JP7590482B2 - Information processing device, information processing program, and information processing method - Google Patents

Description

This disclosure relates to a seismometer that detects S waves from a time series of observation data observed by a ground motion sensor.

A seismometer is a device that can immediately estimate damage immediately after an earthquake occurs, in order to prevent further damage. In order to estimate the epicenter and magnitude from the observed ground motion, the seismometer must accurately detect the timing of the arrival of S waves.

Patent Document 1 discloses a method for detecting the timing of S-wave arrival, called the STA/LTA method, which detects a sudden rise in amplitude. Non-Patent Document 1 discloses a method that uses the ratio of horizontal movement to vertical movement.

Patent No. 6291648

Nakamura, Yutaka. Research Outlook: Research on Comprehensive Earthquake Disaster Prevention Systems. Proceedings of the Japan Society of Civil Engineers. 1996, No. 531, pp. 1-33.

The STA/LTA method has the problem that it is difficult to separate the initial motion of P waves and the initial motion of S waves when they occur close in time. In addition, the method that uses the ratio of horizontal motion to vertical motion has the problem that it is difficult to detect S waves when the difference in amplitude between the horizontal motion and the vertical motion is small. Furthermore, seismometers for railways and emergency earthquake warning systems use different estimation formulas to estimate the magnitude before and after the arrival of S waves. This causes the problem that the accuracy of estimating the magnitude decreases due to the decrease in the accuracy of S-wave detection.

The present disclosure aims to provide a seismometer that can accurately detect the arrival timing of S waves even when the initial motion of P waves and the initial motion of S waves are close in time or when the difference in amplitude between horizontal and vertical motion is small.

The information processing device according to the present disclosure includes:
an amplitude calculation unit for calculating an amplitude due to ground motion;
a frequency analysis unit that calculates frequency characteristics such as a running spectrum in real time using the amplitude;
an S-wave detection unit that detects S-waves generated by the ground motion by using frequency characteristics such as the running spectrum;
Equipped with.

The information processing device according to the present disclosure includes a frequency analysis unit and an S-wave detection unit, and is therefore capable of accurately detecting the timing of arrival of S-waves.

FIG. 1 is a system configuration diagram of a seismometer 30 according to the first embodiment. FIG. 1 is a functional block diagram of an information processing device 20 according to a first embodiment. FIG. 11 is a flowchart showing an S-wave detection process performed by the information processing device 20 according to the first embodiment. FIG. 1 is a diagram of the first embodiment, showing the seismic motion of the 2009 Suruga Bay offshore earthquake. FIG. 2 is a diagram showing the hardware configuration of an information processing device 20 according to the first embodiment.

In the description of the embodiments and in the drawings, the same elements and corresponding elements are given the same reference numerals. Descriptions of elements given the same reference numerals are omitted or simplified as appropriate. In the following embodiments, "part" may be read as "circuit," "process," "step," "processing," or "circuitry" as appropriate.

The symbols used in embodiment 1 are summarized below.

In the following descriptions other than Formula 1 to Formula 34, the lowercase letter l of L will be written as l ^* to distinguish it from the number 1.

<Index and transmitted data>
(1) j: j is the channel number of the ground motion sensor. (j = 1, 2, 3)
1 indicates the north-south direction, 2 indicates the east-west direction, and 3 indicates the up-down direction.
(2) l ^* : l ^* is a counter that counts up with each sampling.
(3) m: m is the index of the AR model.
(4) f: f is frequency (Hz).
(5) Dg _j (l ^* ): Dg _j (l _* ) is the observed digital data. (j = 1, 2, 3)
(6) _xj (l ^* ): _xj (l ^* ) is the amplitude data in physical units (j=1, 2, 3).
(7) PS _j (l ^* , f): PS _j (l ^* , f) is the running spectrum based on the AR model (short-term average). (j = 1, 2, 3)
(8) PL _j (l ^* , f): PL _j (l ^* , f) is the running spectrum by the AR model (long-term average). (j = 1, 2, 3)
(9) HV(l ^* ): HV(l ^* ) is the index value for S wave detection.
(10) l ^* s: l ^* s is the S wave detection timing.

<Internal variables>
(1) μS _j (l ^* ): μS _j (l ^* ) is the average based on the AR model (short-term average) (j=1, 2, 3).
(2) CS _j,m (l ^* ): CS m (l ^* ) is the covariance function based on the AR model (short-term average) (j = 1, 2, 3, m = 0, ..., M).
(3) φS _j,m (l ^* ): φS _j,m (l ^* ) is the AR coefficient of the AR model (short-term average) (j = 1, 2, 3, m = 1, ..., M).
(4) _xSj (l ^* ): _xSj (l ^* ) is an estimate of the amplitude data by the AR model (short-term average). (j=1, 2, 3)
(5) σS _j ² (l ^* ): σS _j ² (l ^* ) is the variance of the estimation error of the amplitude data by the AR model (short-term average). (j=1, 2, 3)
(6) μL _j (l ^* ): μL _j (l ^* ) is the average by the AR model (long-term average). (j = 1, 2, 3)
(7) _CLj,m (l ^* ): CLj _,m (l ^* ) is the covariance function according to the AR model (long-term average) (j = 1, 2, 3, m = 0, ..., M).
(8) φL _j,m (l ^* ): φL _j,m (l ^* ) is the AR coefficient of the AR model (long-term average) (j = 1, 2, 3, m = 1, ..., M).
(9) _xLj (l ^* ): _xLj (l ^* ) is an estimate of the amplitude data by the AR model (long-term average). (j=1, 2, 3)
(10) σL _j ² (l ^* ): σL _j ² (l ^* ) is the variance of the estimation error of the amplitude data by the AR model (long-term average). (j = 1, 2, 3)

<Parameter>
(1) fs: fs is the sampling frequency (Hz) of the observed digital data.
(2) Cf: Cf is a physical value conversion coefficient.
(3) M: M is the order of the AR model.
(4) rS: rS is the forgetting factor of the AR model (short-time averaging). It is a coefficient that determines the window size for smoothing the running spectrum. The larger rS is, the smaller the window size becomes, resulting in a short-time average.
(5) rL: rL is the forgetting factor of the AR model (long-term average). It is a coefficient that determines the window size for smoothing the running spectrum. The smaller rL is, the larger the window size becomes, resulting in a long-term average.
(6) fhv1: fhv1 is the lower limit of the frequency (Hz) for calculating the index value of S wave detection.
(7) fhv2: fhv2 is the upper frequency limit (Hz) for calculating the index value of S wave detection.
(8) TDS: TDS is the threshold for detecting S waves.

Embodiment 1.
A seismometer 30 according to a first embodiment will be described with reference to FIGS.

***Configuration Description***
1 is a system configuration diagram of a seismometer 30. The seismometer 30 includes a ground motion sensor 10 and an information processing device 20. The seismometer 30 is capable of communicating with an external device 40 via a network 50.

2 is a block diagram of the information processing device 20. The information processing device 20 includes, as functional elements, an amplitude calculation unit 21, a frequency analysis unit 22, and an S-wave detection unit 23.
(1) The amplitude calculation unit 21 calculates the amplitude x(l ^* ) caused by ground motion.
(2) The frequency analysis unit 22 calculates the frequency characteristics from the amplitude x(l ^* ) in real time using an autoregressive model. The frequency analysis unit 22 calculates the running spectrum from the amplitude x(l ^* ) in real time using an autoregressive model, and the running spectrum is an example of the frequency characteristics.
The frequency analysis unit 22 also accepts a time range of the ground motion used to calculate the frequency characteristics as a designation of the window size. The frequency analysis unit 22 then calculates, in real time, from the amplitude, the frequency characteristics of the ground motion in the short-term window size and the frequency characteristics of the ground motion in the long-term window size, which has a longer time range than the short-term window size.
(3) The S-wave detection unit 23 detects S-waves generated by ground motion by using the frequency characteristics.

*** Operation Description ***
FIG. 3 is a flowchart showing the operation of the S-wave detection process by the information processing device 20. The operation of the information processing device 20 will be described with reference to FIG. 3. The operation of the information processing device 20 corresponds to an information processing method. The operation of the information processing method corresponds to processing by an information processing program 231 described later. In FIG. 3, the operation of the information processing device 20 is shown as process P201 to process P204. The information processing device 20 acquires ground motion as observed digital data from the ground motion sensor 10 at a time interval of the inverse (fs) ⁻¹ of the sampling frequency fs. Ground motion is vibration of the earth, and among ground motions, vibration of the earth caused by an earthquake is called "earthquake motion". Ground motion other than earthquake motion includes miscellaneous vibration caused by vehicles, background vibration (continuous microtremors), noise, etc. Hereinafter, the inverse (fs) ⁻¹ is called a sampling interval. For each sampling, the information processing device 20 performs S-wave detection process.

ｘ_ｊ（ｌ^＊）：振幅データ
Ｄｇ_ｊ（ｌ^＊）：観測デジタルデータ
Ｃｆ：物理値換算係数。 <Process P201: Calculate the amplitude of observed data>
(1) The amplitude calculation unit 21 acquires, from the ground motion sensor 10, the observed digital data Dg _j (l ^* ) observed by the ground motion sensor 10. The observed digital data Dg _j (l ^* ) is ground motion.
(2) The amplitude calculation unit 21 calculates the amplitude data x _j (l ^* ) using Equation 1 based on the acquired observed digital data Dg _j (l ^* ).

_xj (l ^* ): amplitude data _Dgj (l ^* ): observed digital data Cf: physical value conversion coefficient.

μＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による平均
ｒＳ：ＡＲモデル（短時間平均）の忘却係数。
ｘ_ｊ（ｌ^＊）：振幅データ
（２）周波数解析部２２は、式３で、ＡＲモデル（短時間平均）による共分散関数ＣＳ_ｊ，ｍ（ｌ^＊）を計算する。

ＣＳ_ｊ，ｍ（ｌ^＊）：ＡＲモデル（短時間平均）による共分散関数
ｒＳ：ＡＲモデル（短時間平均）の忘却係数
ｘ_ｊ（ｌ^＊）：振幅データ
μＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による平均
（３）周波数解析部２２は、式４のＭ次連立方程式（ユールウォーカー方程式）を解いて、ＡＲモデル（短時間平均）のＡＲ係数φＳ_ｊ，ｍ（ｌ^＊）を計算する。

ＣＳ_ｊ，ｍ（ｌ^＊）：ＡＲモデル（短時間平均）による共分散関数
φＳ_ｊ，ｍ（ｌ^＊）：ＡＲモデル（短時間平均）のＡＲ係数
Ｍ：ＡＲモデルの次数
（４）周波数解析部２２は、式５および式６で、ＡＲモデル（短時間平均）による振幅データの推定値ｘＳ_ｊ（ｌ^＊）およびＡＲモデル（短時間平均）による振幅データの推定誤差の分散σＳ_ｊ ^２（ｌ^＊）を計算する。

ｘ_ｊ（ｌ^＊）：振幅データ
μＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による平均
φＳ_ｊ，ｍ（ｌ^＊）：ＡＲモデル（短時間平均）のＡＲ係数
ｘＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定値
σＳ_ｊ ^２（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定誤差の分散
Ｍ：ＡＲモデルの次数
ｒＳ：ＡＲモデル（短時間平均）の忘却係数
（５）周波数解析部２２は、式７で、ＡＲモデル（短時間平均）によるランニングスペクトルＰＳ_ｊ（ｌ^＊，ｆ）を計算する。

ＰＳ_ｊ（ｌ^＊，ｆ）：ＡＲモデル（短時間平均）によるランニングスペクトル
σＳ_ｊ ^２（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定誤差の分散
φＳ_ｊ，ｍ：ＡＲモデル（短時間平均）のＡＲ係数
ｆ：周波数
ｆｓ：サンプリング周波数
Ｍ：ＡＲモデルの次数
（６）周波数解析部２２は、長時間平均の場合も、短時間平均の式２から式７のそれぞれに対応する以下の式８から式１３を計算する。

<Process P202: Calculate running spectrum>
The frequency analysis unit 22 first performs smoothing by time averaging on the time series of the amplitude data _xj (l ^* ). Next, it calculates a time-averaged running spectrum of the amplitude data by expressing it as an autoregressive model. In this case, two types of running spectra are calculated using two types of methods, short-term averaging and long-term averaging, which have different smoothing window sizes. Hereinafter, the autoregressive model is referred to as an AR model.
(1) The frequency analysis unit 22 calculates the average μS _j (l ^* ) by the AR model (short-term average) using Equation 2.

μS _j (l ^* ): Average by the AR model (short-time average). rS: Forgetting factor of the AR model (short-time average).
x _j (l ^* ): Amplitude data (2) The frequency analysis unit 22 calculates a covariance function CS _j,m (l ^* ) according to the AR model (short-term average) using Equation 3.

_CSj,m (l ^* ): covariance function by AR model (short-time average) rS: forgetting coefficient of AR model (short-time average) _xj (l ^* ): amplitude data _μSj (l ^* ): average by AR model (short-time average) (3) The frequency analysis unit 22 solves the Mth simultaneous equation (Yule-Walker equation) of Equation 4 to calculate the AR coefficient _φSj,m (l ^* ) of the AR model (short-time average).

_CSj,m (l ^* ): covariance function φSj _,m (l ^* ): AR coefficient of the AR model (short-time average) M: order of the AR model (4) The frequency analysis unit 22 calculates the estimated value _xSj (l ^* ) of the amplitude data by the AR model (short-time average) and the variance _σSj2 (l ^* ) of the estimation error of the amplitude data by the AR model (short-time average) using equations 5 and ⁶ .

_xj (l ^* ): amplitude data _μSj (l ^* ): average by AR model (short-time average) _φSj,m (l ^* ): AR coefficient of AR model (short-time average) _xSj ( ^{l *} ): estimated value of amplitude data by AR model (short-time average) _σSj2 (l ^* ): variance of estimated error of amplitude data by AR model (short-time average)M: order of AR modelrS: forgetting coefficient of AR model (short-time average) (5) The frequency analysis unit 22 calculates the running spectrum _PSj (l ^* ,f) by the AR model (short-time average) using equation 7.

_PSj (l ^{* ,} f): running spectrum by AR model (short-time average) _σSj2 (l ^* ): variance of estimation error of amplitude data by AR model (short-time average)φSj _,m : AR coefficient of AR model (short-time average)f: frequency fs: sampling frequency M: order of AR model (6) In the case of long-term average, the frequency analysis unit 22 calculates the following equations 8 to 13, which correspond to equations 2 to 7 of the short-term average, respectively.

ＨＶ（ｌ^＊）：Ｓ波検出の指標値
ｆ：周波数
ｆｈｖｌ：周波数の下限（Ｈｚ）
ｆｈｖ２：周波数の上限（Ｈｚ）
ＰＳ_ｊ（ｌ^＊，ｆ）：ＡＲモデル（短時間平均）によるランニングスペクトル
ＰＬ_ｊ（ｌ^＊，ｆ）：ＡＲモデル（長時間平均）によるランニングスペクトル <Process P203: Calculate the index value of S wave detection>
The S-wave detection unit 23 calculates the S-wave detection index value HV(l) using Equation 14. The S-wave detection index value HV(l ^* ) is the frequency average of the ratio between the short-term average running spectrum in the AR model calculated from the horizontal motion of the ground motion and the long-term average running spectrum in the AR model calculated from the vertical motion of the ground motion. The calculation of the S-wave detection index value HV(l ^* ) corresponds to a combination of the "STA/LTA method" and the "method using the ratio between horizontal motion and vertical motion" for each frequency component.

HV(l ^* ): Index value of S wave detection f: Frequency fhvl: Lower limit of frequency (Hz)
fhv2: Upper frequency limit (Hz)
PS _j (l ^* , f): Running spectrum by AR model (short-term average) PL _j (l ^* , f): Running spectrum by AR model (long-term average)

ＴＤＳ：Ｓ波を検出するための閾値
ＨＶ（ｌ^＊）：Ｓ波検出の指標値 <Process P204: Detect S waves>
When the S-wave detection index value HV(l ^* ) satisfies formula 15, the S-wave detection unit 23 determines that an S-wave has been detected, and sets the counter l ^* at this time as the S-wave detection timing l ^* s. The S-wave detection unit 23 outputs the S-wave detection timing l ^* s to the external device 40.

TDS: Threshold value for detecting S waves HV(l ^* ): Index value for S wave detection

The above procedure described in FIG. 3 enables highly accurate detection of S waves. In particular, the processing of equation 14 by the S wave detection unit 23 enables highly accurate detection of S waves.

Figure 4 shows the S-wave detection by the information processing device 20 for the seismic motion of the 2009 Suruga Bay earthquake. The horizontal axis of Figure 4 is time, and the vertical axis is the amplitude value of the amplitude data and the index value of the S-wave detection.

***Advantages of First Embodiment***
(1) The information processing device 20 has a property that the index value of S-wave detection is large for S-waves and not large for P-waves. Therefore, compared to the STA/LTA method disclosed in Patent Document 1, there is an advantage that even if the initial motion of the P wave and the initial motion of the S wave are close in time, the two can be separated.
(2) The information processing device 20 detects the difference in amplitude between horizontal and vertical movements for each frequency component as the index value of S-wave detection. Therefore, compared to the method disclosed in Non-Patent Document 1, it has the advantage of being able to detect S-waves even when the difference in amplitude between horizontal and vertical movements when all frequencies are combined is small.
(3) By adjusting the parameters fhvl and fhv2 in equation 14, it is possible to focus only on the desired frequency band, so that it is also possible to detect S waves while avoiding known frequency bands, such as those caused by train vibrations.
(4) A running spectrum is obtained when S waves are detected, which can be used to distinguish whether the detected S waves are due to an earthquake or noise.

The above summarizes the operations of the information processing device. The information processing device can execute the following operations. (1) The amplitude calculation unit 21 acquires observed digital data from the ground motion sensor 10 and calculates the amplitude caused by ground motion. The frequency analysis unit 22 calculates a running spectrum from the amplitude. The S-wave detection unit 23 detects S-waves generated by ground motion by using the running spectrum.
(2) The amplitude calculation unit 21 and the frequency analysis unit 22 are capable of processing the vertical motion component of ground motion. The frequency analysis unit 22 accepts the time range of ground motion used to calculate the running spectrum as a window size designation. The time range is, for example, a short-term window size and a long-term window size. The frequency analysis unit 22 calculates a running spectrum of the vertical motion component in the short-term window size and a running spectrum of the vertical motion component in the long-term window size, which has a longer time range than the short-term window size. The S-wave detection unit 23 detects S-waves generated by ground motion by comparing the running spectrum of the short-term vertical motion component with the running spectrum of the long-term vertical motion component.
(3) The amplitude calculation unit 21 and the frequency analysis unit 22 can process the vertical and horizontal components of ground motion. The frequency analysis unit 22 calculates a running spectrum of the horizontal component and a running spectrum of the vertical component. The S-wave detection unit 23 detects S-waves generated by ground motion by comparing the running spectrum of the horizontal component with the running spectrum of the vertical component.
(4) The amplitude calculation unit 21 and the frequency analysis unit 22 can process the vertical and horizontal components of ground motion. The frequency analysis unit 22 accepts the time range of ground motion used to calculate the running spectrum as a window size designation. The frequency analysis unit 22 calculates a running spectrum of the horizontal motion component in a short-term window size and a running spectrum of the vertical motion component in a long-term window size that has a longer time range than the short-term window size. The S-wave detection unit 23 detects S-waves generated by ground motion by comparing the running spectrum of the short-term horizontal motion component with the running spectrum of the long-term vertical motion component.

φＳ_ｊ，ｍ：ＡＲモデル（短時間平均）のＡＲ係数
ｚＳ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（短時間平均）の特性根
Ｍ：ＡＲモデルの次数
（２）次に、周波数解析部２２は、式１７から式２０でＡＲモデル（短時間平均）によるランニングスペクトルのピーク周波数ｆＳ_ｊ，ｑ（ｌ^＊）とその場合のスペクトルのピーク値ＰＳ_ｊ，ｑ（ｌ^＊）、ＡＲモデル（短時間平均）による損失関数ＬｏｓｓＳ_ｊ（ｌ^＊）、ＡＲモデル（短時間平均）による赤池情報量規準ＡｉｃＳ_ｊ（ｌ^＊）を計算する。

ｚＳ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（短時間平均）の特性根
ｆＳ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルのピーク周波数
ｆｓ：サンプリング周波数

ＰＳ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルのピーク値
σＳ_ｊ ^２（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定誤差の分散
φＳ_ｊ，ｍ（ｌ^＊）：ＡＲモデル（短時間平均）のＡＲ係数
ｆＳ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルのピーク周波数
Ｍ：ＡＲモデルの次数
ｆｓ：サンプリング周波数

ＬｏｓｓＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による損失関数
ｘ_ｊ（ｌ^＊）：振幅データ
ｘＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定値
σＳ_ｊ ^２（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定誤差の分散

ＡｉｃＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による赤池情報量規準
ＬｏｓｓＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による損失関数
Ｍ：ＡＲモデルの次数
（３）周波数解析部２２は、長時間平均の場合も、短時間平均の式１６から式２０のそれぞれに対応する以下の式２１から式２５を計算する。

（４）Ｓ波検出部２３は、式２６から式３１のうちの何れかから、異常検出の指標値ＨＶ（ｌ^＊）を計算する。

ＨＶ（ｌ^＊）：Ｓ波検出の指標値
ｚＳ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（短時間平均）の特性根
ｚＬ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（長時間平均）の特性根

ＨＶ（ｌ^＊）：Ｓ波検出の指標値
ｆＳ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルのピーク周波数
ｆＬ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（長時間平均）によるランニングスペクトルのピーク周波数

ＨＶ（ｌ^＊）：Ｓ波検出の指標値
ＰＳ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルのピーク値ＰＬ_ｊ，ｑ（ｌ^＊）：ＡＲモデル（長時間平均）によるランニングスペクトルのピーク値

ＨＶ（ｌ^＊）：Ｓ波検出の指標値
ｆＳ_ｊ，ｑ’（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルの卓越周波数であり、ｑ’は式１８で計算されるＡＲモデル（短時間平均）によるランニングスペクトルのピーク値ＰＳ_ｊ，ｑ（ｌ^＊）が最大となるｑである。
ｆＬ_ｑ’’（ｌ^＊）：ＡＲモデル（長時間平均）によるランニングスペクトルの卓越周波数であり、ｑ’’は式２３で計算されるＡＲモデル（長時間平均）によるランニングスペクトルのピーク値ＰＬ_ｊ，ｑ（ｌ^＊）が最大となるｑである。

ＨＶ（ｌ^＊）：Ｓ波検出の指標値
ＬｏｓｓＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による損失関数
ＬｏｓｓＬ_ｊ（ｌ^＊）：ＡＲモデル（長時間平均）による損失関数

ＨＶ（ｌ^＊）：Ｓ波検出の指標値
ＡｉｃＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による赤池情報量規準
ＡｉｃＬ_ｊ（ｌ^＊）：ＡＲモデル（長時間平均）による赤池情報量規準
以上のようにＳ波検出の指標値ＨＶ（ｌ^＊）を計算することで、式１４のように多くの周波数ｆについてスペクトルの値を計算することなく、ランニングスペクトルの急激な変化を検出することができるので、計算時間を短縮することが可能である。 In the first embodiment, it is assumed that S-waves are detected using the index value HV(l ^* ) for S-wave detection shown in Equation 14, but the index value HV(l ^* ) for S-wave detection can also be defined in various other ways as an index of the distance between the running spectra PS ₁ (l ^* , f) and PS ₂ (l ^* , f) of horizontal motion based on the AR model (short-time average) and the running spectrum PL ₃ (l ^* , f) of vertical motion based on the AR model (long-term average). For example, the following embodiments are possible.
(1) In the case of short-term average, the frequency analysis unit 22 solves an M-th degree polynomial (characteristic equation) for the complex number z shown in Equation 16, and defines the solutions whose imaginary parts are 0 or positive as the characteristic roots _zSj,q (l ^* ) of the AR model (short-term average) (q is a consecutive number, q = 1, ..., Q).

φSj _,m : AR coefficient _zSj,q (l ^* ): characteristic root of the AR model (short-time average) M: order of the AR model (2) Next, the frequency analysis unit 22 calculates the peak frequency _fSj,q (l*) of the running spectrum by the AR model (short-time average) and the peak value PSj _,q (l ^* ) of the spectrum in that case, the loss function _LossSj (l ^* ) by the AR model (short-time average), and the Akaike information criterion _AicSj (l ^* ) by the AR model (short-time average) using equations 17 ^to 20.

zS _j,q (l ^* ): characteristic root of the AR model (short-time average) fS _j,q (l ^* ): peak frequency of the running spectrum by the AR model (short-time average) fs: sampling frequency

PS _j,q (l ^* ): Peak value of the running spectrum by the AR model (short-time average) σS _j ² (l ^* ): Variance of the estimation error of the amplitude data by the AR model (short-time average) φS _j,m (l ^* ): AR coefficient of the AR model (short-time average) fS _j,q (l ^* ): Peak frequency of the running spectrum by the AR model (short-time average) M: Order of the AR model fs: Sampling frequency

_LossSj (l ^* ): Loss function by AR model (short-time average) _xj (l ^* ): Amplitude data _xSj (l ^* ): Estimated value of amplitude data by AR model (short-time average) _σSj2 (l ^* ): Variance of estimation error of amplitude data by AR model (short- ^time average)

_AicSj (l ^* ): Akaike Information Criterion based on AR model (short-time average) _LossSj (l ^* ): Loss function based on AR model (short-time average)M: Order of the AR model (3) In the case of long-term average, the frequency analysis unit 22 also calculates the following Equations 21 to 25, which correspond to Equations 16 to 20 for the short-term average, respectively.

(4) The S-wave detector 23 calculates the index value HV(l ^* ) for abnormality detection using any one of Equations 26 to 31.

HV(l ^* ): Index value of S wave detection zS _j,q (l ^* ): Characteristic root of AR model (short-term average) zL _j,q (l ^* ): Characteristic root of AR model (long-term average)

HV(l ^* ): Index value of S wave detection fS _j,q (l ^* ): Peak frequency of running spectrum by AR model (short-term average) fL _j,q (l ^* ): Peak frequency of running spectrum by AR model (long-term average)

HV(l ^* ): Index value of S wave detection PS _j,q (l ^* ): Peak value of running spectrum by AR model (short-term average) PL _j,q (l ^* ): Peak value of running spectrum by AR model (long-term average)

HV(l ^* ): Index value fS of S wave detection _j,q' (l ^* ): Dominant frequency of the running spectrum based on the AR model (short-term average), and q' is the q at which the peak value PS _j,q (l ^* ) of the running spectrum based on the AR model (short-term average) calculated by Equation 18 is maximum.
fL _q″ (l ^* ): the dominant frequency of the running spectrum based on the AR model (long-term average), and q″ is the q at which the peak value PL _j,q (l ^* ) of the running spectrum based on the AR model (long-term average) calculated by Equation 23 is maximum.

HV(l ^* ): Index value of S wave detection _LossSj (l ^* ): Loss function by AR model (short-time average) _LossLj (l ^* ): Loss function by AR model (long-time average)

HV(l ^* ): Index value for S wave detection _AicSj (l ^* ): Akaike Information Criterion based on AR model (short-term average) _AicLj (l ^* ): Akaike Information Criterion based on AR model (long-term average) By calculating the index value HV(l ^* ) for S wave detection as described above, it is possible to detect sudden changes in the running spectrum without having to calculate spectral values for many frequencies f as in Equation 14, thereby shortening the calculation time.

As an index of distance between the running spectra PS ₁ (l ^* , f) and PS ₂ (l ^* , f) of horizontal movement based on the AR model (short-term average) and the running spectrum PL ₃ (l ^* , f) of vertical movement based on the AR model (long-term average), other possible embodiments may use the chi-squared kernel, positive definite chi-squared kernel, histogram intersection kernel, Hellinger kernel, correlation coefficient, etc.

In addition, an embodiment is possible in which highly accurate S-wave detection can be achieved by using all or part of PS(l ^* ,f) and PL(l ^* ,f) calculated using Equations 7 and 13 in machine learning such as deep learning to learn the characteristics of S-waves.

In addition, zS _j,q (l ^* ), fS _j,q (l ^* ), PS j,q (l*), zL _{j ,q} (l ^* ), fL _j,q (l ^* ) and PL _j,q (l ^* ) calculated using Equations 16 to 18 and Equations 21 to 23 correspond to a running spectrum having reduced dimensions over all frequencies f. Therefore, by using all or a part of ^these in machine learning such as deep learning to effectively learn the characteristics of S waves, an embodiment can be implemented that performs highly accurate S wave detection.

In the first embodiment, it is assumed that the amplitude data _xj (l ^* ) is used as three spatial components as it is, but an embodiment in which a function value calculated from a plurality of spatial components is used is also possible. For example, it is possible to use one component by vector synthesis of two horizontal motion components.

ＨＶ（ｌ^＊）：異常検出の指標値
ｆＳ_ｊ，ｑ’（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルの卓越周波数であり、ｑ’は式１８で計算されるＡＲモデル（短時間平均）によるランニングスペクトルのピーク値ＰＳ_ｑ（ｌ^＊）が最大となるｑである。

ＨＶ（ｌ^＊）：異常検出の指標値
ＬｏｓｓＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による損失関数

ＨＶ（ｌ^＊）：異常検出の指標値
ＡｉｃＳ_ｊ（ｌ^＊）：ＡＲモデル（短時間平均）による赤池情報量規準 In addition, in embodiment 1, in the S-wave detection unit 23, the index value HV(l ^* ) of S-wave detection is defined using the ratio of the running spectrum PS _j (l ^* , f) based on the AR model (short-time average) to the running spectrum PL _j (l ^* , f) based on the AR model (long-term average) as shown in equation 14. However, embodiments that simply use the dominant frequency itself as shown in equation 32, embodiments that simply use the loss function based on the AR model (short-time average) itself as shown in equation 33, and embodiments that simply use the Akaike Information Criterion based on the AR model (short-time average) itself as shown in equation 34 are also possible.

HV(l ^* ): index value fS for abnormality detection _j,q' (l ^* ): dominant frequency of the running spectrum based on the AR model (short-term average), and q' is the q at which the peak value _PSq (l ^* ) of the running spectrum based on the AR model (short-term average) calculated by Equation 18 is maximized.

HV(l ^* ): Index value of anomaly detection _LossSj (l ^* ): Loss function by AR model (short-term average)

HV(l ^* ): Index value of anomaly detection AicS _j (l ^* ): Akaike information criterion by AR model (short-term average)

In addition, in the first embodiment, the order of the AR model (short-term average) and the AR model (long-term average) is a common M, but there are also embodiments in which the orders of the two are different from each other.

In addition, in the first embodiment, an autoregressive model is used to calculate the running spectrum in the frequency analysis unit 22, but other embodiments are also possible in which the running spectrum is calculated using other methods, such as FFT (Fast Fourier Transform).

(Hardware Supplement)
5 shows a hardware configuration of the information processing device 20. The hardware configuration of the information processing device 20 is shown. The information processing device 20 is a computer. The information processing device 20 includes a processor 210. The information processing device 20 includes, as hardware components, the processor 210, a main storage device 220, an auxiliary storage device 230, and a communication interface 240. The processor 210 is connected to other hardware via a signal line 250 and controls the other hardware.

The information processing device 20 includes an amplitude calculation unit 21, a frequency analysis unit 22, and an S-wave detection unit 23. These functions are realized by an information processing program 231.

The processor 210 is a device that executes an information processing program 231. The processor 210 executes the information processing program 231 to realize the functions of the amplitude calculation unit 21, the frequency analysis unit 22, and the S-wave detection unit 23. The processor 210 is an integrated circuit (IC) that performs arithmetic processing.

Specific examples of the main memory 220 are SRAM (Static Random Access Memory) and DRAM (Dynamic Random Access Memory). The main memory 220 holds the results of calculations by the processor 210.

The auxiliary storage device 230 is a storage device that stores data in a non-volatile manner. A specific example of the auxiliary storage device 230 is a hard disk drive (HDD). The auxiliary storage device 230 may be a portable recording medium. The auxiliary storage device 230 stores an information processing program 231.

The communication interface 240 is a communication port through which the processor 210 communicates with other devices. The communication interface 240 is connected to the network 50.

The processor 210 loads the information processing program 231 from the auxiliary storage device 230 into the main storage device 220. The processor 210 reads the loaded information processing program 231 from the main storage device 220 and executes it.

The information processing program 231 is a program that causes a computer to execute each process, procedure, or step, where each "part" of the information processing device 20 is replaced with a "process," "procedure," or "step."

The information processing method is a method that is performed by the information processing device 20, which is a computer, executing the information processing program 231. The information processing program 231 may be provided by being stored in a computer-readable recording medium, or may be provided as a program product.

Various aspects of the present disclosure are summarized below as appendices.
(Appendix 1)
an amplitude calculation unit for calculating an amplitude due to ground motion;
a frequency analysis unit that calculates a frequency characteristic from the amplitude in real time using an autoregressive model;
an S-wave detection unit that detects S-waves generated by the ground motion by using the frequency characteristics;
An information processing device comprising:
(Appendix 2)
an amplitude calculation unit for calculating an amplitude due to ground motion;
a frequency analysis unit that receives a time range of the ground motion used for calculating frequency characteristics as a designation of a window size, and calculates in real time from the amplitude, frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size;
an S-wave detection unit that detects S-waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
An information processing device comprising:
(Appendix 3)
The frequency analysis unit is
3. The information processing device according to claim 2, wherein the information processing device calculates, in real time, a frequency characteristic of the short-term ground motion and a frequency characteristic of the long-term ground motion from the amplitude using an autoregressive model.
(Appendix 4)
The amplitude calculation unit and the frequency analysis unit are
The vertical motion component of the ground motion can be processed;
The frequency analysis unit is
Calculating a frequency characteristic of the vertical movement component in the short-term window size and a frequency characteristic of the vertical movement component in the long-term window size, the time range of which is longer than the short-term,
The S wave detection unit includes:
An information processing device as described in Appendix 2 or Appendix 3, which detects S waves generated by the ground motion by comparing the frequency characteristics of the short-term vertical motion component with the frequency characteristics of the long-term vertical motion component.
(Appendix 5)
The amplitude calculation unit and the frequency analysis unit are
The vertical and horizontal components of the ground motion can be processed;
The frequency analysis unit is
Calculating a frequency characteristic of a horizontal motion component in the short-term window size and a frequency characteristic of a vertical motion component in the long-term window size;
The S wave detection unit includes:
5. The information processing device according to claim 2, further comprising: a detecting section for detecting an S wave generated by the ground motion by comparing a frequency characteristic of the short-term horizontal motion component with a frequency characteristic of the long-term vertical motion component.
(Appendix 6)
On the computer,
An amplitude calculation process for calculating an amplitude due to ground motion;
A frequency analysis process for calculating a frequency characteristic from the amplitude in real time using an autoregressive model;
an S-wave detection process for detecting S-waves generated by the ground motion by using the frequency characteristics;
An information processing program that executes the above.
(Appendix 7)
On the computer,
An amplitude calculation process for calculating an amplitude due to ground motion;
a frequency analysis process for receiving a time range of the ground motion used for calculating frequency characteristics as a designation of a window size, and calculating in real time from the amplitude, frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size;
an S-wave detection process for detecting S-waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
An information processing program that executes the above.
(Appendix 8)
The frequency analysis process includes:
8. The information processing program according to claim 7, which calculates in real time from the amplitude a frequency characteristic of the short-term ground motion and a frequency characteristic of the long-term ground motion using an autoregressive model.
(Appendix 9)
The amplitude calculation process and the frequency analysis process are
The vertical motion component of the ground motion can be processed;
The frequency analysis process includes:
Calculating a frequency characteristic of the vertical movement component in the short-term window size and a frequency characteristic of the vertical movement component in the long-term window size, the time range of which is longer than the short-term,
The S wave detection process includes:
An information processing program as described in Appendix 7 or Appendix 8, which detects S waves generated by the ground motion by comparing the frequency characteristics of the short-term vertical motion component with the frequency characteristics of the long-term vertical motion component.
(Appendix 10)
The amplitude calculation process and the frequency analysis process are
The vertical and horizontal components of the ground motion can be processed;
The frequency analysis process includes:
Calculating a frequency characteristic of a horizontal motion component in the short-term window size and a frequency characteristic of a vertical motion component in the long-term window size;
The S wave detection process includes:
10. An information processing program according to any one of appendices 7 to 9, which detects S waves generated by the ground motion by comparing the frequency characteristics of the short-term horizontal motion component with the frequency characteristics of the long-term vertical motion component.
(Appendix 11)
The computer
Calculate the amplitude due to ground motion,
Calculating frequency characteristics in real time from the amplitude using an autoregressive model;
An information processing method for detecting S waves generated by the ground motion by using the frequency characteristics.
(Appendix 12)
The computer
Calculate the amplitude due to ground motion,
A time range of the ground motion used for calculating frequency characteristics is accepted as a designation of a window size, and frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size, are calculated in real time from the amplitude;
detecting S waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
Information processing methods.

10 Ground motion sensor, 20 Information processing device, 21 Amplitude calculation unit, 22 Frequency analysis unit, 23 S wave detection unit, 30 Seismometer, 40 External device, 50 Network, 210 Processor, 220 Main memory device, 230 Auxiliary memory device, 231 Information processing program, 240 Communication interface, 250 Signal line.

Claims (9)

an amplitude calculation unit for calculating an amplitude due to ground motion;
a frequency analysis unit that receives a time range of the ground motion used for calculating frequency characteristics as a designation of a window size, and calculates in real time from the amplitude, frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size;
an S-wave detection unit that detects S-waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
An information processing device comprising:
The frequency analysis unit is
an information processing device that calculates, in real time, a frequency characteristic of the short-term ground motion and a frequency characteristic of the long-term ground motion from the amplitude using an autoregressive model. an amplitude calculation unit for calculating an amplitude due to ground motion;
a frequency analysis unit that receives a time range of the ground motion used for calculating frequency characteristics as a designation of a window size, and calculates in real time from the amplitude, frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size;
an S-wave detection unit that detects S-waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
An information processing device comprising:
The amplitude calculation unit and the frequency analysis unit are
The vertical motion component of the ground motion can be processed;
The frequency analysis unit is
Calculating a frequency characteristic of the vertical movement component in the short-term window size and a frequency characteristic of the vertical movement component in the long-term window size, the time range of which is longer than the short-term,
The S wave detection unit includes:
An information processing device that detects S waves generated by the ground motion by comparing the frequency characteristics of the short-term vertical motion component with the frequency characteristics of the long-term vertical motion component. an amplitude calculation unit for calculating an amplitude due to ground motion;
a frequency analysis unit that receives a time range of the ground motion used for calculating frequency characteristics as a designation of a window size, and calculates in real time from the amplitude, frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size;
an S-wave detection unit that detects S-waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
An information processing device comprising:
The amplitude calculation unit and the frequency analysis unit are
The vertical and horizontal components of the ground motion can be processed;
The frequency analysis unit is
Calculating a frequency characteristic of a horizontal motion component in the short-term window size and a frequency characteristic of a vertical motion component in the long-term window size;
The S wave detection unit includes:
An information processing device that detects S waves generated by the ground motion by comparing the frequency characteristics of the short-term horizontal motion component with the frequency characteristics of the long-term vertical motion component. On the computer,
An amplitude calculation process for calculating an amplitude due to ground motion;
a frequency analysis process for receiving a time range of the ground motion used for calculating frequency characteristics as a designation of a window size, and calculating in real time from the amplitude, frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size;
an S-wave detection process for detecting S-waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
An information processing program for executing
The frequency analysis process includes:
An information processing program that calculates, in real time, the frequency characteristics of the short-term ground motion and the frequency characteristics of the long-term ground motion from the amplitude using an autoregressive model. On the computer,
An amplitude calculation process for calculating an amplitude due to ground motion;
a frequency analysis process for receiving a time range of the ground motion used for calculating frequency characteristics as a designation of a window size, and calculating in real time from the amplitude, frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size;
an S-wave detection process for detecting S-waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
An information processing program for executing
The amplitude calculation process and the frequency analysis process are
The vertical motion component of the ground motion can be processed;
The frequency analysis process includes:
Calculating a frequency characteristic of the vertical movement component in the short-term window size and a frequency characteristic of the vertical movement component in the long-term window size, the time range of which is longer than the short-term,
The S wave detection process includes:
An information processing program that detects S waves generated by the ground motion by comparing the frequency characteristics of the short-term vertical motion component with the frequency characteristics of the long-term vertical motion component. On the computer,
An amplitude calculation process for calculating an amplitude due to ground motion;
a frequency analysis process for receiving a time range of the ground motion used for calculating frequency characteristics as a designation of a window size, and calculating in real time from the amplitude, frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size;
an S-wave detection process for detecting S-waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
An information processing program for executing
The amplitude calculation process and the frequency analysis process are
The vertical and horizontal components of the ground motion can be processed;
The frequency analysis process includes:
Calculating a frequency characteristic of a horizontal motion component in the short-term window size and a frequency characteristic of a vertical motion component in the long-term window size;
The S wave detection process includes:
An information processing program that detects S waves generated by the ground motion by comparing the frequency characteristics of the short-term horizontal motion component with the frequency characteristics of the long-term vertical motion component. The computer
Calculate the amplitude due to ground motion,
A time range of the ground motion used for calculating frequency characteristics is accepted as a designation of a window size, and frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size, are calculated in real time from the amplitude;
detecting S waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
1. An information processing method , comprising:
The computer includes :
An information processing method for calculating, in real time, frequency characteristics of the short-term ground motion and frequency characteristics of the long-term ground motion from the amplitude using an autoregressive model. The computer
Calculate the amplitude due to ground motion,
A time range of the ground motion used for calculating frequency characteristics is accepted as a designation of a window size, and frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size, are calculated in real time from the amplitude;
detecting S waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
1. An information processing method , comprising:
The computer includes :
The vertical motion component of the ground motion can be processed;
The computer includes :
Calculating a frequency characteristic of the vertical movement component in the short-term window size and a frequency characteristic of the vertical movement component in the long-term window size, the time range of which is longer than the short-term ,
An information processing method for detecting S waves generated by the ground motion by comparing the frequency characteristics of the short- term vertical motion component with the frequency characteristics of the long-term vertical motion component. The computer
Calculate the amplitude due to ground motion,
A time range of the ground motion used for calculating frequency characteristics is accepted as a designation of a window size, and frequency characteristics of the ground motion in a short-term window size and frequency characteristics of the ground motion in a long-term window size, the time range of which is longer than the short-term window size, are calculated in real time from the amplitude;
detecting S waves generated by the ground motion by comparing a frequency characteristic of the short-term ground motion with a frequency characteristic of the long-term ground motion;
1. An information processing method , comprising:
The computer includes :
The vertical and horizontal components of the ground motion can be processed;
The computer includes :
Calculating a frequency characteristic of a horizontal motion component in the short-term window size and a frequency characteristic of a vertical motion component in the long-term window size ;
An information processing method for detecting S waves generated by the ground motion by comparing the frequency characteristics of the short- term horizontal motion component with the frequency characteristics of the long-term vertical motion component.

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