Reply to comment by Vallée et al. on “Earthquake-induced prompt gravity signals identified in dense array data in Japan”

<jats:title>Abstract</jats:title><jats:p>Density perturbations accompanying seismic waves are expected to generate prompt gravity perturbations preceding the arrival of P-waves. Vallée et al. (Science 358:1164–1168, 2017, https://doi.org/10.1126/science.aao0746) reported the detection of such pre-P-wave signals in broadband seismograms during the 2011 Tohoku-oki earthquake. Kimura et al. (Earth Planets Space 71:27, 2019, https://doi.org/10.1186/s40623-019-1006-x) considered that their detection involved some uncertain points, including a concern regarding their signal processing procedure. Specifically, to remove the instrumental response, Vallée et al. (2017) applied acausal deconvolution to the seismograms truncated at the P-wave arrivals. Generally, acausal deconvolution produces artifacts at the edge of the time window. However, they did not present quantitative assessment whether the detected signals were artifacts due to the signal processing. To avoid this concern, Kimura et al. (2019) employed another procedure that eliminated acausal processes, resulting in the detection of a pre-P-wave signal with a statistical significance of 7σ in stacked broadband seismograms. Subsequently, Vallée et al. (Earth Planets Space 71:51, 2019, https://doi.org/10.1186/s40623-019-1030-x) commented that the procedure employed by Kimura et al. (2019) for the signal detection was inappropriate because it dismissed the low-frequency components of data. Although we admit the loss of low-frequency components in the data in Kimura et al. (2019), Vallée et al. (2019) have not yet provided a full account of the validity of their own procedure. Here, we assessed the validity of the procedure employed by Vallée et al. (2017) by quantitatively evaluating the magnitude of the acausal artifacts. First, we investigated how the input acceleration waveform, having an ideal signal-like shape, was distorted by their procedure. Their acausal deconvolution indeed generated a large-amplitude terminal artifact; however, it was removed by the causal band-pass filtering performed after the deconvolution and consequently became negligible. Next, we constrained the maximum amplitude of the artifact due to the noise in a seismogram and showed that it was sufficiently small compared to the reported signal amplitudes. These results suggest that the signal waveforms seen after their procedure were not artifacts but were representing the input acceleration with sufficient accuracy. Namely, their procedure well functions as a detection method for pre-P-wave signals. In the context of this validation, we replied to the comments of Vallée et al. (2019). </jats:p>