Reply to Comment by Wei and Shen on “Seismic Velocity Variations at Different Depths Reveal the Dynamic Evolution Associated With the 2018 Kilauea Eruption”

We would like to thank Wei and Shen (2023, https://doi.org/10.1029/2022GL102596) (W23) for their comments on our recent article on GRL. In their comments, Wei and Shen argued that tremor signal on the right side of the cross‐correlation function (CCF) of PAUD‐STCD is from Kilauea crater, and they suggested that the observed time‐delay after eruption might be attributed to the noise source change and other factors. After checking the data and the code carefully, we recognize that signal on the right side of CCF of PAUD‐STCD may be due to seismicity from the Kilauea crater. However, we demonstrate here that it does not affect our conclusions.

For the point 1, if the changes are due to source location changes, which may result in permanent time offset on the CCFs of all station pairs.The rapid recovery after the eruption of the station pairs SDH-MITD and MITD-DESD (Figure 1b) is contrary to this assumption, otherwise, all stations pairs should observe the same velocity change pattern.In addition, if the source was moving in east-west direction, the polarity of velocity change might be opposite between the three station pairs on the left side of Kilauea crater (SDH-MITD, SDH-DESD, MITD-DESD) and the three station pairs on the right side.In another word, positive and negative velocity changes may be observed for station pairs on different sides of the crater.
For the point 2, the co-eruption velocity changes between the summit and STCD (SDH-STCD) is about −3%, which is only about half of the magnitude of the change along PAUD-STCD (−6%).
For the point 3, the co-eruption velocity change of SDH-PAUD is about −2%, which is contrary to the velocity increase as stated in this assumption.For their point 4, the combination of the factor 2 and 3 would not cause an obvious velocity change of −6% as shown in Figure 1.Even if we assume that the −2% changes of all other station pairs are due to source change, there is still −4% change that should be attributed to the medium change along the station pair PAUD-STCD.
In fact, their explanation for the recovered Empirical Green's functions (EGFs) of the PAUD-STCD is only based on direct wave theory.The contribution of the scattered waves in the noise filed is actually dominant for long time cross-correlation.Due to the using of one-bit method and the stacking of long time noise data, the influence of direct waves with large amplitude is minimized.And only the signals passing through the PAUD-STCD station pair are causal, and the non-causal signals will offset each other due to the existence of phase difference.For example, previous study suggested that the coda section of the large earthquake can be used to recover the EGF (Campillo & Paul, 2003).
Although the signal (<3 s) of the negative side of the CCF in PAUD-STCD is not as strong and stable as the signal on the positive side (Figure 2 in Liu et al., 2022), but there still exists a signal in period of 1.5 s (black box in Figure 2a), which is not related to the tremor source of the Kilauea crater.Figure 2c displays the velocity change of the negative side of the PAUD-STCD in 1.5 s period.Before eruption, we found similar velocity decrease of 1% as the measured result in positive side of CCF in the same period (Figure 4 in Liu et al., 2022).We also found that the eruption caused a 4% drop in velocity on negative values of CCF, indicating a change in the properties of the medium.
In addition, not only the location of the noise source but also the frequency of noise may affect the velocity change measurements with CCF (e.g., Zhan et al., 2013).The CCFs show clear changes after the eruption (Figures 2a-2f and S2 in Liu et al., 2022), which is likely caused by the source change.The source change might affect different station pairs similarly.To address this question, we compared the CCFs change before and after the Kilauea volcano eruption.Zhan et al. (2013) showed that the frequency variation can cause CCF changes, while the frequency change causes no time delay for the peak value for the surface wave and the waveform is characterized by contraction or expansion around the peak value.But Xu and Song (2009) showed that if velocity decreases, an obvious time delay on the whole surface wave section can be observed and the absolute delay value increases with time.Figure 3 displays surface wave (PAUD-STCD and SDH-PAUD) in period of 2 s before and after eruption, which is in line with Xu and Song's (2009) results.Therefore we can conclude that our result is consistent with a velocity change rather than frequency change.

Conclusion
We conclude that the co-eruption velocity change of PAUD-STCD is mainly due to the medium change between the two stations.To summarize, we agree with them on that the source of the signal on the right side of CCF of PAUD-STCD may be related to seismicity of Kilauea crater, but it does not affect our final conclusion.

Figure 1 .
Figure 1.Velocity changes measured by different station pairs in period of 2 s.(a) Geometry of Station pairs.Red star indicates the tremor source of the Kilauea crater (Soubestre et al., 2021).Black triangles represent location of tremor source of the Kilauea and seismic stations, respectively.Green star indicates M6.9 earthquake occurred on 4 May.Orange circles are small earthquakes.Red curve represents magma dike between Kilauea and ERZ.(b) Time series of velocity changes of SDH-DESD (Blue), SDH-MITD (Red), and MITD-DESD (Brown).(c) Time series of velocity changes of SDH-PAUD (Black), SDH-STCD (Green), and PAUD-STCD (Purple).The corresponding station pairs are shown as straight lines with the same color.

Figure 2 .
Figure 2. Velocity change of the negative side of the CCF of PAUD-STCD in period of 1.5 s.(a) Spectra analysis of the negative side of the CCF of PAUD-STCD.(b) Reference of the CCF of PAUD-STCD in the negative side filtered by 1.5 s period, the signal in the blue box will be used to obtain velocity change.(c) Blue and orange curve indicate the velocity change and corresponding correlation coefficients.

Figure 3 .
Figure 3. Surface wave changes of PADU-STCD and SDH-PAUD in period of 2 s.Black and blue-gray traces indicated CCF before and after the volcano eruption.