Insights Into Hydraulic Fracture Growth Gained From a Joint Analysis of Seismometer‐Derived Tilt Signals and Acoustic Emissions

Hydraulic fracturing is performed to enhance rock permeability, for example, in the frame of geothermal energy production or shale gas exploitation, and can potentially trigger induced seismicity. The tracking of increased permeabilities and the fracturing extent is often based on the microseismic event distribution within the stimulated rock volume, but it is debated whether the microseismic activity adequately depicts the fracture formation. We are able to record tilt signals that appear as long‐period transients ( < $< $ 180 s) on two broadband seismometers installed close (17–72 m) to newly formed, meter‐scale hydraulic fractures. With this observation, we can overcome the limitations of the microseismic monitoring alone and verify the fracture mapping. Our analysis for the first time combines a catalog of previously analyzed acoustic emissions ([AEs] durations of 20 ms), indirectly mapping the fractures, with unique tilt signals, that provide independent, direct insights into the deformation of the rock. The analysis allows to identify different phases of the fracturing process including the (re)opening, growth, and aftergrowth of fractures. Further, it helps to differentiate between the formation of complex fracture networks and single macrofractures, and it validates the AE fracture mapping. Our findings contribute to a better understanding of the fracturing processes, which may help to reduce fluid‐injection‐induced seismicity and validate efficient fracture formation.

2 of 14 of liters of injected volume, acoustic emissions (AEs) with radiated energy in the kHz range are successfully monitored by piezoelectric sensors near the injection well (Amann et al., 2018;Zang et al., 2017). Although this approach provides indications of induced stress changes, the general layout of either simple planar fracture zones or complex networks of fractures (see e.g., McClure & Horne, 2014) and the geometry (orientation and extent) of the hydraulic fractures are only inferred indirectly. AEs are the result of the tensile opening (and closing) of the macrofractures. The response is considered indirect because failure is expected to occur at discontinuities in the process zone surrounding the fracture, due to stress changes produced by the macrofracture (Dahm, 2001;Dahm et al., 1999;. The microseismic approach is limited to cases with abundant seismic signals. In some cases, hydraulic fracturing is only accompanied by a low seismicity rate or no seismicity at all. Processes may be aseismic (e.g., Cornet et al., 1997;Guglielmi et al., 2015) or the seismic signals could be below the detection threshold due to a limited monitoring setup as well as local rock properties (e.g., high damping) and stress conditions. However, a lack of microseismic activity can also be caused by an inefficient fracture formation. This ambiguity cannot be resolved by microseismic analyses alone but requires additional information.
Long-period deformation signals are expected in the near-field of a growing hydraulic fracture and can provide independent, direct information about the geometry and the dynamic parameters of new fractures. However, they are rarely monitored in injection experiments. Such signals are considered to provide direct information on fracture growth, because they measure the deformation of the entire rock volume produced by the opening and growing macrofracture itself. In this sense, the monitoring of broader frequency ranges and the installation of different types of sensors (see e.g., Eaton et al., 2013) can provide independent observations regarding the fracture evolution that are crucial to study for example, stress memory effects within the rock (Kaiser, 1950). The Kaiser effect, reported for many geothermal production/test sites (Zang et al., 2014), implies that seismic activity is only induced in subsequent stimulations once the stress level of the previous stage is reached.
During a series of meter-scale hydraulic fracturing experiments (fracture areas of 10-50 m 2 ) in the Äspö Hard Rock Laboratory (HRL) in Sweden, Zang et al. (2017) set up a complementary monitoring system covering frequency ranges from mHz (long-period transients) to kHz (AEs) in distances of 5 m to several hundred meters.
In this study, we analyze long-period pulses (Figure 1) recorded on the horizontal components of two broadband seismometers (Trillium Compact 120) installed in the tunnels adjacent to the injection borehole of the Äspö experiments. The analysis is complemented by a joint interpretation with the AE activity of the same experiment (Niemz et al., 2020).
Broadband seismometers are known to be sensitive to ground tilting, that causes long-period pulses on the horizontal components, while the vertical component is undisturbed (Rodgers, 1968;Wielandt, 2002;Wielandt & Forbriger, 1999). Such pulses are regularly observed in broadband seismic records  but often treated as noise. In fact, electronic noise can produce very similar signals (Kinoshita, 2008). Usually, tilt-induced signals are attributed to very local effects during the passage of seismic waves (e.g., grains of sand breaking or moving below a seismometer foot or fatigue cracks inside the concrete instrument pier) and need to be corrected before earthquake source studies (Zahradník & Plešinger, 2005. In volcanic settings, however, nearfield rotational motion has been associated with large-scale fluid processes like dyke intrusions (e.g., Battaglia et al., 2000;Gambino et al., 2007) or the inflation of magma chambers (e.g., Aoyama & Oshima, 2008;Genco & Ripepe, 2010;Wielandt & Forbriger, 1999;Wiens et al., 2005). Hydraulic fractures induced by fluid injections from boreholes generate similar, although much smaller, tilt signals. A few previous studies, with injected volumes of 10-85,000 m 3 , showed that these small signals can be measured using surface or borehole tiltmeters (e.g., Holzhausen et al., 1985;Jahr et al., 2008;Lecampion et al., 2005).
Due to the small scale of the experiments with injected volumes below 0.04 m 3 and the complementary monitoring setup of the in situ mine experiments at Äspö HRL, we have the unique opportunity to study independent tilt signals recorded on broadband seismometers in addition to the distribution of high-frequency AEs (presented in Niemz et al., 2020). This analysis allows to obtain more detailed insights into the growth and the orientation of fractures, the fracturing process in general, and the causal connections of tilt signals and AE activity during the opening and the growth of hydraulic fractures.
The hydraulic fracturing experiments were conducted in granitic basement rocks and with multiple injection schemes, mainly differing in the pressurization strategy. A conventional, continuous injection strategy was applied in the experiments HF1, HF2, HF4, and HF6 (see injection parameters in Figure 3). During HF3 a cyclic, progressive pressurization was used in the initial fracturing stages ( Figure S5). A detailed description of the injection strategies can be found in Zang et al. (2017). During each experiment 25-30 L of water were injected into the sealed packer intervals in multiple stages in order to break the intact rock and grow hydraulic fractures. The experiments comprise an initial fracturing stage and up to five refracturing stages. Each stage consists of three phases: (a) in the injection phase, water is injected with a constant flow rate. (b) In the shut-in phase, the injection is stopped (flow rate is zero), but the borehole interval is still closed, so the pressure is maintained or slowly decreasing. (c) In the bleed-off phase, the interval is opened and previously injected water is allowed to flow back, while the remaining pressure is quickly decreasing (see flow and pressure in Figure 3).

Seismometer Response to Tilt
Long-period pulses are present in the horizontal traces of all injection experiments, except HF5, but most clearly seen for the experiments HF1-HF3 and for HF6. The lack of such signals on the vertical component is a strong argument for the observation of a tilt signal, as is the correlation with the injection phases ( Figure 1).
Tilt is affecting a seismometer by a small horizontal axis rotation of its reference frame deflecting the horizontal components away from the gravitational Figure 1. The lowpass-filtered (0.05 Hz) raw waveforms recorded by the broadband seismometer BB1 during the injection experiment HF2 show multiple long-period pulses on the horizontal components (common scaling for all traces). For an explanation of the color-coded injection phases, see Section 2.1.

Figure 2.
Experimental setup: the injection borehole with the color-coded injection intervals of six hydraulic fracturing (HF) experiments is surrounded by uniaxial acoustic emission (AE) borehole sensors for high-frequency monitoring (beige cones pointing into the direction of the sensor orientation). Two seismometers (green cubes, BB1/BB2) for long-period observations were installed on the floor of adjacent horizontally excavated tunnels (gray). potential plane (inset of Figure S1, Wielandt, 2012). This leads to a horizontal component of the gravitational acceleration, proportional to the sine of the tilt angle, which is measured in addition to a horizontal inertia motion (Rodgers, 1968;Wielandt, 2002). Consequently, the seismometer output is the superposition of two response functions: one denoted as "tilt-induced," leading to a transient signal in velocity, and another one for the "normal" translational motion (Kinoshita, 2008).
The seismometer response to tilt is the response to a step in acceleration that can be instantaneous (i.e., shorter than the corner period of the seismometer, Zahradník & Plešinger, 2005) or a time-dependent, ramp-like step (Kinoshita, 2008), depending on the tilt being transient or permanent. In the presence of translational motion from seismic waves, the tilt signal generally only becomes dominant below the lower corner frequency f c of the seismometer (Wielandt & Forbriger, 1999), when the frequency response to the true acceleration decays (Figure S1). The tilt magnitude can either be estimated by forward modeling the response of the seismometer to a given input signal (e.g., Zahradník & Plešinger, 2005 or be directly read from the tilt signal extracted from the raw waveforms (e.g., Aoyama & Oshima, 2008;Battaglia et al., 2000;Genco & Ripepe, 2010). Both methods are based on the assumptions described above.
We apply the second approach to obtain a tilt time series Θ(t) following Battaglia et al. (2000): with p(t) being the seismometer output corrected for the velocity response of the instrument and g being the acceleration constant. The correction for the instrument response includes a band-pass filter with corner frequencies depending on the experiment and the instrument location. The lower corner frequency of the passband is set to 0.00005 Hz for BB1 and to 0.00075 Hz for BB2, the upper corner frequency is set to 0.05 Hz for both seismometers.
The small amplitude of the tilt-related signals and the presence of spontaneous high-amplitude pulses disturbing the records of BB2 require an increased lower corner frequency. The pulses may be attributed to non-tilt-related The long break is caused by experimental delays, but it shows how the seismometer slowly tilts back. The backflow was only tracked during the beginning of the bleedoff. Noise is stronger during HF1 compared to HF2 due to the smaller amplitudes of the transients.
phenomena, for example, instrumental artifacts (Zahradník & Plešinger, 2010) or spontaneous tilt signals with uncertain cause (Zahradník & Plešinger, 2005) at any given time. Such signals are present in both seismometer records. Examples of spontaneous tilt signals disturbing the records are shown in Figure S2. We refer to those non-injection-related signals as noise signals. They contain high-frequency signals on all three components, which is not observed for the injection-induced tilt signals. As mentioned above, these noise signals could be attributed to electronic spikes or local events induced by the activity within the tunnel (see Figure S3). Apart from spontaneous events, for example, from thermally induced cracking in the floor , hammer hits or dropping gear during the operations might induce small local events (high-frequency content) that trigger movements of grains below the seismometer feet, which in turn induces a tilt signal. Due to the low corner frequency of the used band-pass filters, the noise signals need to be removed by a linear interpolation (see, e.g., Figure S4 after stage HF2-RF1), limiting the contamination of the small-amplitude tilt signals recorded during the injection.
With very small tilt angles (here, in the range of 1e−7 rad) there is no need to distinguish between the tilt angle and its sine. For the Äspö experiments, studied here, there is no superposition of seismic (translational) signals and tilt signals, as reported for earthquakes or in volcanic settings (Kinoshita, 2008;Wielandt & Forbriger, 1999;Zahradník & Plešinger, 2005). The AEs accompanying the fracture growth have dominant frequencies of above 3 kHz, which is well beyond the upper corner frequency of the seismometer ( Figure S1).
Generally, the tilt increases during the injection phase, reduces during the shut-in phase, and falls off more steeply during the bleed-off phase of each stage (Figures 3 and S4-S7). In the latter stage, the negative tilt gradient indicates that the instrument is partly tilting back to its previous level, while the open hydraulic fracture is partly closing. In the lowpass-filtered (0.05 Hz) raw seismogram, the end of the shut-in phase and the partial closing of the fracture is manifested as a signal with flipped polarity (Figure 1). The tilt time series shows a good correlation with the cumulative injected volume. The cumulative volume takes into account the backflow measured after the interval is opened (Zimmermann et al., 2019).
We observe a strong stage-wise correlation between the injection duration and the tilt duration, which we define as the time between the start of the injection and the maximum tilt within the stage ( The tilt magnitude, which is defined as the difference between the tilt at the beginning of the injection and the maximum tilt within each stage (see label in Figure 3a), is correlated with the injected volume ( Figure 4b). A similar correlation is found with the cumulative injected volume. The increasing tilt magnitude can be explained if the intact rock is fractured in the initial fracturing stage, and subsequently the fracture grows gradually and the opening increases due to the increasing amount of injected fluid. While the opening of a fracture requires high pressure, we observe no clear correlation between the tilt magnitude and injection pressure (see maximum and shut-in pressure in Figure S9). However, we observe an increase in tilt during the pressurization of the packer and the integrity test before HF2-F ( Figure 3a) and during the fracturing stage of HF3 ( Figure S5) before the rock fails and a fracture opens. This deformation is attributed to purely elastic deformation due to pressure inside the interval, which does not require the opening of a fracture. Apart from mapping fractures using AEs, we can differentiate pure elastic deformation and fracture growth by considering the formation breakdown pressure and the fracture reopening pressure, respectively, that is, a pressure drop when the fracture opens and grows, which is not expected in pure elastic deformation.
The mean tilt rate, computed by dividing the tilt magnitude by the tilt duration, correlates with the mean flow rate (Figure 4c). We assume that higher flow rates accelerate the fracture growth resulting in a faster tilting of the seismometer, thus a steeper tilt signal and an increased tilt rate. The fluid also fills preopened fractures quicker when the flow rate is increased. This implies an increase in channel width or diffusivity, respectively, as predicted by Dahm et al. (2010) and Weise et al. (1998).
There is no clear tilt signal for the initial fracture stages of the experiments HF1 and HF3, as will be discussed in Section 3. Additionally, long-period noise and gaps in the continuous recordings hinder an unambiguous tilt extraction for the initial fracturing stage of HF6.

Dislocation Modeling of Tilt
During the six injection experiments at Äspö HRL, approximately 20.000 AEs were detected and localized based on the continuous waveform data (Niemz et al., 2020). Based on the analysis of AEs only, Niemz et al. (2020) showed that planar single fractures of several meters length ( Figure 5a) are a good first-order approximation for the tensile fractures induced during most of the HF experiments. Kwiatek et al. (2018) estimated moment magnitudes of −4.2 to −3.5 for the largest 196 events from triggered recordings. This magnitude range comprises picoseismic events with source dimensions in the order of centimeters to decimeters. Kwiatek et al. (2018) also inverted for moment tensors for a subset of the aforementioned AEs and found heterogeneous mechanisms, well described by double couple mechanisms, which indicates that these events have only small tensile components that could be attributed to the opening of the fracture. Additionally, the identified fault plane orientations do not coincide with the orientation of the macrofracture as mapped by the AEs. The different dimensions of the single AEs and the macrofractures, and the deviation in the orientation of fault/fracture planes show that AEs and tilt represent different aspects of the fracturing process. We interpret the AE activity as slip along preexisting joints/ weaknesses within the fracture damage zone. These joints may slip when the opening macrofracture introduces local stress changes at its tip. In this model, AEs map the stress changes in the direct vicinity (damage or process zone) of the opening fracture, not the opening itself.
The linear correlation between the tilt magnitude and the number of AEs in the stage-wise catalog of Niemz et al. (2020) (Figure 4d) provides evidence for the causal connection between the two parameters and the injected volume, respectively. We study this causal connection by modeling the induced tilt based on dislocation sources, representing a tensile fault/fracture as mapped by the AE activity. The forward models were calculated using the approach of Okada (1992) as implemented in the Pyrocko toolbox (Heimann et al., 2017). The length and the width of each rectangular dislocation source were defined based on the cumulative fracture area and the ratio of the two half-axes of the elliptical fracture zones from Niemz et al. (2020). The opening of the tensile dislocation  (Table 1). During experiment HF3, no continuously growing macrofracture was formed, but multiple fractures (Niemz et al., 2020). In this case, we used the stage-wise, noncumulative fracture area.
However, the small number of observations using only two seismometers is not sufficient to resolve all parameters of the extended dislocation source (Lecampion et al., 2005). The small fracture extent of only a few meters poses additional limitations to the analysis. At distances larger than approximately twice the fracture's half-lengtheven less if the fracture is oriented parallel to the alignment of the instruments-tilt measurements cannot resolve the fracture extent and the opening independently (Lecampion et al., 2005). The seismometers are installed more than 17 m away from the mapped fractures, which have half-lengths of less than 6 m. Under this condition, the tilt signal is only sensitive to changes in fracture volume and fracture orientation. Consequently, we limit our analysis to a comparison of the observed tilt, described by magnitude and direction, with the theoretical tilt from forward models based on the fracture properties (Table 1) estimated from the AE activity (Niemz et al., 2020). We describe the tilt by its magnitude and direction. The direction corresponds to the maximum spatial gradient of the vertical displacement obtained as the azimuth from the north and the east component.
To include both seismometers, the lower corner frequency of the band-pass filter in the tilt extraction was set to 0.00075 Hz. The models show a good fit to the observed tilt magnitudes for most refracturing stages (Figure 5c). For the tilt directions indicated by the two seismometers, we find deflections of 30°-40° in opposite directions (Figure 5d).

Discussion
Considering the variety of factors influencing both measurements and modeling, we find a good agreement between the fracture plane approximations based on the AE analysis of Niemz et al. (2020) and the tilt signals reported in this study (discrepancies are discussed in a later paragraph). For experiments HF1 and HF2, the assumption of single planar macrofractures, as inferred by the AE hypocenter analysis, is independently confirmed by the modeling of the tilt signals. In the fracture analysis for HF3, Niemz et al. (2020) found that the orientation of fitted planes changes substantially during the refracturing stages, as expected from the more compact, cloud-like AE distribution. Hence, the fracture geometry was assumed to be more complicated than a single macrofracture. The tilt observations provide additional evidence for this finding. The tilt direction rotates during the injections of HF3, even when considering the single stages separately (see Figure S10). This indicates that the fracture geometry is complex. It possibly formed a network of fractures with varying orientations developing farther away from the borehole wall. At the borehole wall, only two fractures were mapped after experiment HF3 in the previously intact interval using an impression packer test, in which a rubber sleeve is pressed against the borehole wall and cracks are imprinted (Zang et al., 2017).
The tilt signals provide an independent confirmation of the fracture orientation and the first-order geometry of the fracture as inferred from the AE activity (Niemz et al., 2020). It also shows that for this particular experimental setup, AEs are able to map the full extent of the opening macrofractures. As an additional test, we modeled the tilt signals using the stage-wise, not the cumulative injected volumes. In this case, the offset between modeled and observed tilt magnitudes (as shown in Figure 5c) becomes even larger. This shows that the fluid remaining inside the fractured rock volume plays an important role in the following stages. Furthermore, the theoretical modeling for the initial fracturing stages of HF1 and HF3 with less than 1 L of injected fluid explains the lack of a tilt signal in these stages. The theoretical tilt signal is too small to emerge out of the noise of the recorded traces.
The difference in the fracturing processes of HF2 and HF3 is documented in Figure 6. For the conventional, continuous experiment HF2, we observe that the increase of the tilt signal is largest at the beginning and then reduces during the injection (Figures 6a and 6c). This is even more evident by directly plotting the tilt rate, here the time derivative of the tilt signal (Figure 6c). The increased tilt rate at the beginning of the refracturing stages (Figure 6c, RF4 and RF5) can be explained by a quicker flow of the fluid into the previously opened fracture. After the reopening, the further growth is represented by a reduced rate of tilting. During the initial fracturing stage HF2-F, when a new hydraulic fracture is opening, the tilt rate is stable during the injection (Figure 6c).
The quick rise of the tilt rate at the beginning of refracturing stages is followed by a delayed increase of the AE rate. The temporal offset between the maximum tilt rate and the maximum AE rate is largest for the refracturing Note. Only stages with clear tilt signals and fracture plane estimates in Niemz et al. (2020) are considered for the tilt modeling at stations BB1 and BB2 (modeling marked by "m" in the last columns). The experiment-wise cumulative volume was corrected for the back flow which was measured manually (Zimmermann et al., 2019).

Table 1
The Input Parameters for the Forward Models of the Rectangular Dislocation Sources stages RF4 and RF5 (Figure 6c). This observation can be attributed to the Kaiser effect. In this context, it implies that significant AE activity is only induced after the previously opened hydraulic fracture is reinflated and the fracture continues to grow at the fracture tip.
For experiment HF3, the tilt rate and the AE rate increase simultaneously (Figure 6d), which indicates that the fracture/fractured volume did not experience excessive loading before, thus in each stage a new fracture or a new part of the fracture network is opened or activated. This is contrary to the reopening of the single macrofractures in experiments HF1 and HF2.
By studying the relation between the maximum AE rate and the mean tilt rate (Figure 4e), we identify several stages that deviate from an assumed linear relation: HF2-RF2 and the refracturing stages of HF6. We exclude HF6 at this point, because the tilt magnitudes are not corrected for the varying distances between injection interval and seismometer. The increased tilt magnitudes and mean tilt rates in this experiment (Figures 4b-4d) are attributed to its location close to the tunnel system (see Figure 2). For HF2-RF2, the mean tilt rate is considerably large, but due to technical reasons the continuous AE recording was only active during the last quarter of the interrupted injection, with only three AEs induced in this period. Despite the lack of data for the first part of the injection, we can assume that the maximum AE rate was not reached before. This assumption is based on the observation that in the other refracturing stages of HF2, the AE rate reaches its maximum during the last quarter of the injection. The absence of increased AE activity in the case of HF2-RF2 can be explained as follows: the previously opened fracture was only (partially) reinflated, without substantial AE activity (Kaiser effect), but could not grow farther, due to the small injected volume and the interruption of the injection, respectively.
Several limitations arising from the experimental setup hinder the forward modeling of the tilt signals of HF4-HF6. The timing between the injection time series of HF4-HF6 and the seismograms is not precisely known. Furthermore, the test interval of HF6 is located at a distance of only 4.8 m to the tunnel wall, which may bias the Figure 6. For the experiment HF2, the tilt (a) and more specifically the tilt rate (c) show distinct differences between the initial fracturing stage (F) and later refracturing stages (RF4, RF5). During HF2-F, the tilt rate is stable during the injection, while for RF4 and RF5, it is largest at the beginning of the injection and decreases afterward indicating that the fracture is reopened first and then continues to grow. The further growth is accompanied by an increase in AE activity (filled curves in the background, common scale at the right) as observed after the maximum tilt rate. Aftergrowth, a further growth of the fracture after the stop of the injection is observed for the refracturing stages showing considerable AE activity and a kink in the tilt signal. (b) For experiment HF3, we observe no/less activity after the shutin, thus no aftergrowth. During the experiment HF3, the AE rates temporally coincide with the tilt rates (d), which points to the formation of new fractures. The initial fracturing stage of HF3 is not shown because we do not observe a tilt signal due to the small amount of injected water (see Table 1).
tilt signal. The conventional experiment HF4 did only induce few AEs above the detection threshold. Therefore, the planar fracture approximation has a large uncertainty (Niemz et al., 2020). The forward modeling failed to reproduce the observed signal, indicating that the number of AEs is insufficient to reliably map the fracture. The tilt signal of the initial fracturing stage of HF4 strongly deviates from the close correlation between tilt and injection duration (Figures 4a and S6), while the tilt magnitude and the mean tilt rate are in correspondence with the general correlations (Figures 4b and 4c). The tilt signal is much longer than anticipated from the linear relation to the injection duration (Figure 4a), suggesting that the fracture initiation in this experiment is different compared to HF1-HF3 and HF6. While the detected AE activity is too sparse to map stage-wise hydraulic fracture planes (Niemz et al., 2020) or a possibly reactivated fault, the period of increased AE rate coincides well with the tilt duration for HF4-F and HF4-RF1 ( Figure S6b). In contrast to the other experiments where the increase in tilt, and therefore the fracture growth, is driven by the increasing amount of water injected into the rock, the tilt signal during HF4-F appears to be decoupled from the supply of fluid. The cause for this peculiar observation remains unclear since we have no detailed knowledge about the fault and fracture geometry farther away from the borehole.
During HF5 (pulse hydraulic fracturing with a secondary pumping system, see Zang et al., 2017), no AEs were detected. This could be attributed to the detection threshold (Niemz et al., 2020), to less favorable transmission properties of the rock type stimulated during HF4 and HF5 compared to the rock type stimulated in HF1 to HF3 (Zang et al., 2017), or to aseismic processes. In contrast to HF4, which is still showing small tilt signals (Figure S6), there was no injection-induced tilt signal recorded on BB1 during experiment HF5 ( Figure S8). While aseismic fracture growth could be hypothesized when considering the lack of AEs, the missing of an injection-induced tilt signal shows that no hydraulic macrofracture was generated. This is important for the interpretation of induced seismicity and could only be found from the joint interpretation of the tilt signal and the AE activity. The high-frequency injection pulses of the secondary pump used during HF5 may have hindered the growth of a hydraulic fracture.
The models (see example for HF2-RF5 in Figure 5b) provide a good fit for the refracturing stages (darker tones in Figure 5c), only slightly underestimating the tilt magnitude for both broadband sensors. Increased model deviations are observed for the initial fracturing stages (light tones in Figure 5c), in which smaller injected volumes result in less induced AEs. The plane fitting approach applied by Niemz et al. (2020) may in these cases result in larger uncertainties and overestimated fracture extents. With a fixed injected volume, the estimated opening and, consequently, the tilt magnitude would be underestimated in the models. The modeled tilt direction of each stage shows a constant deflection of approximately 40° compared to the observed tilt direction for BB1 (Figure 5d). The model results for sensor BB2 show a varying deflection of opposite sign. As predicted by the model, the far-field sensor BB2 cannot resolve the rotation of the fracture planes within each experiment (see also Table 1). Scatter in the observed tilt directions is caused by a reduced signal-to-noise ratio (SNR) on instrument BB2, introducing larger uncertainties in tilt direction and magnitude (see an example of a tilt trace from BB2 in Figure S4). In this case, the seismometers even come close to the resolution limit of a fraction of nrad of common tiltmeters (e.g., Gebauer et al., 2009).
Deviations between observed and modeled tilt magnitudes and tilt directions may result from the simplified homogeneous model without taking into account the tunnel geometry, local heterogeneities in the elastic properties of the surrounding rock, and nearby fault zones. Wielandt and Forbriger (1999) and Rohde et al. (2017) report considerable differences in tilt magnitude and tilt direction (up to 25°) even between collocated instruments in the same vault/location. Wielandt and Forbriger (1999) attributed this deflection to strain-tilt coupling influenced by an interaction of vault walls, filling, and the seismometer. Such cavity effects (Forbriger, 2012;Gebauer et al., 2009;Harrison, 1976a) are expected to be more important close to the tunnel wall, where the two seismometers were located (see Figure S3). Additionally, local inhomogeneities in rock types reflected by different elastic constants (e.g., Young's modulus [E] or Poisson ratio [ν]) can introduce very local strain-induced tilt signals (Gebauer et al., 2009;Harrison, 1976b) that could explain differences in closely located tiltmeter records. Geologically, the Äspö HRL is situated in Äspö diorite cut by granitic and pegmatitic dykes (SKB, 2013). However, the variety in E and ν between samples of the same rock type is larger than the variety between rock types. The different rock types have mean Poisson ratios of 0.23-0.24 and mean E modulus between 73 and 78 GPa (Stille & Olsson, 1996). Consequently, we do not expect a significant influence of the lithology onto the tilt signal, but very local effects cannot be ruled out. Besides the rock type itself, fracture zones and faults can influence the deformation/tilt pattern in magnitude and direction (Jentzsch & Koβ, 1997). There are several faults and hydraulically conductive zones between the two seismometers and also partly between the seismometers and the injection intervals (dashed lines in Figure 5b) that could deflect the tilt direction. Quantifying the biases is beyond the scope of this study, if it is feasible at all, due to a lack of information about rock parameters and detailed knowledge about the fault zone geometry. Estimating a first-order influence of the complex tunnel system onto the tilt signals would require a 3D-modeling of stress changes based on discrete elements (DEM) or finite elements (FEM).
The dip angle, and especially the fracture volume, which relates to the fracture opening, has a major influence on the modeled tilt magnitude, while the orientation of the tilt signal is mostly influenced by the strike of the modeled fracture (Lecampion et al., 2005). The steep decay of the tilt signal in the bleed-off phase is directly caused by the outflow of the injected fluid which reduces the fracture volume (see negative flow in Figure 3).
Additionally, we observe a moderate decay of the tilt signal in the shut-in phase (∼10%). This can be explained by the diffusion of fluids under high pressure into the rock, which is also causing a volume loss. However, the diffusivity of granitic rock is rather low and, therefore, we assume that other processes contribute to this decay. We assessed the sensitivity of the fracture parameters which are not resolved due to the limitation arising from the relatively small fracture extents compared to the sensor distances (e.g., area or length/width ratio) by calculating the theoretical tilt for a set of seismometers located at a distance of less than one half-length away from each mapped fracture (here 2 m for all experiments). To test the influence of each parameter, we forward model the induced tilt for a range of values around the parameters given in Table 1. In the azimuthal direction of the seismometer BB1, we find that the decay of the tilt signal after the end of the injection can be explained by aftergrowth, the growth of the fracture (increase of the fracture area) after stopping the injection (see also Dahm et al., 2010). A dominance of either diffusion or aftergrowth cannot be resolved by using the limited tilt data from the seismometers, but the hypothesis of aftergrowth is supported when considering the AE activity. AEs are predominately induced not only during the injection phases but also during the shut-in phases (Niemz et al., 2020). For HF1 and HF2, the tilt rate drops quickly and becomes negative (backward tilting) at the beginning of the shut-in phase, while the AE rate is decaying more slowly (Figure 6c). In this phase, AEs occur predominately at the outermost part of the macrofracture (Niemz et al., 2020), implying a dominance of aftergrowth instead of diffusion processes that would be expected to occur all along the macrofracture. In general, diffusion cannot be ruled out, but the low porosity of the stimulated granitic rocks of 0.2%-0.4% (Johansson et al., 1998) is supposed to inhibit a dominance of this process.
For the progressive injection experiment HF3, the tilt rate and the AE rate decay simultaneously (Figure 6d), which indicates a lack or a reduction of aftergrowth. This is favorable because the reduction of post shut-in growth can lead to a safer stimulation aiming for the mitigation of seismic hazard , since many important injection-induced events, such as in Basel or Pohang (Grigoli et al., 2018;Häring et al., 2008), occurred after the borehole was shut-in.
The insights obtained from the tilt signals presented in this study stress the advantage of considering low-frequency signals in addition to high-frequency AEs in HF monitoring. The in-depth analysis relying on a unique combination of tilt signals from broadband seismometers and AE activity provides independent constraints on fracture parameters, that can help to understand differences between injection schemes and the energy partition during HF in crystalline rock . For future in situ experiments, we think this broad monitoring setup should be extended by precise measurements of the backflow and by the installation of tiltmeters. While the resolution of the tilt measurements is expected to be similar (in the range of nrad), this would avoid dealing with the manifold of tilt-like disturbances in broadband recordings (Zahradník & Plešinger, 2010). The combination of tiltmeters and broadband seismometers in a controlled environment may also serve as a calibration experiment which could help the interpretation of tilt observations on broadband sensors during volcanic intrusions. The analysis presented here using broadband seismometer-derived tilt signals can be applied to tiltmeter records directly. When aiming for an inversion for additional fracture parameters (e.g., fracture extent), the installation of borehole tiltmeters or fiber optic strainmeters very close to the fracture or within the well behind the packers could overcome the resolution limitations arising from using only two seismometers and contribute to a better understanding of the fracture growth in future in situ experiments.

Conclusion
During a mine-scale injection experiment in crystalline rock at Äspö HRL at a depth of 410 m, we were able to record tilt-induced transients on broadband seismometers installed close to the injection intervals. Correlations of the tilt magnitude and the tilt duration with the injected volume and the injection duration, respectively, indicate that these tilt signals are directly caused by the (re)opening, the growth, and the closing of meter-scale hydraulic fractures. The complementary monitoring setup of AE sensors and broadband seismometers close to the hydraulic fractures provided the unique opportunity to jointly analyze AEs, which are the high-frequency, indirect response of the rock around the opening fracture, and tilt signals, the low-frequency, direct response to the deformation of the entire rock volume due to the fracture formation. Hence, the two observations depict different aspects of the fracturing process. We link these observations by modeling the theoretical deformation, thus the tilt at the position of the seismometers, caused by an opening fracture based on the fracture extent obtained in a previous study of the AE activity. The theoretical dislocation models with pure tensile opening provide similar tilt magnitudes as the observed ones, but the complex tunnel geometry and other influences deflect the observed tilt direction. The models do not only provide evidence for the interpretation of the tilt signal to be induced by the opening and closing of hydraulic fractures, but also show that the AE activity successfully mapped the fracture extent in most experiments. The models and the observations further depict a clear difference between the opening of single macrofractures in the experiments HF1 and HF2 and a complex fracture network in experiment HF3. The tilt signal shows that in one experiment no efficient macrofracture was created, as indicated, but not proven, by a lack of AE activity. The joint analysis presented in this study has implications going beyond the particular experiments. We show that the combination of AE and tilt signals can potentially differentiate between newly opened and reinflated macrofractures. The latter are influenced by the Kaiser effect, which is revealed by a delay in AE activity compared to the tilt signal which is increasing directly when the injection starts. For the macrofractures, we found evidence for aftergrowth reflected in AE activity while the tilt signal is slowly decaying. The identification and the study of aftergrowth processes is particularly important for the mitigation of induced seismicity, since many case of induced seismic events occurred after the stop of the injection. For future in situ experiments, we propose the installation of additional borehole tiltmeters to take full advantage of the joint interpretation of AE/microseismic activity and independent tilt measurements, eventually aiming for an inversion for fracture properties.