A Robust Real-Time S-Wave Detection Method with Low Computational Cost Based on Modified STA/LTA

doi:10.21203/rs.3.rs-3209398/v1

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A Robust Real-Time S-Wave Detection Method with Low Computational Cost Based on Modified STA/LTA

https://doi.org/10.21203/rs.3.rs-3209398/v1

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Since October 2007, the Japan Meteorological Agency has been operating an Earthquake Early Warning (EEW) System in Japan. To ensure the timely estimation of magnitude immediately after the detection of an earthquake, the EEW process utilizes two types of magnitude calculation formulas: one for the P-wave phase and another after the arrival of S-wave. The process dynamically switches between these two formulas, depending on the estimated arrival time of the S-wave at each observation point. Misidentifying the amplitude of S-wave as a P-wave may lead to an overestimation of the magnitude, which results in the issuance of a wide-area warning for a region with only weak ground motion. However, real-time picking of S-wave arrivals with low computational costs poses a challenge. In this study, we developed a novel robust method to determine the arrival time of S-waves in real time with a low computational cost while adhering to the basic algorithm of short-term average/long-term average (STA/LTA). This approach deliberately introduces additional noise prior to the identified P-wave to enhance the differentiation between the P- and S-waves. Subsequently, the STA/LTA method is reapplied to detect the S-wave. This method was effective in determining the S-wave arrival time, with the residuals (automatic reading minus manual reading) revealing that the percentage of correct decisions (residual < 1.5 s) for all earthquakes with all observation points was 67%. However, the percentage of correct decisions for earthquakes of magnitude 5.5–6.5, which may cause excessive alarms, with observation points at the epicentral distance less than 100 km was 81%. The error in automatic readings can be reduced by optimizing the parameters for each earthquake and possibly for each station. However, because this method is designed for real-time operation, the optimal parameters must be set after the occurrence of an earthquake. It may be feasible to analyze numerous earthquakes and empirically determine the parameters based on information such as STA/LTA and P-wave amplitude.

Real-time S-wave picking

Earthquake Early Warning

STA/LTA

To mitigate earthquake disasters, the Japan Meteorological Agency (JMA) has developed an earthquake early warning (EEW) system, which has been fully operational since October 2007 (Hoshiba et al. 2008; Kamigaichi et al. 2009). EEW systems rapidly analyze seismic waveforms acquired from stations in close proximity to the hypocenter and estimate critical parameters, such as hypocentral distance, back azimuth, and magnitude (e.g., Nakamura 1988; Allen and Kanamori 2003; Odaka et al. 2003; Horiuchi et al. 2005; Noda et al. 2012; Noda et al. 2016; Iwata et al. 2020). The swift and accurate determination of magnitudes is a crucial element of the EEW system. Magnitudes are usually calculated using the epicentral distance estimated through the aforementioned process as well as the maximum amplitude recorded at each station. To facilitate the timely estimation of magnitude immediately after an earthquake detection, the EEW process employs two types of magnitude calculation formulas, one for the P-wave phase (P-wave magnitude) and the other after the arrival of the S-wave (all-phase magnitude). The process dynamically switches between the two formulas depending on the estimated arrival time of S-wave at each observation point. When calculating the magnitude of P-wave in the practical implementation of EEW, the maximum amplitude within a time interval of 0.7 times the theoretical S-P wave time from the P-wave arrival is utilized. In their analysis of earthquake waveforms with epicenters up to 100 km, Hoshiba et al. (2009) observed that even for earthquakes with a magnitude of 5, the maximum displacement amplitude between the arrival of P and S waves occurs not immediately after the P-wave arrival in the former half of S-P time, but rather in the latter half. This may lead to an incorrect interpretation of the S-wave amplitude as that of a P-wave, resulting in an overestimation of the P-wave magnitude. Conversely, this may also mistakenly treat the P-wave amplitude as that of a S-wave, resulting in an underestimation of the P-wave magnitude. Hence, the accurate real-time determination of the S-wave arrival time is important for precise magnitude estimation.

Real-time detection of S-waves is challenging. The differences in vibration characteristics (e.g., amplitude and frequency) between background noise and P-waves are more pronounced, resulting in a high success rate of P-wave detection based on recorded waveform characteristics. Real-time detection of S-waves necessitates the identification of subtle features of S-waves while the P-waves are being recorded. The differences between the features of S-waves and P-waves are less pronounced compared to the disparities between the background noise (prior to the arrival of P-waves) and the P-waves. Numerous techniques exist for the real-time picking of P waves; however, relatively few techniques are available for S-waves. Examples of S-wave picking methods incorporate various advanced techniques such as higher-order statistics, including kurtosis (Baillard et al. 2014), improved short-term average/long-term average (STA/LTA) method by introducing the envelope function (Baer and Kradolfer 1987), machine learning algorithms such as neural networks and trees (Wang and Teng 1997; Gentili and Michelini 2006), and nearest-neighbor-based approaches (Rawles and Thurber 2015). However, these methods are unsuitable for real-time processing because of the onerous computational burdens required for filtering and Fourier conversion.

The STA/LTA method is valued for determining the arrival time of P-waves in real time (Allen 1978; Allen 1982). The STA/LTA algorithm is highly efficient for real-time processing owing to its low computational cost. Wu et al. (1997) develop the two steps STA/LTA for P & S arrival picking has been used in the Central Weather Bureau, Taiwan since 1995. For P-wave detection, they compute STA/LTA for the vertical component waveform of the seismometer, and for S-wave detection, the other STA/LTA is calculated for the horizontal component waveform of the seismometer. However, when implementing STA/LTA for real-time S-wave detection, using P-wave amplitudes to calculate the LTA poses challenges. These challenges include the significant amplitude variation of P-waves in comparison with the background noise and the limited S-P time available for calculating LTA at stations near the hypocenter. For instance, when examining the STA/LTA values obtained at a seismometer close to the epicenter, the S wave arrives before the STA/LTA value, which initially increases upon the arrival of the P wave, has fully returned to its baseline. Conversely, as the S-P time interval elongates, the proportion of the P wave in the amplitude used for calculating LTA gradually rises, leading to a gradual increment in the LTA value. Consequently, the STA/LTA value at the moment of S-wave arrival fluctuates with the S-P time interval, rendering the establishment of a distinct STA/LTA threshold for S-wave detection more intricate than that for P-waves.

In this study, we developed a novel method that robustly determines the arrival time of S-waves in real time. This method effectively stabilizes the STA/LTA fluctuations in the P-wave prior to the arrival of the S-wave while adhering to the basic STA/LTA algorithm and clarifies the characteristic difference between P- and S-waves.

We developed a real-time method for determining the arrival times of S-waves based on the principles of the STA/LTA method. First, the arrival time of the P wave was determined using a conventional STA/LTA approach. Artificial noise, quantified in terms of the P-wave amplitude, was then introduced into the signal. Subsequently, STA/LTA was applied to the modified signal to determine the arrival time of S-wave.

The STA/LTA method has been used in many P-wave detection systems owing to its computational efficiency. For P-wave detection, the real-time calculation of ${STA}_{p}$ and ${LTA}_{p}$ was performed on the seismic waveform data:

$$\begin{array}{c}{STA}_{p}\left(k\right)=\frac{1}{{\alpha }_{p}}\sum _{i=k-{\alpha }_{p}}^{k}\left|{x}_{i}\right|;\#\left(1\right)\end{array}$$

$$\begin{array}{c}{LTA}_{p}\left(k\right)=\frac{1}{{\beta }_{p}}\sum _{i=k-{\beta }_{p}}^{k}\left|{x}_{i}\right|;\#\left(2\right)\end{array}$$

$$\begin{array}{c}\frac{{STA}_{p}}{{LTA}_{p}}>{th}_{p}.\#\left(3\right)\end{array}$$

Specifically, the time k, at which Eq. (3) was first satisfied, was identified as the P-wave arrival time γ. Next, the 90th percentile of the P-wave, denoted as q, was calculated from γ to γ + δ s as follows:

$$\begin{array}{c}q={percentile}_{90\%}\left\{{x}_{\gamma },{x}_{\gamma +1},{x}_{\gamma +2},\bullet \bullet \bullet ,{x}_{\gamma +\delta }\right\}.\#\left(4\right)\end{array}$$

Subsequently, the random noise N with values ranging from 0 to 1, was multiplied by q to generate a noise waveform that incorporates the amplitude information of the P-wave from γ to γ + δ. The noise waveform, which is the product of q and N, was replaced with the original signal waveform ${x}_{i}$ from time γ + δ-β to time γ + δ. Therefore, waveform ${y}_{i}$ was generated to detect the S-wave as follows:

$$\begin{array}{c}{y}_{i}=\left\{{q*N}_{\gamma +\delta -\beta },{q*N}_{\gamma +\delta -\beta +1},{q*N}_{\gamma +\delta -\beta +2},\bullet \bullet \bullet ,q*{N}_{\gamma +\delta },{x}_{\gamma +\delta +1},\bullet \bullet \bullet \right\}.\#\left(5\right)\end{array}$$

Although creating ${y}_{i}$ from a time earlier than γ + δ-β presents no problem, we generated only the essential ${y}_{i}$ required to compute the LTA to minimize the cost of the real-time computation. Next, the STA/LTA analysis was performed on the modified waveform ${y}_{i}$ to establish the threshold, th_s for detecting the S-wave.

$$\begin{array}{c}{STA}_{s}\left(k\right)=\frac{1}{{\alpha }_{s}}\sum _{i=k-{\alpha }_{s}}^{k}\left|{y}_{i}\right|.\#\left(6\right)\end{array}$$

$$\begin{array}{c}{LTA}_{s}\left(k\right)=\frac{1}{{\beta }_{s}}\sum _{i=k-{\beta }_{s}}^{k}\left|{y}_{i}\right|.\#\left(7\right)\end{array}$$

$$\begin{array}{c}\frac{{STA}_{s}}{{LTA}_{s}}>{th}_{s}.\#\left(8\right)\end{array}$$

where the parameters ${\alpha }_{s}$ and ${\beta }_{s}$ represent the length of time used to calculate the average value. ${\alpha }_{s}$ and ${\beta }_{s}$ can have values identical to those of ${\alpha }_{p}$ and ${\beta }_{p}$. Finally, the time k at which Eq. (8) was first satisfied was designated as the S-wave arrival time.

The δ, q, and ${y}_{i}$ values were updated if the ${STA}_{s}/{LTA}_{s}$ value did not surpass the threshold (th_s). The amplitude of P-wave underwent gradual changes, leading to the q value becoming insufficient a few seconds after the P-wave arrival. Hence, we incremented the δ value each second and updated the q and ${y}_{i}$ till the ${STA}_{s}/{LTA}_{s}$ exceeded the th_s. First, we generated the q and ${y}_{i}$based on the data between γ and γ + 2 s and applied ${STA}_{s}/{LTA}_{s}$. If the ${STA}_{s}/{LTA}_{s}$ values did not exceed the th_s by γ + 3 s, we updated the q and ${y}_{i}$ again based on the data between γ and γ + 3 s, followed by performing the ${STA}_{s}/{LTA}_{s}$till γ + 4 s using updated ${y}_{i}$. This iterative process continued until γ + 6 s, beyond which the q and ${y}_{i}$ were not updated.

The objective of this method was to stabilize the temporal fluctuations of the STA/LTA till arrival of S-waves. Directly following the onset of P-wave, the computed LTA encompassed both the pre-P-wave noise and P-wave itself until the time window β allocated for the LTA computation expired. Consequently, the LTA value gradually escalated. In such instances, the STA/LTA required time to stabilize, and the configuration of the threshold became intricate, leading to the risk of overlooking the arrival of S-wave. Hence, by incorporating noise and the parameter q, the temporal fluctuation of STA/LTA, commencing promptly after the arrival of the P-wave (more precisely, after δ has passed), could be assessed based on the interplay between P-waves and S-waves. This augmented the reliable detection of S-waves.

In this study, we selected earthquakes of magnitude ≥ M5.5 and depths ≤ 100 km, occurred between 2003 and 2018, and manually picked S-wave arrival times on the seismic waveforms recorded by Kyoshin Network (K-NET) for the selected earthquakes. The data used in this study were obtained from K-NET stations, located within approximately 200 km from the epicenter of each earthquake. Only seismic events with 20 or more K-NET stations where the S-wave arrival times could be interpreted manually were considered. The 65 earthquakes considered in this analysis are listed in Table 1. In this study, we computed the ${STA}_{p}/{LTA}_{p}$ for the vertical component of waveforms, whereas the parameters q and ${STA}_{s}/{LTA}_{s}$ were derived from the combined horizontal components of the waveforms. The acceleration waveforms recorded by K-NET were integrated into velocity waveforms before the analysis. This was done to augment the amplitude variation in the time domain and aid in the detection of S-waves. The bandwidth range of the dataset used in this study was 0.1–20 Hz.

Figure 1 shows the application of the proposed method to a specific seismic waveform recorded at a given K-NET station. The absolute value of the vertical component is presented in Fig. 1a, and the absolute value of the composite waveform of the two horizontal velocity components is shown in Fig. 1b. Figure 1c illustrates the calculated ${STA}_{p}/{LTA}_{p}$, which determines the arrival time of P-wave (γ) when the threshold value (4.5 s in this instance) is exceeded. The red waveforms in Fig. 1d indicate the composite waveform, which is used to calculate the percentile parameter q. Figure 1e shows the waveform ${y}_{i}$, in which q ×N is substituted from γ + δ-β to γ + δ. Finally, Fig. 1f shows the ${STA}_{s}/{LTA}_{s}$ which determines the arrival time of S wave when the threshold value (3.5 s in this case) is exceeded. A comparison of Figs. 1a and 1c, which are aligned on the same temporal axis, shows that the ${STA}_{p}/{LTA}_{p}$ surpasses the threshold precisely at the moment of P-wave arrival. Similarly, by comparing Figs. 1b and 1f, which are also aligned on the same temporal axis, it can be observed that the ${STA}_{s}/{LTA}_{s}$ of the proposed method surpasses the threshold precisely at the moment of S-wave arrival.

The proposed method was used to determine the arrival times of S-waves for the 65 earthquakes listed in Table 1. The parameters th_p = 5.0, ${\alpha }_{p}=0.5$, ${\beta }_{p}=5.0$, th_s = 2.2, ${\alpha }_{s}=0.5$, ${\beta }_{s}=10.0,$and $\delta =2.0$ (initial value) were utilized in this study. In addition, manual and automatic readings were compared for 65 earthquakes. Further, the S-wave arrival time detected by the proposed method (Ta, automatic reading) was compared with that determined through manual picking (Tm, manual reading). The results of the comparison between Tm and Ta at each K-NET station for 12 earthquakes are shown in Fig. 2. The results show that the Ta values are accurate and aligned with the Tm values as they are roughly aligned in a straight line. However, at certain stations, the S-wave arrival times were not accurately determined using the proposed method. This can be attributed to two primary factors that hinder the accurate automatic picking: 1) in cases where the STAs/LTAs exceed the threshold value th_s prior to the actual S-wave arrival (minus reading; ${T}_{a}-{T}_{m}<-2.0$), which is mainly evident in the comparison of Ta and Tm in Fig. 2 for earthquakes #14, #30, and #40; 2) when the STAs/LTAs do not exceed the designated th_s value.

Figure 3a shows the histograms of the residuals (Ta–Tm) for both datasets. The percentage of correct decisions ($\left|{T}_{a}-{T}_{m}\right|\le 1.5$) for all earthquakes with all observation points was approximately 67.7% (Fig. 3a). Moreover, the percentage of correct decisions decreases as the hypocenter distance increases, as shown in Fig. 3b. As the hypocenter distance increases, the percentage of stations that do not exceed th_s and thus cannot determine the S-wave arrival time also increases (Fig. 3b). The percentage of correct answers tends to decrease slightly as the magnitude of the earthquake increases (Fig. 3c). As stated in the Introduction, when the S-wave arrival time cannot be determined, the S-wave amplitude is utilized instead of P-wave amplitude to estimate the earthquake magnitude, and the estimated magnitude exceeds the actual one, leading to an overestimation of the warning range. This issue is particularly crucial for small earthquakes because issuing warnings in unnecessary areas can have a significant social impact. Using the proposed method, 81.0% accuracy was achieved in detecting earthquakes of magnitude 5.5–6.5 (small earthquake), which tend to trigger superfluous alerts, within 100 km of the hypocenter where warnings are required urgently (Fig. 3a).

As with other phase detection methods, it is important to assess the accuracy of the described method. The increase in the number of observation points that do not exceed the threshold level with increasing epicentral distance (Fig. 3b) can be attributed to the attenuation of the amplitude of the rising portion of the P-wave and the decrease in the difference between the amplitudes of P- and S-waves owing to the prevalence of reflected waves. In the real-time magnitude calculation, if the STAs/LTAs do not exceed the th_s threshold, it is assumed that there are no S-waves, and the magnitude estimation equation for P-wave is used for S-wave, causing an overestimation of the magnitude. Nevertheless, the increase in the number of observation points that do not exceed th_s is more prominent for distant epicenters, which is not a significant concern for stations near the epicenter—a crucial aspect for EEW systems.

Conversely, the phases generated by the sedimentary layers, such as PS-converted- and SP-converted waves, could potentially influence the minus readings. This phenomenon is more likely to occur when a notable discontinuity surface exists directly beneath a station, such as for a station situated in a basin. In such cases, even though it is a P-wave, the S-wave magnitude calculation formula is used, resulting in a much smaller magnitude than the actual one, which hinders the system from issuing warnings in regions where warnings are required. This phenomenon occurs irrespective of the hypocenter distance of the observation point, as depicted in Fig. 2. To minimize the number of minus readings, a parameter study of the th_s was conducted. The th_s varied from 1.0 to 4.0 (th_p fixed at 5.0) for all stations situated within a hypocenter distance of less than 200 km for 65 earthquakes. Among the picks computed using our method, N1 represents the count of picks with $\left|{T}_{a}-{T}_{m}\right|\le 1.5$, N2 represents the count of picks where the STAs/LTAs did not surpass th_s, and N3 represents the count of picks with ${T}_{a}-{T}_{m}\le -2.0$ (minus reading), as shown in Fig. 4a. N1 was the highest when th_s was 2.2, and as th_s increased, N2 increased and N3 decreased. The decrease in N3 with increasing th_s was due to the fact that the threshold is surpassed by the S wave rather than PS or SP converted waves. However, an elevated threshold value may lead to a delayed Ta in comparison to Tm because the threshold is exceeded at higher amplitudes. As an example, the results for earthquake #40 computed with th_s = 1.0 and th_s = 4.0 are presented in Figs. 4b and 4c, respectively. The figures illustrate that reducing the th_s increases the number of minus readings, while increasing the th_s reduces the number of picks and leads to a delay in Ta. Owing to the inherent variability in the observed seismic waveforms caused by factors such as source, propagation path, and site effects, it is theoretically essential to establish a specific threshold value for each station to accurately determine ${T}_{a}$. However, this method is designed for real-time operation, and the optimal th_p and th_s must be set after the occurrence of an earthquake. It may be feasible to analyze numerous earthquakes and determine thresholds empirically based on information such as ${STA}_{p}/{LTA}_{p}$ and the P-wave amplitude.

The bandwidth of the recorded seismic trace plays an important role in the performance of a phase detector, i.e., a bandwidth that is too narrow can deteriorate the efficiency of the employed algorithm (Longbottom et al. 1988). Saragiotis et al. (2002) indicated that a strong bandwidth dependence of the STA/LTA algorithm is expected for P-wave detection, and that the STA/LTA algorithm requires a minimum bandwidth more than 15 Hz to reliably estimate the phase arrival for less than 10 samples. Here, we compared the results of the our analysis of the seismic waveforms using five bandpass filters (0.01–20 Hz, 0.05–20 Hz, 0.1–20 Hz, 0.5–20 Hz, and 1–20 Hz). The target earthquakes and parameters are consistent with those presented in the Results section. The percentage of correct decisions ($\left|{T}_{a}-{T}_{m}\right|\le 1.5, \le M6.5, \le 100 km$) obtained using five bandpass filters were 80.5%, 80.0%, 81.0%, 60.2%, and 75.3%, respectively (Figs. 2a and S1a–4a). The percentage increased with the inclusion of low-frequency components. Nonetheless, the optimal bandwidth configuration may vary based on such factors as the magnitude of dominant frequency and attenuation at a hypocentral distance of the station.

Although not in a real time, previous studies have shown that in automated S-waves picking, the percentage of correct decisions often exceeds 90% with $\left|{T}_{a}-{T}_{m}\right|\le 0.1$ (e.g., Rawles and Thurber 2015). This is in contrast to the 81.0% correct decisions with $\left|{T}_{a}-{T}_{m}\right|\le 1.5$ observed in this study. In machine learning and statistical applications, ensemble methods, which incorporate multiple methods, outperform single-model techniques when there is a diversity among them (Kuncheva and Whitaker 2003). This phenomenon was also observed in phase picking (Diehl et al. 2009). Considering the objective of real-time S-wave picking, we acknowledge the constraints on our capacity to perform intricate computations. However, we propose the integration of our methodology with existing event and phase detection techniques to enhance the accuracy of the picking process.

Precise determination of magnitude plays a crucial role in mitigating disruptions to societal activities. Particularly, in the case of an EEW system implemented on a vast railway network across Japan, the halting of train operations due to safety concerns and the need for operational adjustments, such as train re-routing, requires substantial time and effort. While it is imperative to promptly halt moving trains to avert potential derailments following an earthquake, it is equally vital to continuously advance the development of warning systems that provide accurate predictions. This is essential for minimizing the adverse impact on economic activities in a country prone to frequent seismic events.

We developed a robust method to determine the arrival time of S-waves in real time with a low computational cost while adhering to the basic algorithm of STA/LTA. In this approach, noise was intentionally added to the waveform ahead of the P-wave to accentuate the contrast between the P- and S-waves, followed by a renewed implementation of the STA/LTA to detect S-waves once the P-wave was successfully identified. The method can effectively determine the S-wave arrival time. The residuals (automatic reading minus manual reading) for both datasets indicated that the percentage of correct answers for all earthquakes with all observation points was 67.7%. However, the percentage of correct answers for earthquakes of magnitude 5.5–6.5 with observation points at the epicentral distance less than 100 km was 81.0%. The error in automatic readings can be minimized by optimizing the parameters for each individual earthquake and potentially for each station. Nevertheless, given that this method is intended for real-time applications, the optimal parameter values must be established post-event. It may be viable to analyze multiple earthquakes and empirically determine the parameters using information such as STA/LTA and P-wave amplitude. We suggest integrating our methodology with established event and phase detection techniques to enhance the precision of picking process.

Availability of data and materials

The waveform data used in this study were obtained from https://www.kyoshin.bosai.go.jp (National Research Institute for Earth Science and Disaster Resilience, 2019). The seismic data used in this study were obtained from the Japan Meteorological Agency (JMA, https://www.data.jma.go.jp/eqev/data/daily_map/index.html).

Competing interests

The authors declare that they have no competing interests.

Funding

Not applicable.

Authors' contributions

SK (corresponding author) performed the analyses and drafted the manuscript. NI supervised the study. All the authors have read and approved the manuscript.

Acknowledgments

Some figures were prepared using Generic Mapping Tools (Wessel et al., 1998).

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A Robust Real-Time S-Wave Detection Method with Low Computational Cost Based on Modified STA/LTA

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