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The use of strongly biased data generally leads to large distortions in a trained machine learning model. We face this problem when constructing a predictor for earthquake-generated ground-motion intensity with machine learning. The machine learning predictor constructed in this study has an underestimation problem for strong motions, although the data fit on relatively weak ground motions is good. This underestimation problem is caused by the strong bias in available ground-motion records; there are few records of strong motions in the dataset. Therefore, we propose a hybrid approach of machine learning and conventional ground-motion prediction equation. This study demonstrates that this hybrid approach machine learning technology and physical model reduces the underestimation of strong motions and leads to better prediction than either of the individual approaches applied alone. [ABSTRACT FROM AUTHOR]

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]

We analyzed strong-motion and broadband recordings of two moderate-magnitude earthquakes that occurred in the Nankai Trough. The first event was the 2004 Mw 6.5 southeast off-Kii peninsula earthquake, an aftershock event inside the Philippine Sea Plate near the Nankai Trough axis. The second event was the 2016 Mw 5.8 southeast off-Mie Prefecture earthquake, an independent event in the rupture area of the 1944 Mw ~ 8 Tonankai earthquake. The centroid depths were 11 and 14 km for the 2004 and 2016 events, respectively. Despite a large difference in the moment magnitude between the two events, the JMA magnitude (Mj) was 6.5 for both the events. We found that the short-period ground motions (e.g., response spectra at periods < 1 s) as well as the much longer-period ground motions (> 20 s) for the 2016 event scaled generally well with the moment magnitude of the event. In contrast, the ground motions from the 2016 event were comparable to those for the larger-moment-magnitude 2004 event at equal distances at periods of about 2-20 s in wide areas and the observed acceleration response spectra at those periods were noticeably underestimated for the 2016 event by the ground motion prediction equation (GMPE) that employs Mw. An examination of the existing subsurface velocity model suggested that the difference in the relative location of the two events with respect to the thick accretionary prism of low seismic velocity most probably caused the comparable amplitude of the seismic waves at those periods. As a result, we posit that the values of Mj are equal for the two events because Mj is estimated using the displacement amplitude of ground motions at periods smaller than about 6 s. On the other hand, GMPE employing Mj generally described the observed data well. The results suggested that the plate boundary earthquakes in the Nankai Trough may excite strong long-period ground motions of engineering importance, and these ground motions appear to be better explained by Mj than by Mw in GMPEs for moderate-magnitude earthquakes in the Nankai Trough subduction zone. [ABSTRACT FROM AUTHOR]