JP6872794B2 - Seismic motion measuring device, seismic motion measuring system using it, and tilt correction method of seismograph - Google Patents

Description

The present invention particularly relates to a seismic motion measuring device for measuring shaking caused by an earthquake generated on the seabed, a seismic motion measuring system using the device, and a method for correcting the inclination of a seismograph.

Since it is extremely difficult to predict the occurrence of an earthquake, immediately after the occurrence of an earthquake, the initial tremors (P waves) of the earthquake are observed at a large number of pre-established earthquake observation points, and based on this observation information, they have not arrived. An earthquake warning system that notifies the arrival time of the main vibration (S wave) of an earthquake and the intensity of earthquake motion has been proposed in the area.

In recent years, attempts have been made to provide a large number of seismic observation points as described above on the seabed. In such an attempt, the seismic motion caused by an earthquake that occurred in the sea area is measured by a submarine seismometer installed offshore, and the possibility of the earthquake motion invading the land area is determined at an early stage based on the measured value (Non-Patent Documents). 1. Non-patent document 2).

FIG. 10 is a diagram illustrating an outline configuration of a seismic motion measuring device 10 having a plurality of submarine seismometers (seismometer housing 20). The seismic motion measuring device 10 is installed on the seabed and has a plurality of seismograph housings 20 for measuring seismic motion with a built-in accelerometer.

The plurality of seismograph housings 20 are connected by a cable 40. The cable 40 includes an optical fiber for transmitting and receiving optical signals, a data signal line for transmitting and receiving electric signals, a power supply line for supplying power to electric and electronic circuits in the seismograph housing 20, and the like. In the example shown in FIG. 10, both ends of the cable 40 connecting the plurality of cylindrical seismograph housings 20 communicate with a data processing device (not shown) installed in the data center 50 in the land area. The measurement data is connected so as to be possible, and the measurement data acquired by each seismograph housing 20 is processed by the data processing device.

FIG. 11 is a diagram illustrating a configuration of a seismograph housing 20 used in the seismic motion measuring device 10. An X-axis component accelerometer 25, a Y-axis component accelerometer 26, and a Z-axis component accelerometer 27 are built in the seismograph housing 20. Accelerometer data acquired by each accelerometer in the seismograph housing 20 is signal-converted by a signal conversion unit (not shown) or the like, and transmitted to a data processing device installed in the data center 50 via a cable 40. It has become.

In the above-mentioned seismic motion measuring device 10, the P wave (preliminary tremors) and S wave (primary tremors) of the seismic motion are superior to the vertical component (vertical motion) and the horizontal component, respectively. ), It is necessary to convert the seismic motion into a vertical component and two horizontal components. However, since the inclination angle and the like in the installed state are often not clear in the submarine seismometer (seismometer housing 20), a special method is required for the inclination correction.

When a 3-axis accelerometer is used as the sensor of the seismic motion measuring device 10, the measured value of the 3-axis accelerometer is set to the vertical component and two horizontal by utilizing the fact that the gravitational acceleration is measured by the accelerometer. Can be converted into components. To perform this conversion, for example, the method shown in Non-Patent Document 3 may be followed.
"Submarine Earthquake Observation System", Noriyuki Fujiwara, Kenji Hishiki, Takeshi Katayama http://jpn.nec.com/techrep/journal/g09/n04/pdf/090413.pdf#search=%27%E6%B5%B7 % E5% BA% 95% E5% 9C% B0% E9% 9C% 87% E8% A6% B3% E6% B8% AC% E3% 82% B7% E3% 82% B9% E3% 83% 86% E3 % 83% A0 +% E8% 97% A4% E5% 8E% 9F% 27 "Data processing for utilizing submarine seismometer information for early earthquake warnings of railways" Hiroyuki Miyakoshi et al., Railway Technical Research Institute Report (RTRI REPORT) Vol. 29, No. 1, Jan. 2015 "About the calculation method of the three components (upper and lower, north and south, east and west) of the system repeater type submarine seismometer off Cape Muroto and off Kushiro and Tokachi", (Germany) Japan Agency for Marine-Earth Science and Technology Earthquake Tsunami and Disaster Prevention Research Project http: // www.jamstec.go.jp/scdc/docs/info/3comp#201308a.pdf#search=%27%E5%AE%A4%E6%88%B8%E5%B2%AC%E6%B2%96+% E9% 87% A7% E8% B7% AF +% E5% 8D% 81% E5% 8B% 9D% E6% B2% 96% E3% 82% B7% E3% 82% B9% E3% 83% 86% E3% 83% A0% E4% B8% AD% E7% B6% 99% E5% 99% A8% E5% 9E% 8B% E6% B5% B7% E5% BA% 95% E5% 9C% B0% E9% 9C% 87% E8% A8% 88% 27

As described above, the P wave (preliminary tremors) of the seismic motion predominates in the vertical component (vertical tremors), and the S wave (main motion) predominates in the horizontal component. It is important to accurately grasp the vertical direction. On the other hand, since the seismograph housing 20 of the seismograph housing 10 has a cylindrical shape, the posture changes on the seabed, and the posture of each acceleration clock built in the seismograph housing 20 also changes accordingly. Therefore, the directional component of the vibration acceleration data is corrected according to the gravitational acceleration direction detected by each accelerometer.

However, in the conventional method, when obtaining the gravitational acceleration component measured on each axis of the accelerometer, it is necessary to take the average value for a certain period of time with respect to the measured value of each axis of the accelerometer, and the correction is intermittent. Can only be done. As a result, there is a problem that the acceleration value after the installation inclination correction may be discontinuous in the switching section of the average value, which is not suitable for the alarm processing that is always continuously performed. It is also conceivable that the conventional method is continuously performed using a method such as a moving average or a moving median, but it is necessary for calculating the average value when the alarm processing is performed at 0.01 second intervals. There was also a problem that the processing and storage capacity became excessive.

An object of the present invention is to provide a seismic motion measuring device capable of continuously and continuously performing tilt correction, a seismic motion measuring system using the seismic motion measuring device, and a seismograph tilt compensating method in order to solve such a problem. And.

The present invention solves the above-mentioned problems, and the seismic motion measuring device according to the present invention includes a ground motion acceleration time series acquisition means for acquiring a ground motion acceleration time series of three orthogonal components and the ground motion acceleration time series acquisition. Gravity acceleration and tilt angle are determined from the smoothing means that smoothes the ground motion acceleration time series sent from the means to obtain the smoothing time series and the smoothing time series sent from the smoothing means. An inclination angle determining means for obtaining a gravity acceleration time series and an inclination angle time series, and an inclination angle determining means for determining the validity of the gravity acceleration time series and the inclination angle time series sent from the inclination angle determining means. Using the tilt angle time series sent from the tilt angle determining means, the tilt correction of the ground acceleration time series sent from the ground motion acceleration time series acquisition means is performed to obtain a tilt corrected acceleration time series. It is characterized by comprising a correction means.

Further, the seismic motion measuring device according to the present invention is characterized in that the smoothing process in the smoothing means is a multi-stage low-pass filter process.

Further, the seismic motion measuring device according to the present invention is characterized in that the multi-stage low-pass filter processing is performed by the equation (7) using a multi-stage filter in which M-order infinite impulse response filters are connected in N-stage columns.

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
M is the order of the filter,
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is.

Further, the seismic motion measuring device according to the present invention is characterized in that the multi-stage low-pass filter processing is performed by the equation (34) using a multi-stage filter in which M-order infinite impulse response filters are connected in N-stage columns.

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
M is the order of the filter,
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is.

Further, the seismic motion measuring device according to the present invention is characterized in that equations (28) and (29) are used as calculations for a multi-stage filter in which first-order infinite impulse response filters are connected in N-stage columns.
When k = 0

ｋ>0の場合

When k> 0

ここで、
kは時間ステップ数、
X_i[k]はi段目のフィルタ処理への入力時系列、
X_i+1[k]はi段目のフィルタ処理からの出力時系列、
Nはフィルタの段数、
a_ijはフィルタ係数、
b_ijはフィルタ係数、
1≦i≦N、
である。

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is.

Further, the seismic motion measuring device according to the present invention is characterized in that equations (31), (32), and (33) are used as calculations for a multi-stage filter in which second-order infinite impulse response filters are connected in N-stage columns. To do.
When k = 0

ｋ=1の場合

When k = 1

ｋ>1の場合

When k> 1

ここで、
kは時間ステップ数、
X_i[k]はi段目のフィルタ処理への入力時系列、
X_i+1[k]はi段目のフィルタ処理からの出力時系列、
Nはフィルタの段数、
a_ijはフィルタ係数、
b_ijはフィルタ係数、
1≦i≦N、
である。

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is.

Further, the seismic motion measuring device according to the present invention is characterized in that the equation (10) is used as a coefficient of a multi-stage filter in which first-order infinite impulse response filters are connected in N-stage columns.

また、本発明に係る地震動計測装置は、２次の無限インパルス応答フィルタをN段縦列
接続した多段フィルタの係数として、式（１１）を用いることを特徴とする。

Further, the seismic motion measuring device according to the present invention is characterized in that the equation (11) is used as the coefficient of the multi-stage filter in which the second-order infinite impulse response filters are connected in N-stage columns.

ここで、
ω_i=2πf_i、
f_iはi段目のフィルタのカットオフ周波数、
h_iはi段目のフィルタのダンピング
である。

here,
ω _i = 2πf _i ,
f i is the cutoff frequency of the _{i-th stage filter,}
h i is the damping of the _{i-th stage filter.}

Further, the seismic motion measuring device according to the present invention is characterized in that the equation (12) is used as the coefficient of the multi-stage filter in which the second-order infinite impulse response filters are connected in N-stage columns.

ここで、
ω_i=2πf_i、
f_iはi段目のフィルタのカットオフ周波数、
h_iはi段目のフィルタのダンピング
である。

here,
ω _i = 2πf _i ,
f i is the cutoff frequency of the _{i-th stage filter,}
h i is the damping of the _{i-th stage filter.}

Further, the seismic motion measuring device according to the present invention is characterized in that N = 4 is used as the number of stages of the filter and f _i = 0.01 Hz is used as the cutoff frequency of the i-th stage filter.

Further, the seismic motion measuring device according to the present invention is characterized in that the gravitational acceleration and the inclination angle in the inclination angle determining means are determined by the equations (40), (41), (42) and (43). And.

here,
k is the number of time steps,
S _X [k], S _Y [k], S _Z [k] are smoothing time series,
S [k] is the gravitational acceleration time series,
β [k] and γ [k] are tilt angle time series,
Is.

Further, in the seismic motion measuring device according to the present invention, in the determination of the validity of the gravitational acceleration and the inclination angle in the inclination angle determining means, the equation (1), the equation (2), the equation (3), the equation (4), the equation. It is characterized in that it is determined to be abnormal when either (5) or (6) is satisfied.

ここで、
kは時間ステップ数、
S₀、β₀、γ₀、S_th、β_th、γ_th、ΔS_th、Δβ_th、Δγ_thは判定に用いる閾値、
ΔTは時系列のサンプリング間隔、
である。

here,
k is the number of time steps,
S ₀ , β ₀ , γ ₀ , S _th , β _th , γ _th , ΔS _th , Δβ _th , Δγ _th are threshold values used for judgment.
ΔT is the time-series sampling interval,
Is.

Further, the seismic motion measuring device according to the present invention is characterized in that the tilt correction in the tilt correction means is performed by the formulas (44), (45), and (46).

here,
k is the number of time steps,
A _X [k], A _Y [k], A _Z [k] are the ground motion acceleration time series,
A _H1 [k], A _H2 [k], A _U D [k] are tilt-corrected acceleration time series,
β [k] and γ [k] are tilt angle time series,
Is.

Further, in the seismic motion measuring device according to the present invention, the inclination correction in the inclination correction means is performed by the equations (40), (41), (47), (52), (53) and (54). It is characterized by doing.

here,
k is the number of time steps,
A _X [k], A _Y [k], A _Z [k] are the ground motion acceleration time series,
A _H1 [k], A _H2 [k], A _U D [k] are tilt-corrected acceleration time series,
S _X [k], S _Y [k], S _Z [k] are smoothing time series,
Is.

Further, the seismic motion measurement system according to the present invention is a seismic motion measurement system using the seismic motion measuring device, and is connected to a communication network so as to be communicable, and has a plurality of seismographs for measuring seismic motion and the plurality of seismographs. It is characterized in that the measured ground motion acceleration is acquired by the seismic motion measuring device via the communication network, and the tilt correction of the ground motion acceleration acquired by the tilt correction means of the seismic motion measuring device is performed.

Further, the inclination correction method of the seismometer according to the present invention includes a ground motion acceleration time series acquisition step for acquiring a ground motion acceleration time series of three orthogonal components and a smoothing process for smoothing the ground motion acceleration time series to obtain a smoothed time series. Regarding the smoothing step, the tilt angle determination step in which the gravity acceleration and the tilt angle are determined from the smoothing time series and the gravity acceleration time series and the tilt angle time series are obtained, and the gravity acceleration time series and the tilt angle time series. It is characterized by including a tilt angle determination step for determining validity and a tilt correction step for obtaining a tilt-corrected acceleration time series by performing tilt correction of the ground motion acceleration time series using the tilt angle time series. And.

Further, the method for correcting the inclination of a seismograph according to the present invention is characterized in that the smoothing process in the smoothing step is a multi-stage low-pass filter process.

The method for correcting the inclination of the seismograph according to the present invention is characterized in that the multi-stage low-pass filter processing is performed by the equation (7) using a multi-stage filter in which M-order infinite impulse response filters are connected in N-stage columns. ..

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
M is the order of the filter,
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is.

The method for correcting the inclination of the seismograph according to the present invention is characterized in that the multi-stage low-pass filter processing is performed by the equation (34) using a multi-stage filter in which M-order infinite impulse response filters are connected in N-stage columns. ..

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
M is the order of the filter,
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is.

Further, in the seismograph tilt correction method according to the present invention, a first-order infinite impulse response filter is used.
Eqs. (28) and (29) are used as the calculation of the multi-stage filter connected in columns.
When k = 0

ｋ>0の場合

When k> 0

ここで、
kは時間ステップ数、
X_i[k]はi段目のフィルタ処理への入力時系列、
X_i+1[k]はi段目のフィルタ処理からの出力時系列、
Nはフィルタの段数、
a_ijはフィルタ係数、
b_ijはフィルタ係数、
1≦i≦N、
である。

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is.

Further, in the seismograph tilt correction method according to the present invention, a second-order infinite impulse response filter is used.
Eqs. (31), (32), and (33) are used as the calculation of the multi-stage filter connected in columns.
When k = 0

ｋ=1の場合

When k = 1

ここで、
kは時間ステップ数、
X_i[k]はi段目のフィルタ処理への入力時系列、
X_i+1[k]はi段目のフィルタ処理からの出力時系列、
Nはフィルタの段数、
a_ijはフィルタ係数、
b_ijはフィルタ係数、
1≦i≦N、
である。

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is.

Further, in the seismograph tilt correction method according to the present invention, a first-order infinite impulse response filter is used.
Eq. (10) is used as the coefficient of the multi-stage filter connected in columns.

また、本発明に係る地震計の傾斜補正方法は、２次の無限インパルス応答フィルタをN
段縦列接続した多段フィルタの係数として、式（１１）を用いることを特徴とする。

Further, in the seismograph tilt correction method according to the present invention, a second-order infinite impulse response filter is used.
Eq. (11) is used as the coefficient of the multi-stage filter connected in columns.

ここで、
ω_i=2πf_i、
f_iはi段目のフィルタのカットオフ周波数、
h_iはi段目のフィルタのダンピング
である。

here,
ω _i = 2πf _i ,
f i is the cutoff frequency of the _{i-th stage filter,}
h i is the damping of the _{i-th stage filter.}

Further, in the seismograph tilt correction method according to the present invention, a second-order infinite impulse response filter is used.
Eq. (12) is used as the coefficient of the multi-stage filter connected in columns.

ここで、
ω_i=2πf_i、
f_iはi段目のフィルタのカットオフ周波数、
h_iはi段目のフィルタのダンピング
である。

here,
ω _i = 2πf _i ,
f i is the cutoff frequency of the _{i-th stage filter,}
h i is the damping of the _{i-th stage filter.}

The method for correcting the inclination of the seismograph according to the present invention is characterized in that N = 4 is used as the number of stages of the filter and f _i = 0.01 Hz is used as the cutoff frequency of the i-th stage filter.

Further, in the inclination correction method of the seismograph according to the present invention, the gravitational acceleration and the inclination angle in the inclination angle determination step are determined by the equations (40), (41), (42), and (43). It is characterized by that.

here,
k is the number of time steps,
S _X [k], S _Y [k], S _Z [k] are smoothing time series,
S [k] is the gravitational acceleration time series,
β [k] and γ [k] are tilt angle time series,
Is.

Further, in the inclination correction method of the seismograph according to the present invention, in the determination of the validity of the gravitational acceleration and the inclination angle in the inclination angle determination step, the equations (1), (2), (3), and (4) are used. ), Eq. (5), and Eq. (6) are satisfied, it is determined to be abnormal.

ここで、
kは時間ステップ数、
S₀、β₀、γ₀、S_th、β_th、γ_th、ΔS_th、Δβ_th、Δγ_thは判定に用いる閾値、
ΔTは時系列のサンプリング間隔、
である。

here,
k is the number of time steps,
S ₀ , β ₀ , γ ₀ , S _th , β _th , γ _th , ΔS _th , Δβ _th , Δγ _th are threshold values used for judgment.
ΔT is the time-series sampling interval,
Is.

Further, the inclination correction method of the seismograph according to the present invention is characterized in that the inclination correction in the inclination correction step is performed by the equations (44), (45) and (46).

here,
k is the number of time steps,
A _X [k], A _Y [k], A _Z [k] are the ground motion acceleration time series,
A _H1 [k], A _H2 [k], A _U D [k] are tilt-corrected acceleration time series,
β [k] and γ [k] are tilt angle time series,
Is.

Further, in the seismograph tilt correction method according to the present invention, the tilt correction in the tilt correction step is performed by the formula (40), the formula (41), the formula (47), the formula (52), the formula (53), and the formula ( It is characterized in that it is performed in 54).

here,
k is the number of time steps,
A _X [k], A _Y [k], A _Z [k] are the ground motion acceleration time series,
A _H1 [k], A _H2 [k], A _U D [k] are tilt-corrected acceleration time series,
S _X [k], S _Y [k], S _Z [k] are smoothing time series,
Is.

The tilt correction method of the seismic motion measuring device, the seismic motion measuring system, and the seismograph according to the present invention uses the tilt angle time series sent from the tilt angle determining means (step) from the ground motion acceleration time series acquisition means (step). A tilt correction means (step) for correcting the tilt of the sent ground motion acceleration time series and obtaining the tilt-corrected acceleration time series is provided, and the seismic motion measuring device, the seismic motion measuring system, and the seismograph according to the present invention are provided. According to the inclination correction method, the inclination correction means (step) makes it possible to perform the inclination correction of the ground motion acceleration time series at the time interval of the sampling frequency, which can contribute to quick and accurate alarm processing. Further, according to the present invention, it is not necessary to continuously perform using a method such as a moving average or a moving median, and the processing and the storage capacity required for the calculation are not excessive.

It is a block diagram of the seismic motion measuring apparatus 10 which concerns on embodiment of this invention. It is a figure which shows the main structure of the inclination correction part 120 of the seismic motion measuring apparatus 10 which concerns on embodiment of this invention. It is a flowchart which shows the algorithm of the inclination correction calculation method in the inclination correction unit 120 of this embodiment. It is a figure which shows the measurement axis of each seismograph mounted on the seismograph housing 20 of this embodiment. It is a flowchart which shows the process of the multi-stage filter which obtains _{S X [k] from A X [} k] by the smoothing means 122 of this embodiment. It is a figure explaining the measurement axis before tilt correction and after tilt correction of the seismograph housing 20 of this embodiment. It is a figure which shows the difference of the inclination correction between this embodiment and the conventional method. It is a figure which shows the structure of the outline of the seismic motion measurement system 1 which concerns on embodiment of this invention. It is a figure which shows the comparison between this embodiment and the conventional method at the time of initialization. It is a figure explaining the structure of the outline of the seismic motion measuring apparatus 10. It is a figure explaining the structure of the seismograph housing 20 used for the seismic motion measuring apparatus 10.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 is a diagram showing a main configuration of the seismic motion measuring device 10 according to the embodiment of the present invention. In the figure, 10 is a seismic motion measuring device, 100 is a processing unit, 110 is a control / calculation unit, 115 is a measuring unit, 120 is an inclination correction unit, 130 is an alarm processing unit, 150 is a power supply device, and 20 is a seismograph housing. Reference numeral 25 is an X-axis component accelerometer, 26 is a Y-axis component accelerometer, and 27 is a Z-axis component accelerometer.

The seismic motion measuring device 10 uses the component AD converters (35, 36, 37) to measure the acceleration measured by the X-axis component accelerometer 25, the Y-axis component accelerometer 26, and the Z-axis component accelerometer 27 of the seismograph housing 20. The seismic motion is measured by inputting to the control / calculation unit 110 of the processing unit 100 via. Further, the seismic motion measuring device 10 can also input the seismic motion measured by the seismograph 200 at a remote location via the communication network N. (See the example shown in FIG. 8)
In the present embodiment, the seismograph housing 20 will be described based on an example in which the seismograph housing 20 is installed on the seabed and connected to the measuring unit 115 by a cable 40. However, in the seismic motion measuring device 10 according to the present invention, the seismograph housing 20 is used. It can also handle forms that are installed on land.

For example, the ground motion acceleration time series measured by each accelerometer of the seismograph housing 20 at a sampling interval ΔT = 0.01 seconds (sampling frequency 100 Hz) is input to the measuring unit 115. Further, the measuring unit 115 transmits the ground motion acceleration time series to the tilt correction unit 120.

The processing unit 100 has a control / calculation unit 110 driven by the power supply device 150. The control / calculation unit 110 of the present embodiment gives an alarm using the measurement unit 115 that inputs / outputs the ground motion acceleration time series, the tilt correction unit 120 that performs the tilt correction of the ground motion acceleration time series, and the measured ground motion acceleration time series. It has an alarm processing unit 130 for processing the above.

The control / calculation unit 110 inputs a GNSS (Global Navigation Satellite System) signal in order to know the time accurately via the time calibration unit 147. Further, each calculated value or the like can be transmitted / received through the communication unit 141. Further, it is also possible to output a display or an alarm notifying the occurrence of an earthquake via the alarm output unit 145.

FIG. 2 is a diagram showing a main configuration of an inclination correction unit 120 of the seismic motion measuring device 10 according to the embodiment of the present invention. In the figure, 121 indicates a ground motion acceleration time series acquisition means, 122 indicates a smoothing means, 125 indicates an inclination angle determining means, 126 indicates an inclination angle determining means, and 128 indicates an inclination correction means.

In the tilt correction unit 120, the ground motion acceleration time series acquisition means 121 acquires the ground motion acceleration time series of three orthogonal components and sends the ground motion acceleration time series to the smoothing means 122 and the tilt correction means 128.

Further, the smoothing means 122 smoothes the ground motion acceleration time series sent from the ground motion acceleration time series acquisition means 121, obtains the smoothing time series, and sends it to the inclination angle determining means 125.

Further, the tilt angle determining means 125 determines the gravitational acceleration and the tilt angle from the smoothing time series sent from the smoothing means 122, obtains the gravitational acceleration time series and the tilt angle time series, and obtains the tilt angle determining means 126. It is sent to the tilt correction means 128.

Further, the tilt angle determining means 126 determines the validity of the values of the gravitational acceleration time series and the tilt angle time series sent from the tilt angle determining means 125.

Further, the inclination correction means 128 uses the inclination angle time series sent from the inclination angle determining means 125 to perform inclination correction of the ground movement acceleration time series sent from the ground motion acceleration time series acquisition means 121, and the inclination corrected acceleration. Obtain a time series and output it.

Next, the calculation method of the tilt correction performed by the tilt correction unit 120 of the seismic motion measuring device 10 will be described.

FIG. 3 is a flowchart showing an algorithm of the inclination correction calculation method in the inclination correction unit 120 of the present embodiment. The tilt correction unit 120 realizes the above calculation in each step shown in the flowchart shown in FIG.

First, in step 1, the ground motion acceleration time series of three components orthogonal to the X-axis component accelerometer 25, the Y-axis component accelerometer 26, and the Z-axis component accelerometer 27 A _X [k], A _Y [k], A _Z Get [k] (ST1). Here, k is a time step. The time-series sampling interval ΔT is 0.01 seconds (sampling frequency 100 Hz) in this embodiment.

FIG. 4 is a diagram showing measurement axes of each seismograph mounted on the seismograph housing 20 of the present embodiment. As shown in FIG. 4, the cable-type submarine seismograph of the present embodiment has three components in a tubular pressure-resistant container (seismometer housing 20) having sensitivity axes in three directions of X-axis, Y-axis, and Z-axis. It is equipped with an accelerometer.

The X-axis coincides with the major axis direction (cable axis) of the seismograph housing 20, and the X-axis, Y-axis, and Z-axis form a right-handed system orthogonal to each other. A _X [k], A _Y [k], and A _Z [k] are time series of ground motion acceleration in the X-axis, Y-axis, and Z-axis directions, respectively.

If the three-component accelerometer constitutes a left-handed system, it is possible to invert the polarity of the Z-axis component and convert it to a right-handed system. This is the time series of ground motion acceleration measured by the left-handed system B _X [k]
, B _Y [k], B _Z [k], A _X [k] = B _X [k], A _Y [k] = B _Y [k], A _Z [k] = −B _Z [k] And it is sufficient.

Subsequently, in step 2, the filtering process specified by the calculation A described later is performed, and the smoothing time series S _X [k] is _{obtained from the ground motion acceleration time series A X} [k], A _Y [k], and A _{Z [k].} , S _Y [k], S _Z [k] (ST2).

Subsequently, in step 3, according to the operation B described later, the inclination angle time series β [k] and γ [k] are obtained from _{the smoothing time series S X} [k], S _Y [k], and S _{Z [k].} (ST3).

Subsequently, in step 4, the validity of the gravitational acceleration time series S [k] and the inclination angle time series β [k] and γ [k] is determined (ST4). S [k] is the gravitational acceleration at that location, and it is unlikely that it will differ significantly from the standard gravitational acceleration. Therefore, in the present embodiment, it is determined that the obtained gravitational acceleration lacks validity when it is determined that there is a large difference from the standard gravitational acceleration.

β [k] is the pitch angle of the seismograph housing and is almost along the inclination angle of the seafloor, so it is unlikely that it will be a large angle. Therefore, in the present embodiment, when this pitch angle becomes a large angle, it is determined that the validity is lacking.

In addition, γ [k] is the roll angle of the seismograph housing, and it is unlikely that it will rotate significantly from the roll angle at the initial stage of installation. Therefore, if the required γ [k] is significantly different from the roll angle at the initial stage of installation, it is judged to be invalid.

Moreover, it is unlikely that S [k], β [k], and γ [k] all change rapidly with time.

From each of the above viewpoints, in the present embodiment, when any of the following equations is satisfied, it is determined to be abnormal and a warning is issued.

ただし、β[k]、β[k−1]、β_th、β₀、Δβ_thΔTのとりうる値の範囲は−π/2からπ/2、γ[k]、γ[k−1]、γ_th、γ₀、Δγ_thΔTのとり得る値の範囲は−πからπ、とする。

However, the range of possible values of β [k], β [k−1], β _th , β ₀ , and Δβ _th ΔT is −π / 2 to π / 2, γ [k], γ [k−1]. , Γ _th , γ ₀ , and Δγ _th ΔT have a range of possible values from −π to π.

Here, S _th , β _th , γ _th , ΔS _th , Δβ _th , and Δγ _th are threshold values used for determination. In the examples, S ₀ is the standard gravity acceleration (980.665 gal), β ₀ and γ ₀ are the initial angles of installation obtained by the conventional method, S _th is 10 gal, β _th and γ _th are 45 degrees, and ΔS _th. Was 1 gal per second, and Δβ _th and _{Δγ th} were 1 degree per second. As described above, in the present embodiment, since it is possible to determine the validity of the gravitational acceleration time series and the inclination angle time series, it is possible to verify whether the inclination correction is performed correctly.

Then, in step 5, according to the calculation C described later, from the ground motion acceleration time series A _X [k], A _Y [k], A _Z [k] and the inclination angle time series β [k], γ [k], Obtain the tilt-corrected acceleration time series A _H1 [k], A _H2 [k], and A _U D [k] (ST5).

Here, A _H1 [k] and A _H2 [k] are tilt-corrected acceleration time series in the horizontal plane, and A _UD [k] is tilt in the vertical axis (UD axis) direction. Corrected acceleration time series. In this way, the tilt correction calculation is completed by obtaining the time series of ground motion acceleration when the seismograph housing 20 is virtually installed horizontally.

Next, operation A will be described. The smoothing process uses the ground motion acceleration time series A _X [k], A _Y [k], and A _Z [k] as inputs, and the smoothing time series S _X [k], S _Y [k], and S _Z [k]. ] Is output as a low-pass filter process.

In this embodiment, as a low-pass filter for obtaining a smoothing time series, a multi-stage filter in which M-order infinite impulse response filters are connected in N-stage columns is used. The i-th stage processing of this filter is as follows, with X _i [k] as the input time series for the i-th stage filter processing and X _{i + 1} [k] as the output time series from the i-th stage filter processing. It can be realized according to the formula of.

式（７）はi段目の処理であるため、これを、iについて1を初期値として1ずつ増加させながらNまで行う。なお、

Since the equation (7) is the process of the i-th stage, this is performed up to N while increasing by 1 with 1 as the initial value for i. In addition, it should be noted.

はフィルタ係数である。また、フィルタ全体の入出力は、
入力がX₁[k]= A_X[k]のとき、出力はS_X[k]=X_N+1[k] 、
入力がX₁[k]=A_Y[k]のとき、出力はS_Y[k]=X_N+1[k] 、
入力がX₁[k]=A_Z[k]のとき、出力はS_Z[k]=X_N+1[k] 、
となる。

Is the filter coefficient. Also, the input / output of the entire filter is
When the input is X ₁ [k] = A _X [k], the output is S _X [k] = X _{N + 1 [} k],
When the input is X ₁ [k] = A _Y [k], the output is S _Y [k] = X _{N + 1} [k],
When the input is X ₁ [k] = A _Z [k], the output is S _Z [k] = X _{N + 1} [k],
Will be.

Here, as the filter coefficients of Eqs. (8) and (9), in the case of the first-order filter (M = 1), if f i is the cutoff frequency of the _{i-th stage filter,}

2次フィルタ（M=2）の場合は、f_iをi段目のフィルタのカットオフ周波数、h_iをダンピ
ングとすれば、

In the case of a second-order filter (M = 2), if f i is the cutoff frequency of the _{i- th stage filter and h i} is damping,

または、

Or

本実施形態では、N=4、M=1、を用いた。なお、i段目のフィルタごとにフィルタの次数Mを可変とする構成も可能である。

In this embodiment, N = 4 and M = 1 are used. It is also possible to make the order M of the filter variable for each filter in the i-th stage.

FIG. 5 is a flowchart showing the processing of the multi-stage filter for obtaining _{S X [k] from A X [} k] in the smoothing means 122 of the present embodiment. The smoothing means 122 realizes the above calculation in each step shown in the flowchart shown in FIG.

In the flowchart of FIG. 5, first, in step 11, as an input process to the multi-stage filter.

とする（ST11）。

(ST11).

Next, in step 12, as the first-stage filtering process,

とする（ST12）。

(ST12).

Next, in step 13, as the second-stage filtering process,

とする（ST13）。

(ST13).

Next, in step 14, as the third-stage filtering process,

とする（ST14）。

(ST14).

Next, in step 15, as the fourth-stage filtering process,

とする（ST15）。

(ST15).

Finally, in step 16, as output processing from the multi-stage filter

とする（ST16）。

(ST16).

Note that X ₁ [k−1], X ₂ [k−1], X ₃ [k−1], X ₄ [k−1], and X ₅ [k−1] are the processes of the time step k−1. It is known in.

The filter coefficient is

また、

Also,

である。

Is.

The above processing is performed for each time step. In this way, the smoothing time series S _X [k] can be obtained from the ground motion acceleration time series A _{X [k].} The same applies to the case of obtaining _{S Y} [k] and S _{Z [k] from A Y} [k] and A _Z [k]. In this embodiment, in order to obtain the _{output X 5} [k] from _{the input X 1} [k] of the multi-stage filter _{, X 1} [k−1], X ₂ [k−1], X ₃ [k−1] Since it is only necessary to store the five values of, X ₄ [k−1], and X ₅ [k−1], it is possible to reduce the storage capacity required in the hardware.

Here, the processing when the seismograph housing 20 of the seismic motion measuring device 10 is initially started will be described.

In the case of the first-order filter (M = 1), among the values required at the time of starting the device, that is, at the time step k = 0, X _i [-1] and X _{i + 1} [-1] are unknown. In the case of a second-order filter (M = 2), among the values required in time step k = 0, X _i [-1], X _i [-2], X _{i + 1} [-1], X _{i + 1} [-2] is unknown.

In such a case, conventionally, all unknown values have been set to 0 as described in P115. Subroutine (recfil) of Saito (1978) "Automatic design of recurrence digital filter". It was. (See Non-Patent Document 4: Saito, "Automatic Design of Recurrence Digital Filters," Geophysical Exploration, 32, 240--263.)
this is,
When M = 1, when the filter operation is k = 0

ｋ>0の場合

When k> 0

と式を切り替えて実行することに相当する。
また、
M=2のときは、フィルタ演算を
ｋ=0の場合

Is equivalent to switching and executing the expression.
Also,
When M = 2, when the filter operation is k = 0

ｋ=1の場合

When k = 1

ｋ>1の場合

When k> 1

と式を切り替えて実行することに相当する。

Is equivalent to switching and executing the expression.

Furthermore, instead of equation (7),

として実行することに相当する。

Equivalent to executing as.

However, in the case of smoothing processing having a long time constant as performed in the present embodiment, if an unknown value is set to 0, it takes a long time for the initial response of the filter to settle. This is not preferable for immediately starting the alarm processing. Therefore, in this embodiment, it is assumed that X _i [-1] and X _i [-2] whose _{values are unknown are equal to X i} [0]. We also _{assume that X i + 1} [-1] and X _{i + 1} [-2] are _{equal to X i + 1} [0].

this is,
When M = 1, perform filter operation

とすること、よって、
ｋ=0の場合

So,
When k = 0

ｋ>0の場合

When k> 0

と式を切り替えることに相当する。

Is equivalent to switching the expression.

Also,
When M = 2, filter operation

とすること、よって、
ｋ=0の場合

So,
When k = 0

ｋ=1の場合

When k = 1

ｋ>1の場合

When k> 1

と式を切り替えることに相当する。

Is equivalent to switching the expression.

Furthermore, instead of equation (7),

It can also be executed as.

FIG. 9 is a diagram comparing the results of smoothing by the conventional method of initializing an unknown value to 0 and smoothing by initialization of the present embodiment. According to this, it can be seen that in the method of the present embodiment, the time until the initial response of the filter is settled is shortened.

Next, operation B will be described.

As shown in FIG. 4, the cable-type submarine seismograph is X in a tubular pressure-resistant container (seismometer housing 20).
It is equipped with a three-component accelerometer that has sensitivity axes in the three directions of axis, Y axis, and Z axis. The X-axis coincides with the major axis direction (cable axis) of the seismograph housing 20, and the X-axis, Y-axis, and Z-axis form a right-handed system orthogonal to each other.

FIG. 6 is a diagram illustrating measurement axes before and after tilt correction of the seismograph housing 20 of the present embodiment. Here, as the tilt-corrected state (state A), each measurement axis of the three-component accelerometer is arranged as shown in FIG. 6 (1). That is, the X axis coincides with the reference axis H1 axis in the horizontal plane, and the Z axis coincides with the vertical direction (UD axis) with the upward direction as positive. At this time, the Y axis coincides with the H2 axis in the horizontal plane. Here, it is assumed that each of the X, Y, and Z axes is fixed to the seismograph housing 20 instead of the coordinate system.

Next, consider the state B shown in FIG. 6 (2) as a state in which the state A is rotated by β [k] around the Y axis. Here, β [k], which is the rotation angle around the Y-axis, is the inclination angle (pitch angle) of the seismograph housing 20 from the horizontal plane in the time step k. Further, consider the state C shown in FIG. 6 (3) as a state in which the state B is rotated by γ [k] around the X axis. Here, γ [k], which is the rotation angle around the X axis.
Is the rotation angle (roll angle) around the long axis of the seismograph housing 20 in the time step k. The rotation angle around the Z axis is always 0. The state C corresponds to the state in which the tilt correction is not performed.

The transition from state A to state C is made by first rotating β [k] around the Y axis and then γ [k] around the X axis. Therefore, A _X [k], A _Y [k], A _Z [k] are the acceleration time series in the X, Y, Z axis directions, A _H1 [k], A _H2 [k], A _U D [k]. Assuming that the acceleration time series is in the H1, H2, and UD axis directions, the rotation matrix is used.

However,

Is converted by. Also, from state C to state A, first, -γ [k] rotation around the X axis,
Next, the transition is made by rotating −β [k] around the Y axis. Therefore,

Is converted by.

When a 3-axis accelerometer is used as a sensor for the submarine seismograph (seismometer housing 20), it is possible to obtain the installation tilt angle by using the gravitational acceleration measured by the accelerometer. ..

Ground motion acceleration time series A _X [k], A _Y [k], A _Z [k] smoothed smoothing time series S _X [k], S _Y [k], S _Z [k] from the vibration component Is removed, so only the effect of gravitational acceleration remains. At this time, the following holds from equations (38) and (A _H1 [k] = 0, A _H2 [k] = 0, A _UD [k] = _AG ).

Where A _G is the gravitational acceleration at that location,

Can be calculated with.
At this time,

Then, according to the equation (36), the equation (37), the equation (39), the equation (40), and the equation (41),

Will be.

Equation (43) can be obtained as γ [k] = atan2 (G _Y , G _Z ) by using the 4-quadrant inverse tangent function (atan2). It is assumed that β [k] takes a value from −π / 2 to π / 2 and γ [k] takes a value from −π to π.

In this way, using Eqs. (40), (41), (42), and (43), S [k], β [k], and γ [k] are S _X [k], Calculated from S _Y [k] and S _Z [k].

Next, the operation C will be described.
If β [k] and γ [k] can be continuously obtained, the inclination can be continuously corrected by the equation (38).

From equation (36), equation (37), equation (38),

Will be.

Also,

given that,

From, formula (44), formula (45), formula (46),

And can be expressed without using β [k] and γ [k].

In this way, using equations (44), (45), and (46), the ground motion acceleration time series A _X [k], A _{Y [} k], A _Z [k] and the inclination angle time series β From [k] and γ [k], the tilt-corrected acceleration time series A _H1 [k], A _H2 [k], and A _U D [k] can be obtained.

Further, by using the equations (52), (53), and (54), the ground motion acceleration time series A _X [k], A _Y [k], and A _Z [k] and the smoothing time series S _X [k] are used. ], S _Y [k], S _Z [k], the tilt-corrected acceleration time series A _H1 [k], A _H2 [k], and A _U D [k] can be obtained.

FIG. 7 is a diagram showing a horizontal component (H2 axis component) of the seismic motion that has been tilt-corrected by the method of the present embodiment and a horizontal component (H2 axis component) of the seismic motion that has been tilt-corrected by the conventional method based on the average value processing for 60 seconds. Is. It can be seen that the tilt correction of the present embodiment is continuously corrected as compared with the conventional method.

Next, other embodiments of the present invention will be described.

FIG. 8 is a diagram showing a case where the seismic motion measuring device 10 of the present embodiment is constructed as a system. In the figure, 10 indicates a seismic motion measurement system, 200 indicates a seismograph, and N indicates a communication network.

In this seismic motion measurement system 1, the seismic motion observed by a plurality of seismographs 200 is transferred to another device or a data center through the communication network N, and the seismic motion measuring device having an inclination correction unit 120 at a place away from the observation point. The inclination is corrected by 10.

Here, a plurality of seismic motion measuring devices 10 that perform tilt correction processing may exist on the communication network N. Even in such a seismic motion measurement system 1, the advantage of this method that tilt correction can be continuously executed at all times is utilized.

As described above, the seismic motion measuring device 10, the seismic motion measuring system 1, and the seismograph tilt correction method according to the present invention use the tilt angle time series sent from the tilt angle determining means (step) to obtain the ground motion acceleration time series. The seismic motion measuring device 10 and seismic motion measurement according to the present invention are provided with the tilt correction means (step) for correcting the tilt of the ground motion acceleration time series sent from (step) and obtaining the tilt corrected acceleration time series. According to the tilt correction method of the system 1 and the seismograph, the tilt correction means (step) enables the tilt correction of the ground motion acceleration time series at the time interval of the sampling frequency, which contributes to prompt and accurate alarm processing. Can be done. Further, according to the present invention, it is not necessary to continuously perform using a method such as a moving average or a moving median, and the processing and the storage capacity required for the calculation are not excessive.

1 ... Seismic motion measurement system 10 ... Seismic motion measuring device 20 ... Seismometer housing 25 ... X-axis component accelerometer 26 ... Y-axis component accelerometer 27 ... Z-axis component accelerometer 35 ... AD converter 36 ... AD converter 37 ... AD converter 40 ... Cable 50 ... Data center 100 ... Processing unit 110 ... Control / calculation unit 115 ... Measurement Unit 120 ... Tilt correction unit 121 ... Ground motion acceleration time series acquisition means 122 ... Smoothing means 125 ... Tilt angle determining means 126 ... Tilt angle determining means 128 ... Tilt correction means 130 ...・ ・ Alarm processing unit 141 ・ ・ ・ Communication unit 142 ・ ・ ・ Display unit 145 ・ ・ ・ Alarm output unit 147 ・ ・ ・ Time calibration unit 149 ・ ・ ・ Power supply unit 150 ・ ・ ・ Power supply device 153 ・ ・ ・ Storage battery 200 ・・ ・ Seismometer N ・ ・ ・ Communication network

Claims (29)

A ground motion acceleration time series acquisition means for acquiring a ground motion acceleration time series of three orthogonal components, and a ground motion acceleration time series acquisition means.
A smoothing means for obtaining a smoothing time series by smoothing the ground acceleration time series sent from the ground acceleration time series acquisition means.
An inclination angle determining means for determining the gravitational acceleration and the inclination angle from the smoothing time series sent from the smoothing means and obtaining the gravitational acceleration time series and the inclination angle time series.
An inclination angle determining means for determining the validity of the gravitational acceleration time series and the inclination angle time series sent from the inclination angle determining means.
Using the inclination angle time series sent from the inclination angle determining means, the inclination correction of the ground motion acceleration time series sent from the ground motion acceleration time series acquisition means is performed, and the inclination correction to obtain the inclination corrected acceleration time series is obtained. A seismic motion measuring device characterized by comprising means. The seismic motion measuring device according to claim 1, wherein the smoothing process in the smoothing means is a multi-stage low-pass filter process. The seismic motion measuring apparatus according to claim 2, wherein the multi-stage low-pass filter processing is performed by the equation (7) using a multi-stage filter in which M-order infinite impulse response filters are connected in N-stage columns.

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
M is the order of the filter,
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is. The seismic motion measuring apparatus according to claim 2, wherein the multi-stage low-pass filter processing is performed by the equation (34) using a multi-stage filter in which M-order infinite impulse response filters are connected in N-stage columns.

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
M is the order of the filter,
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is. As an operation of a multi-stage filter in which first-order infinite impulse response filters are connected in N-stage columns, the equation (
28) The seismic motion measuring device according to claim 3, wherein the formula (29) is used.
When k = 0

When k> 0

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is. As an operation of a multi-stage filter in which a second-order infinite impulse response filter is connected in N-stage columns, the equation (
31), the seismic motion measuring device according to claim 3, wherein the formula (32) and the formula (33) are used.
When k = 0

When k = 1

When k> 1

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is. As the coefficient of a multi-stage filter in which first-order infinite impulse response filters are connected in N-stage columns, the equation (
The seismic motion measuring device according to any one of claims 3 to 5, wherein 10) is used.

As the coefficient of a multi-stage filter in which a second-order infinite impulse response filter is connected in N-stage columns, the equation (
11) The seismic motion measuring device according to claim 3, claim 4, or claim 6, wherein 11) is used.

here,
ω _i = 2πf _i ,
f i is the cutoff frequency of the _{i-th stage filter,}
h i is the damping of the _{i-th stage filter.} As the coefficient of a multi-stage filter in which a second-order infinite impulse response filter is connected in N-stage columns, the equation (
12) The seismic motion measuring device according to claim 3, claim 4, or claim 6, wherein the seismic motion measuring device according to claim 4 or claim 6 is used.

here,
ω _i = 2πf _i ,
f i is the cutoff frequency of the _{i-th stage filter,}
h i is the damping of the _{i-th stage filter.} N = 4 is used as the number of filter stages, and f _i = 0.01Hz is used as the cutoff frequency of the i-th stage filter.
The seismic motion measuring device according to claim 7, wherein the seismic motion measuring device is used. Any of claims 1 to 10, wherein the gravitational acceleration and the inclination angle in the inclination angle determining means are determined by the equations (40), (41), (42), and (43). The seismic motion measuring device according to item 1.

here,
k is the number of time steps,
S _X [k], S _Y [k], S _Z [k] are smoothing time series,
S [k] is the gravitational acceleration time series,
β [k] and γ [k] are tilt angle time series,
Is. In the determination of the validity of the gravitational acceleration and the inclination angle in the inclination angle determining means, any one of the equations (1), (2), (3), (4), (5), and (6). The seismic motion measuring device according to any one of claims 1 to 11, wherein the seismic motion measuring device is determined to be abnormal when the condition is satisfied.

here,
k is the number of time steps,
S ₀ , β ₀ , γ ₀ , S _th , β _th , γ _th , ΔS _th , Δβ _th , Δγ _th are threshold values used for judgment.
ΔT is the time-series sampling interval,
Is. The seismic motion measuring device according to any one of claims 1 to 12, wherein the tilt correction in the tilt correction means is performed by the formulas (44), (45), and (46).

here,
k is the number of time steps,
A _X [k], A _Y [k], A _Z [k] are the ground motion acceleration time series,
A _H1 [k], A _H2 [k], A _U D [k] are tilt-corrected acceleration time series,
β [k] and γ [k] are tilt angle time series,
Is. Claims 1 to claim that the tilt correction in the tilt correction means is performed by the formulas (40), (41), (47), formula (52), formula (53), and formula (54). Item 12. The seismic motion measuring device according to any one of items 12.

here,
k is the number of time steps,
A _X [k], A _Y [k], A _Z [k] are the ground motion acceleration time series,
A _H1 [k], A _H2 [k], A _U D [k] are tilt-corrected acceleration time series,
S _X [k], S _Y [k], S _Z [k] are smoothing time series,
Is. A seismic motion measurement system using the seismic motion measuring device according to any one of claims 1 to 14.
Multiple seismographs that are communicably connected to a communication network and measure seismic motion,
It is characterized in that the ground motion acceleration measured by the plurality of seismographs is acquired by the seismic motion measuring device via the communication network, and the tilt correction of the ground motion acceleration acquired by the tilt correction means of the seismic motion measuring device is performed. Seismic motion measurement system. The ground motion acceleration time series acquisition step for acquiring the ground motion acceleration time series of three orthogonal components, and the ground motion acceleration time series acquisition step.
A smoothing step of smoothing the ground motion acceleration time series to obtain a smoothing time series,
A tilt angle determination step in which the gravitational acceleration and the tilt angle are determined from the smoothing time series and the gravitational acceleration time series and the tilt angle time series are obtained.
An inclination angle determination step for determining the validity of the gravitational acceleration time series and the inclination angle time series,
Using the inclination angle time series, the inclination correction step of performing the inclination correction of the ground motion acceleration time series and obtaining the inclination corrected acceleration time series, and the inclination correction step.
A method for correcting the inclination of a seismograph, which comprises. The method for correcting the inclination of a seismograph according to claim 16, wherein the smoothing process in the smoothing step is a multi-stage low-pass filter process. The inclination correction method for a seismograph according to claim 17, wherein the multi-stage low-pass filter processing is performed by the equation (7) using a multi-stage filter in which M-order infinite impulse response filters are connected in N-stage columns.

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
M is the order of the filter,
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is. The inclination correction method for a seismograph according to claim 17, wherein the multi-stage low-pass filter processing is performed by the equation (34) using a multi-stage filter in which M-order infinite impulse response filters are connected in N-stage columns.

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
M is the order of the filter,
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is. As an operation of a multi-stage filter in which first-order infinite impulse response filters are connected in N-stage columns, the equation (
28), The method for correcting the inclination of a seismograph according to claim 18, wherein the formula (29) is used.
When k = 0

When k> 0

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is. As an operation of a multi-stage filter in which a second-order infinite impulse response filter is connected in N-stage columns, the equation (
31), the method for correcting the inclination of a seismograph according to claim 18, wherein the equations (32) and (33) are used.
When k = 0

When k = 1

When k> 1

here,
k is the number of time steps,
X _i [k] is the input time series for the i-th stage filtering,
X _{i + 1} [k] is the output time series from the i-th stage filtering process.
N is the number of filter stages,
a _ij is the filter coefficient,
b _ij is the filter coefficient,
1 ≤ i ≤ N,
Is. As the coefficient of a multi-stage filter in which first-order infinite impulse response filters are connected in N-stage columns, the equation (
The method for correcting the inclination of a seismograph according to any one of claims 18 to 20, wherein 10) is used.

As the coefficient of a multi-stage filter in which a second-order infinite impulse response filter is connected in N-stage columns, the equation (
11) The method for correcting the inclination of a seismograph according to claim 18, claim 19, or claim 21, wherein 11) is used.

here,
ω _i = 2πf _i ,
f i is the cutoff frequency of the _{i-th stage filter,}
h i is the damping of the _{i-th stage filter.} As the coefficient of a multi-stage filter in which a second-order infinite impulse response filter is connected in N-stage columns, the equation (
12) The method for correcting the inclination of a seismograph according to claim 18, claim 19, or claim 21, wherein 12) is used.

here,
ω _i = 2πf _i ,
f i is the cutoff frequency of the _{i-th stage filter,}
h i is the damping of the _{i-th stage filter.} N = 4 is used as the number of filter stages, and f _i = 0.01Hz is used as the cutoff frequency of the i-th stage filter.
22. The method for correcting the inclination of a seismograph according to claim 22. Any of claims 16 to 25, wherein the gravitational acceleration and the inclination angle in the inclination angle determination step are determined by the equations (40), (41), (42), and (43). The method for correcting the inclination of the seismograph according to item 1.

here,
k is the number of time steps,
S _X [k], S _Y [k], S _Z [k] are smoothing time series,
S [k] is the gravitational acceleration time series,
β [k] and γ [k] are tilt angle time series,
Is. In the determination of the validity of the gravitational acceleration and the inclination angle in the inclination angle determination step, any one of the equations (1), (2), (3), (4), (5), and (6). The method for correcting the inclination of a seismograph according to any one of claims 16 to 26, wherein an abnormality is determined when the condition is satisfied.

here,
k is the number of time steps,
S ₀ , β ₀ , γ ₀ , S _th , β _th , γ _th , ΔS _th , Δβ _th , Δγ _th are threshold values used for judgment.
ΔT is the time-series sampling interval,
Is. The tilt correction of the seismograph according to any one of claims 16 to 27, wherein the tilt correction in the tilt correction step is performed by the formulas (44), (45), and (46). Method.

here,
k is the number of time steps,
A _X [k], A _Y [k], A _Z [k] are the ground motion acceleration time series,
A _H1 [k], A _H2 [k], A _U D [k] are tilt-corrected acceleration time series,
β [k] and γ [k] are tilt angle time series,
Is. Claims 16 to 16, wherein the tilt correction in the tilt correction step is performed by the formula (40), the formula (41), the formula (47), the formula (52), the formula (53), and the formula (54). Item 2. The method for correcting the inclination of the seismograph according to any one of items 27.

here,
k is the number of time steps,
A _X [k], A _Y [k], A _Z [k] are the ground motion acceleration time series,
A _H1 [k], A _H2 [k], A _U D [k] are tilt-corrected acceleration time series,
S _X [k], S _Y [k], S _Z [k] are smoothing time series,
Is.

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