lead to significant changes in the S wave velocity, which also dominates the surface wave velocity. This mechanism can explain the observed velocity change in the order of 10 −4 . In the observed time series, a combination of all described effects is realistic.

Second Order Effect: Temperature Changes
We recognize a strong daily variation in the day's temperature and seismic velocity (see Figure 3). The influence of temperature changes on dv/v is discussed in Mao et al. (2019), Oakley et al. (2021), and Schönfelder and Eulenfeld (2019). For the S 1 , thermoelastic strain is estimated to be on the order of 10 −8 . This is in the same range as the estimated strain caused by the displacement of the water table. According to Ben-Zion and Leary (1986), the strain induced by the S 2 variation is smaller, but yet not quantified. We notice that the ratio between the amplitudes at the dominant peaks changes with frequency. Decay in the amplitude of S 1 is observed while S 2 increases. Within a few meters, S 1 is not dominating anymore. We interpret that as a decreasing influence of thermoelastic strain with increasing depth. This leads to the conclusion that we can explain the behavior of dv/v as a superposition of thermal and pressure effects, but it is dominated by the latter over depth (see Figures S2 and S3 in Supporting Information S1).

Comparison With Other Studies
In our study, we observe a strong S 1 effect. This is in good agreement with other studies on the daily behavior of dv/v (Mao et al., 2019;Oakley et al., 2021;Schönfelder & Eulenfeld, 2019). All studies interpret this cycle as an imprint of temperature changes. In addition, Mao et al. (2019) have evoked tidal forcing to explain this peak. Unlike other studies with this high temporal resolution (Mao et al., 2019;Schönfelder & Eulenfeld, 2019), we do not consistently observe the M 2 peak caused by the tidal deformation of the Earth (Figure 3 inset). An M 2 peak is observable for some station pairs only, but much weaker than in other studies. This could be because this effect is too small to be detected with our accuracy or within our geological setting. A similar conclusion was reached from a study of monochromatic seismic signals at the same place (Baisch & Bokelmann, 1999). The other mentioned studies had been performed primarily in sedimentary settings. Compared with the hard-rock environment, the stiffness of sedimentary rocks is lower (Karagianni et al., 2010). That means that they deform more under tidal stressing than hard rocks. The absence of an M 2 peak could also be associated with the location of our test site, far away from coastal lines, which are affected by oceanic tides (which would give rise to a strong M 2 peak). Since we cannot observe that tidal constituent, we can neglect tidal effects as driving force for the daily velocity variations. Oakley et al. (2021) do not observe the strong S 2 component, as we see it in our data. They use higher frequencies and show that their experiment is under dry conditions. In some special cases, coda wave sensitive close to the depth of the groundwater table observe a weak S 2 component. Oakley et al. (2021) interpret this effect also as water table migration. This strengthens our argument about the interaction of aquifers and atmospheric tides in the behavior of dv/v in a day.
The comparison with other studies shows the complexity of the problem. It seems that the character of velocity variations depends somewhat on the test site. This includes the geological setting as well as their location. Further, the outcome depends on the chosen frequency bands. Lower frequencies are more sensitive to greater depth and are potentially stronger influenced by the interaction of aquifers and atmospheric tides. The higher the frequency, the lower this influence.

Perspectives
Ambient seismic monitoring has been found to be very useful for geophysical monitoring, to better understand the behavior of Earth's crust before, during and after tectonic events, especially in active seismic regions (Brenguier et al., 2008;Ellsworth & Beroza, 1995). This is also motivated by recent laboratory studies that suggest that seismic velocity variations have important predictive capabilities (Dresen et al., 2020;Scuderi et al., 2016). The determined velocity time series however contain multiple imprints of environmental effects, which can be relatively strong compared to the small changes due to tectonic stress changes or earthquakes. Our study helps to filter out those interferences to reveal the response of the Earth to stress changes, and preseismic effects in particular. The results also manifest the strong influence of water/fluids on the dv/v, which may also be of more direct use itself (Roeloffs, 1988). That we can observe the relatively small changes of the groundwater table suggests that the technique may have sufficient sensitivity to also see other perturbations of the groundwater system, and that it may open new perspectives in groundwater geophysics, for example, for reservoir characterization; it may perhaps also help to better understand geothermal reservoirs. The non-intrusive nature of seismic methods may indeed be particularly useful in hydrogeophysics in general. Somewhat surprisingly, the field of hydrogeophysics appears to be largely devoid of "transmission" seismic methods so far.

Conclusions
We use ambient noise monitoring to show daily and sub-daily seismic velocity variations with a magnitude of 10 −4 . We achieve a high temporal resolution for the velocity time series by using a small and relatively dense array. By calculating the spectrum of the dv/v, we reveal strong daily and sub-daily components. To some extent, we confirm the results and proposed driving forces from earlier studies of the daily variation. In contrast, we do not observe a strong influence of Earth's tides. Instead, we detect a strong influence of atmospheric pressure variations (atmospheric tides) on the behavior of relative seismic velocity changes. We thus introduce a model that connects atmospheric loading and the observed dv/v changes. There is ample room for more seismic studies of groundwater and groundwater reservoir. The sensitivity to groundwater indicates that these effects may need to be taken into account if one wants to connect temporal velocity changes with tectonic stress changes. Different sites and experimental settings may lead to different dominating effects and varying strengths. Nevertheless, a step in the direction of high temporal resolution monitoring of crustal deformation is made.