- Open Access
Comment on “Earthquake-induced prompt gravity signals identified in dense array data in Japan” by Kimura et al.
© The Author(s) 2019
- Received: 3 April 2019
- Accepted: 20 April 2019
- Published: 29 April 2019
- Prompt elastogravity signals
- Tohoku earthquake
- Instrument response
- Noise levels
The reasons why K19 failed to confirm the observations by V17 are trivial (“Biased observational analysis made by K19” section). We show that the data processing used by K19 involves an incomplete correction for instrument response that de-emphasizes the low-frequency components of the data. However, PEGS are intrinsically low-frequency signals. The very clear signals shown by V17 are weaker or even unobservable in the analysis of K19 because the latter did not consider a suitable frequency band. In this section, we will also demonstrate the robustness of the V17 data processing.
In addition to their inappropriate data processing, K19 do not take into account station quality and erroneously discard high-quality signals on the basis of noisy signals from neighboring stations. If K19 had used appropriate data processing and quality control criteria, their study would have simply confirmed the V17 observations.
The claims of originality by K19 are invalid because they are based on inappropriate data processing. Failing to detect PEGS on data from individual stations (with incorrect processing), K19 showed that PEGS are detected after stacking data from multiple stations. But by doing so, the detection significance of their stack remains lower than even only one of the individual signals shown in V17. Based on this stacking of incorrectly processed data, K19 incorrectly claimed their result provides the first reliable PEGS observation.
Inappropriate data processing also misled K19 into questioning the PEGS modeling made in V17. The argument put forward by K19 is that the amplitude of their stack (of incorrectly processed data) is smaller than the signals observed and modeled by V17. We will show (in the “Erroneous conclusions about PEGS amplitudes” section) that stacking the same data as K19, but after instrument response correction following V17’s procedure, results in a signal stack with the same amplitude as predicted by V17’s model and with a much higher significance than K19’s sub-optimal stack.
Inappropriate data processing with incomplete instrument response correction
K19 used the following data preprocessing steps: (1) Raw data were divided by the sensitivity coefficient of the broadband seismometers, which is defined as the velocity-to-counts conversion factor in the frequency band where the instrument response is flat, and (2) the result was converted into acceleration by differentiation. The frequency-independent conversion factor applied in step 1 is adequate for signals whose frequencies of interest are between a few 0.01 Hz to ~ 10 Hz, but is insufficient for PEGS observation. As shown in the theoretical study of Harms et al. (2015), the accelerations in PEGS are related to the second time integral of the seismic moment function, and thus their spectrum behaves as 1/f3 at frequencies f lower than the earthquake corner frequency. PEGS are therefore low-frequency signals, and the potential to observe them with seismometers is maximized when the lowest reliable frequencies are fully used. That is why V17 deconvolved the raw data by the instrument response and carefully used a causal high-pass filter at 0.002 Hz to mitigate the instrumental noise at even lower frequencies.
It is therefore obvious that the K19 processing lowers the PEGS detection potential, but it is much less clear why they used such an observational strategy. K19 justify their processing strategy as a way to avoid the non-causality of the instrument response deconvolution. Such a non-causality effect indeed exists, but is a problem only if the deconvolution is applied to a time series containing an undesirable subsequent signal. That is why it is crucial to cut the signals at the P-wave arrival, as done in the V17 procedure, to avoid any contamination. Once this operation is done, it is difficult to imagine how a signal removed from the analysis (i.e., the P direct wave) could still have an adverse role. As K19 possibly worried about an influence of the limits of the original time windows, we show in Fig. 2 that their arbitrary choice does not have any role on the obtained accelerations: As long as a sufficiently long pre-origin time signal is used and the P-wave is not included, the V17 procedure gives the same acceleration signals in the 0.002–0.03 Hz frequency range regardless of the choice of time window. We also recall that V17 provided in their Supplementary Material (Additional data) their exact data processing procedure (using Seismic Analysis Code—SAC), so that every reader can assess its robustness.
Mixing high-quality with low-quality sensors
PEGS are not equally well recorded by all sensors, because of their intrinsic characteristics combined with differences in site quality. However, K19 used in their Figs. 2 and 3 all the existing broadband sensors in a given area, regardless of their quality, as an argument to discard the direct PEGS observations. They made the same error when they directly compared the signals recorded by the Matsushiro gravimeter and by the collocated MAJO seismometer, without acknowledging that the pre-event seismic noise at MAJO is much lower (see V17). Their Figure 3a, b is also particularly misleading because signals are not shown with the same vertical scale. Finally, in Fig. 3a of K19, despite the deficient data processing, a signal is still visible at the excellent STS1 sensor of station MDJ. K19 reject this evidence by judging it is inconsistent with data at neighboring stations. However, the difference is simply explained by the much lower noise at MDJ.
In contrast, the V17 study considered all the signals that satisfy an objective quality control criterion: their amplitude in the 1800 s preceding the earthquake had to be below a given amplitude threshold. This threshold was set at ± 0.8 nm/s2 so that a signal with an amplitude of − 1 nm/s2 occurring just before the P arrival time is unlikely to be random noise. All the sensors shown in Fig. 3 of K19, except for the NE93 and MDJ sensors used by V17, have pre-event noise amplitude levels of more than ± 2 nm/s2, and often much more. Such noisy data were not shown in the V17 study, and they are of little use to invalidate PEGS observations.
At this stage, it is interesting to mention a specific point about the MDJ station. If K19 had used the V17 data processing, they would have obtained the clear MDJ signals that can be seen in Figs. 1, 2, and 3 of V17. When quantified by the signal-to-noise ratio (SNR) criterion that K19 used to evaluate the stack significance (i.e., the ratio between the amplitude at the P arrival time and the standard deviation σ of the seismic noise), the SNR reaches ~ 9 at station MDJ. When properly processed, this unique sensor has a better SNR than the stack of 27 stations considered by K19, whose SNR is only 7. The V17 study did not require any stacking because it was based on signals that could be directly observed at several stations (and confirmed by signal modeling).
Objective comparisons confirm V17 observations
Based on the aforementioned considerations, Figs. 2 and 3 of K19 do not bring any valid argument to question the observations made by V17. On the contrary, the sensors in Southwest Japan used in Fig. 2 of K19 confirm the V17 observations. Some of these sensors, in addition to FUK also used in V17, indeed meet the pre-event noise quality criterion required by V17. This is expected because V17 explicitly mentioned that, to avoid redundant signals at similar locations, not all the high-quality F-net sensors were used in their analysis.
In practice, after application of the V17 data processing, four stations (FUK, SBR, IZH, and INN) have pre-event noise whose absolute values remain below 0.8 nm/s2, and therefore offer an unbiased opportunity to validate the FUK observations shown in V17. Not surprisingly, these four signals, shown in Fig. 3, strongly support the FUK observations: They all exhibit a clear downward trend after the earthquake origin time (with an optimal SNR at the STS1 sensors FUK and SBR), with consistent amplitudes reaching values of ~ − 1 nm/s2 at the P arrival time.
The K19 study does not provide any valid modeling of the expected PEGS amplitudes. Although, based on the works of Heaton (2017) and V17, K19 correctly described that PEGS originate from two effects, a direct gravity perturbation and an induced ground acceleration, they only modeled the first effect. In their Fig. 1, K19 only show the direct gravity term, in the very crude approximation of an infinite space. The values shown in their Fig. 1 differ by a factor of ~ 100 compared to the amplitudes of their stack (their Fig. 7a), but K19 did not comment on why it is so.
Despite being unable to model their own observations, K19 try to discard the modeling made by V17. While K19 correctly noted that the signals simulated by V17 were on the order of − 1 nm/s2, they compared these amplitudes obtained in the 0.002–0.03 Hz frequency band with their observed stack amplitude (− 0.25 nm/s2), which suffers from strong deficit in this frequency band (Fig. 1 and previous sections). K19 therefore appear unaware that meaningful comparisons between two signals can only be done if they have been processed in the same way.
Contrary to the opinion expressed by K19, there is no urgent need to improve the V17 modeling approach and to develop a “better theoretical model […] that addresses the fully coupled equations between the elastic deformation and gravity”. The adequacy of the V17 and Juhel et al. (2019) approaches is not only supported by their agreement with the observations, but V17 showed that the error made by neglecting the full coupling (i.e., by neglecting that gravity-induced motion itself creates a gravity perturbation, and so on) is only a few percent. Additionally, Juhel et al. (2019) numerically modeled the direct gravity perturbation with and without self-gravitation and found only minor differences in the 0.002–0.03 Hz frequency band of interest. Solving the fully coupled equations is therefore a numerical challenge that would offer a more elegant solution, but is not a prerequisite to model the PEGS observations.
K19’s study illustrates the difficulties to observe a small-amplitude signal when using non-optimal data processing or non-optimal sensors. This trivial finding does not provide any valid argument to challenge previous observations made by V17 using a better processing applied to objectively selected data. K19’s claims to discard previous PEGS modeling is based on an obviously biased use of their observations. In light of these two major errors, their claims of pioneering findings are invalid.
The K19 study provides only a modest contribution to the recent PEGS observations made by other groups, in particular, by the V17 study. Recent progress in the research on PEGS has yielded new advances that go far beyond the K19 study. Readers interested in how PEGS can be optimally observed may refer to the more sophisticated stacking approaches described by Montagner et al. (2016) and Vallée and Juhel (2019). Vallée and Juhel (2019) also show how multiple PEGS observations made for earthquakes of different focal mechanisms and depths are accurately modeled by the methods described by V17 and Juhel et al. (2019). Therefore, the remaining challenges today are no longer to show that PEGS are well understood, modeled, and observed for magnitudes larger than 8, but to lower this magnitude threshold and to reduce the detection delay, in order to make PEGS even more valuable for early warning systems.
MV designed this comment, with inputs from KJ and JPA. MV performed the data analysis, produced the associated figures and wrote the text with JPA. KJ, JPM, MB, and PB commented the initial versions of the manuscript. All authors read and approved the final manuscript.
The SAC (http://ds.iris.edu/ds/nodes/dmc/software/downloads/sac/) free software was used for data processing. Most numerical computations were performed on the S-CAPAD platform, Paris, France.
The authors declare no competing interests.
Availability of data and materials
Data from the F-net network are publicly available at the NIED F-net server: http://www.fnet.bosai.go.jp. MAJO station belongs to the GSN network (https://doi.org/10.7914/SN/IU), MDJ station to the NCDSN network (https://doi.org/10.7914/SN/IC), and NE93 to the NECESS/UT network (https://doi.org/10.7914/SN/YP_2009). Data from the GSN, NCDSN and NECESS/UT networks are publicly available at the IRIS data management center (http://ds.iris.edu/ds/nodes/dmc/).
Consent for publication
Ethics approval and consent to participate
We acknowledge the financial support from the UnivEarthS Labex program at Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02) and from the Agence Nationale de la Recherche (Grant ANR-14-CE03-0014-01).
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