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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). [ABSTRACT FROM AUTHOR]

Seismic waves radiated from an earthquake induce mass redistribution in the Earth, which in turn generates prompt gravity perturbations at all distances before the arrival of seismic waves. Here, we obtain an analytic solution for the transient elastic response to prompt gravity perturbations induced by a portion of earthquake mass redistribution in an infinite homogeneous isotropic non-self-gravitation elastic medium. This solution reveals the fundamental nature of an unusual net-inner-force-free deformation regime that emerges between the onset of an earthquake and P -wave arrival, which we find inherent in action at a distance with the inverse-square law. These results provide physical insights into why a gravimeter installed in the Earth is characterized by significantly decreased sensitivity to earthquake-induced prompt gravity perturbations. [ABSTRACT FROM AUTHOR]

Abstract: The relative state transition of spacecraft formation flying is considered in this paper. In eccentric orbits, the Tschauner–Hempel (TH) equations are used to express the relative motion between a deputy spacecraft and a chief spacecraft. Perturbation forces are not considered in the TH equations, and the relative distance between two spacecraft is limited to a short range. In this paper, the effects of the J 2 perturbation forces are considered, and the case of relatively long distance between two spacecraft is focused. A state transition matrix applicable to such cases is derived. The state transition matrix is expressed by adding some compensating terms to the state transition matrix of the TH equations. The usefulness of the proposed state transition matrix relative to the state transition matrix of the TH equations is shown through numerical simulations from the viewpoint of position error. [Copyright &y& Elsevier]

A state transition matrix for formation flying in eccentric orbits is considered in this paper. The relative motion of the formation flying obeys the Tschauner-Hempel equations, which are extended for the presence of a J2 perturbation. Furthermore, the state transition matrix of the Tschauner-Hempel equations is extended for J2, and it is demonstrated that the extended state transition matrix becomes the solution of the extended Tschauner-Hempel equations. Because the extended state transition matrix only uses osculating orbital elements in the initial state and does not use mean orbital elements, an analytical treatment of the state transition matrix is possible. When the state transition matrix uses only the first-order term of J2, the errors sometimes become large compared with the relative distance multiplied byJ2 in a time range that is longer than one orbit period. A method to suppress errors numerically is also proposed. [ABSTRACT FROM AUTHOR]