Keywords

1 Introduction

In the current scenario, the earthquake early-warning system plays a vital role in the prediction of the most damaging earthquake, but still, it is in developing stage. There were many countries like Japan, Taiwan, and Southern California that provide an early warning during an earthquake was in good agreement with an source parameters of the earthquake. But for providing the early warning, there were many parameters used like predominant period, cumulative average velocity, average ground motion period, peak displacement amplitudes, etc. Researchers in this field are still developing new applications for improving the accuracy of the early-warning period in the earthquake early-warning system. In the past and present, there were many early-warning signal parameters are found they are ground motion average period τc and peak displacement amplitude Pd and it shows a good improvement for measurement of the earthquake size. During the origin of the earthquake, the early-warning waveform of three seconds time window was taken into account to determine the early-warning parameters like τc and Pd. In Taiwan, the experiment conducted for the onsite early-warning approach suggested that both τc and the peak displacement amplitude were possible to give a reliable threshold warning during the earthquake and stated that those given parameters had the complement usage for the regional approach in Taiwan [1]. Wu and Zhao [2] clearly explained the earthquake early-warning practice, and peak displacement amplitude provides a more advanced warning period from the three seconds of the early-warning signal. They have shown the magnitude determination from the Pd parameter with lesser uncertainty, and this parameter is used to reduce the false alarms caused by the small and moderate earthquake [3]. For many practical early warning purposes, the considered magnitude was greater than 6 is resulted in a betterment way during the warning period compared with lower size of the magnitude  and it suggested that the future work like uncertainties findings in the estimation of magnitude and intensity from the initial P-wave motion. Authors [4, 5] suggested that the relationship between τc and M shows a better fit in the regression analysis, and they were used the high-pass filter with a cutoff frequency of 0.075 Hz for removing the noise data in the collected waveform. Wu et al. [6] shows the linear relationship of the τc and Pd parameters with the function of the magnitude in the range of 4–8 by using the regression analysis with a better fit of lesser standard deviation. Bhardwaj [7] concluded that the magnitude obtained from the τc of the initial P-wave provided a satisfactory solution. The comparison was made between the τc and Pd with the function of the magnitude by using linear regression analysis with the considered Indian dataset [8]. The logarithmic τc with magnitude shows a better correlation with a positive slope in regression analysis [9]. This study deals with, by comparing the early warning parameters with epicentral distance and the average shear wave velocity were shown the influence of local site effects in the initial P-wave of three seconds time window.

2 Data Analysis

This study considered the bedrock and surface vertical component waveform of the seven individual station records with the single earthquake event. The data were collected in a Japanese strong motion database in KIK-net sensors installed in both borehole and the surface at the sites with a magnitude of 6.7 within the covered epicentral distance of 18 to 66 km. In the considered seven-station records, each station has two sets of motion that is bedrock motion and the  surface motion, so it covered 14 vertical component of the P-wave motion. The site characterization details were also collected from the KIK-net Web site, it includes the soil profile data for each station, and these collected soil profile data are used to classify the sites based on average shear wave velocity for each site. The earthquake event details are given in Table 1.

Table 1 List of stations and earthquakes used in this study
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3 Methodology

In this study, the waveform data of the vertical component of bedrock and surface acceleration recorded by the KIK-net seismic networks of the National Research Institute for Earth Science and Disaster Prevention (NIED-Japan) are used. The selected stations are near to the epicenter, and the collected data for each station show an uncorrected value of the acceleration records, so here linear baseline correction is carried out by using SeismoSignal software for the betterment of the results. The value of τc and Pd has been determined at the level of bedrock and the surface motion for each station record. Then, the site classification is made for the selected sites based on average shear wave velocity followed by NEHRP [10].

4 τc and Pd Method

Toward finding the magnitude of the earthquake, it is essential to describe whether the occurrence of slip motion is stationary or it is still developing, which is usually revealed in the period of the primary motion. The minor events produce a short period, and the extended events yield a longer period of the initial motions, respectively. Normally, the slip motion is a difficult measurement, and also, a large event often begins with a short period, followed by a long period motion. Accordingly, it is significant to define the average period during the first motion. τc is a measurement of the average period of the ground motion with a three-second time window of P waves developed [1]. τc is determined as

$$\tau_{c} = \frac{2\pi }{{\sqrt r }}$$

where \(r = \frac{{\mathop \smallint \nolimits_{0}^{{\tau_{0} }} \dot{u}^{2 } \left( t \right){\text{d}}t}}{{\mathop \smallint \nolimits_{0}^{{\tau_{0} }} u^{2 } \left( t \right){\text{d}}t}}\), \(\tau_{0}\) = duration of the time window (generally 3 s),

\(\dot{u}\)(t) = velocity and \(u\left( t \right)\) = vertical displacement obtained from ground motion record on double integration.

Pd is the peak displacement amplitude in the first three seconds after the arrival of P waves, it is the robust measurement for determining the magnitudes of earthquakes, and it has practical application in the earthquake early-warning systems [2].

5 Results and Discussions

5.1 Variation of τc in bedrock and Surface motion

The motion at the base of the soil deposit (also the top of the rock) is known as bedrock motion, and the free surface in the top of the soil deposit is known as surface motion. The acceleration data were collected from the Kiban Kyoshin network (KIK-net) strong motion seismograph network, which consists of pairs of seismographs installed in a borehole and surface at a different site. In the borehole and the surface, the recorded motion was considered as a bedrock and surface motion for the analysis. The collected acceleration data are not about the zero axis line, so here the baseline correction analyses were carried out in the SeismoSpect software v18, and these records were integrated to obtain velocity and displacement. A bandpass second-order Butterworth filter with cutoff frequency 0.07–30 Hz was applied on the record to remove the low-frequency drift in the velocity and displacement signal. The average ground motion period (τc) and the peak displacement amplitude (Pd) for the bedrock and the surface motion estimated with the selected time window of the 3 s.

In Fig. 1, the comparison is made for logarithmic τc of bedrock and surface motion with different sites for the magnitude of 6.7. The surface motion early-warning parameter shows higher than the bedrock motion parameter for all sites. It represents that the surface amplification is higher than the bedrock amplification due to softer soil conditions in all sites.

Fig. 1
figure 1

τc recorded at different sites for the considered earthquake of magnitude 6.7

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The logarithmic parameter τc increased with increasing epicentral distance. Figure 2 represents that the surface motion parameter is high compared to the bedrock motion parameter, and it reveals that with the increasing epicentral distance, the surface motion parameter is increasing. And also, it shows that the surface motion has a higher difference with a distance greater than 35 km due to site effects.

Fig. 2
figure 2

Variation of log(τc) with epicentral distance

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5.2 Variation of Pd in Bedrock and Surface Motion

The logarithmic peak displacement amplitude of the early-warning parameter Pd is compared with the different sites with a magnitude of 6.7 in Fig. 3. It shows that most of the site surface motion parameter is lower than the bedrock motion parameter, the observation made in Pd has very low-level amplitudes that were represented in negative log parameter, and the positive Pd parameter reflected as a higher amplitude due to the considerable soil amplification. The site IBUH01 has a higher surface motion parameter than the bedrock motion parameter, and it may due to high-level amplification of the motion.

Fig. 3
figure 3

Pd recorded at different sites for the considered earthquake of magnitude 6.7

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5.3 τc on the Different Type of Sites Based on the Average Velocity of the Shear Wave

The wave propagation theory clearly explains that the surface motion amplitude depends on the density and shear wave velocity of the subsurface material. Generally, in-situ density has a relatively smaller variation with depth. So, here the shear wave velocity plays an important part in representing the soil site effects. According to National Earthquake Hazard Reduction Program (NEHRP) and Uniform Building Code (UBC), the average shear wave velocity has been calculated by

$${\text{Average Shear wave velocity}}\left( {V_{s} } \right) = \frac{{\sum {\text{d}}i}}{{\sum \frac{{{\text{d}}i}}{Vi}}}$$

\(di\)—thickness of soil layers (m)

\(Vi\)—shear wave velocity of the soil layers (m/s) (Table 2).

Table 2 Site Classification based on Average Shear-wave Velocity
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5.3.1 Influence of Average Shear Wave Velocity on τc and Pd for Surface Motion

The average shear velocity is one of the most vital properties in the site effect characterization. In Fig. 4, the logarithmic parameter of τc is compared with the function of average shear wave velocity and it states that log τc is decreased with increasing average shear wave velocity, and also it shows the site which has the lowest shear wave velocity, there the τc parameter shows the highest value in the surface motion.

Fig. 4
figure 4

Variation of τc with average shear wave velocity of the site

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Fig. 5
figure 5

Variation of Pd with average shear wave velocity of the site

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The logarithmic parameter of Pd is compared with the function of average shear wave velocity (Fig. 5). The above mentioned graphical representation explains that the log Pd is decreased with increasing average shear wave velocity, and also it shows the site which has the lowest shear wave velocity, there the Pd parameter shows the highest value in the surface motion.

6 Conclusions

This work endeavored to study the effects of local site conditions on earthquake early-warning parameters of the bedrock and the surface motion. The sites considered in this study show the increment in the early-warning parameters τc and Pd for the surface motion compared to bedrock motion irrespective of the magnitude of an earthquake. Similarly, the τc parameter is increasing in surface motion compared to the bedrock motion with respective epicentral distance. The increase in τc and Pd values in the surface motion is certainly due to soil amplification. There is a decrease in the value of τc and Pd parameters with an increase in the average shear wave velocity of the site. The site which has the lowest average shear wave velocity shows the highest increment of the early-warning parameters of τc and Pd. It reflects that the sites which have the soft soil type show higher amplification in earthquake early-warning parameters. But further studies are needed for justifying the relationship between the modifications of early-warning parameters with a change in the average shear wave velocity and the epicentral distance of the site.