JP2006194619A - Real-time earthquake response waveform estimation method utilizing real-time earthquake information - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a real-time earthquake response waveform estimation method utilizing real-time earthquake information capable of estimating earthquake response waveform at an assumed point in real time before the motion of an earthquake reaches a specific assumed point when an earthquake occurs and hence predicting the occurrence of an earthquake disaster more precisely. <P>SOLUTION: The transfer function of the earthquake motion between an earthquake observation point between a predicted region and the assumed point for a plurality of earthquake occurrence predicted regions, and the assumed point is obtained in advance. The transfer function to an earthquake occurrence prediction region closest to an epicenter position is extracted from real-time earthquake information related to the epicenter position sensed at the time of the occurrence of an earthquake. Then, an earthquake motion waveform obtained at an observation point at the time of the occurrence of an earthquake is acquired in real time, and an earthquake response waveform at the assumed point is estimated in real time before the motion of the earthquake reaches the assumed point from the transfer function. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention provides real-time earthquake response waveform estimation using real-time earthquake information that enables real-time estimation of an earthquake response waveform at an assumed point before the earthquake motion reaches a specific assumed point when an earthquake occurs. It is about the method.

  As is well known, seismic waves include P-waves (initial tremors) with a fast propagation speed and S-waves (major movements) with a large amplitude that cause a large vibration but slow propagation speed. In recent years, the P wave detected near the epicenter at the time of the earthquake, such as the Earthquake Early Warning (Nowcast) of the Japan Meteorological Agency and the Real-time Earthquake Information Utilization System (REIS) of the National Research Institute for Earth Science and Disaster Prevention, Various systems have been developed to obtain real-time earthquake information immediately.

  In addition, a network system that distributes real-time earthquake information obtained by the system via the Internet or satellite communication is also being put into practical use. By using the real-time earthquake information, the magnitude of the earthquake that occurred within a few seconds after the earthquake occurred. And information on the location of the epicenter.

On the other hand, at a point that is several kilometers away from the epicenter, there is a margin of several seconds to several tens of seconds before the main motion of the ground motion caused by the S wave arrives. For this reason, research on so-called real-time earthquake disaster prevention that uses the margin time to prevent occurrence of earthquake damage using the real-time earthquake information has been actively conducted.
JP-A-2003-114281

  However, currently, the real-time earthquake information is limited to information such as the magnitude of the earthquake that occurred, the location of the epicenter, and the depth of the seismic source. However, there is a problem that it is impossible to know what kind of ground motion will occur before the earthquake reaches, such as the change of ground motion, the arrival time of the peak, or the duration.

  The present invention has been made in view of such circumstances, and when an earthquake occurs, the earthquake response waveform at the assumed point can be estimated in real time before the earthquake motion reaches a specific assumed point. It is an object of the present invention to provide a real-time earthquake response waveform estimation method using real-time earthquake information that can predict the occurrence of the earthquake with higher accuracy.

  In order to solve the above-described problem, the invention according to claim 1 is a method for estimating an earthquake response waveform at an assumed point in real time before the earthquake motion reaches a specific assumed point when an earthquake occurs. In advance, a seismic observation point between the prediction area and the assumption point for a plurality of earthquake occurrence prediction areas and a transfer function of the ground motion between the assumption point are obtained in advance and detected when an earthquake occurs. The transfer function for the predicted earthquake occurrence area closest to the source location is extracted from the real-time earthquake information related to the source location, and the information on the seismic motion waveform obtained at the observation point is obtained in real time, and the transmission is performed. An earthquake response waveform at the assumed point is estimated in real time based on a function.

  In this case, the invention according to claim 2 is characterized in that the transfer function is a seismic motion waveform x (t) (at the earthquake observation point with respect to the earthquake occurrence prediction area obtained by past earthquake observation records and / or theoretical simulations. t is time (seconds), and the same applies hereinafter) and the seismic wave waveform y (t) at the above assumed point. Are Fourier transforms of x (t) and y (t), f is the frequency (Hz), and so on), and an approximate function W (f) of the frequency transfer function F (f) is obtained. This is a recurrence formula obtained by converting this into a differential equation of time by inverse Laplace transform, and further discretizing the differential equation at a time interval Δt, and the seismic motion waveform obtained at the observation point over time Information into the recurrence formula The Rukoto, is characterized in that calculating the seismic response waveform at the assumed point in real time.

In addition, the above assumption points are built on the ground, at any position on the ground, such as in the ground such as the earthquake base (Vs = 3 km / s) or engineering base (Vs = 700 m / s). It is possible to take any position of the constructed structure (pile, foundation, floor, etc.) and any position of the equipment installed in the structure (including installation stand of the equipment, seismic isolation floor, etc.). Is possible.
The earthquake occurrence prediction area refers to a specific earthquake occurrence prediction point or an earthquake occurrence prediction area having a certain area including a plurality of points concerned.

  According to the first or second aspect of the present invention, when an earthquake occurs, first, for example, from information related to the epicenter position of real-time earthquake information obtained by a P wave indicating initial tremor detected at the time of the earthquake, Of the many transfer functions prepared above, transfer functions for the predicted earthquake occurrence area closest to the epicenter location are extracted, and then the seismic motion waveforms obtained at the seismic observation point used to calculate this transfer function are extracted. By acquiring in real time, the seismic response waveform at the assumed point can be estimated in real time before the ground motion of the earthquake reaches the assumed point.

  As a result, a specific seismic response waveform such as the change in ground motion, peak arrival time, or duration at the above assumption point can be obtained tens of seconds before the arrival of the earthquake. Can be suppressed with higher accuracy.

FIGS. 1-7 is for demonstrating one Embodiment of the real-time earthquake response waveform estimation method using the real-time earthquake information based on this invention.
In this real-time earthquake response waveform estimation method, as shown in FIG. 2 in advance, a plurality of earthquake occurrence prediction points P ₁ , P ₂ , P ₃ or a specific assumption point Y for estimating the earthquake response waveform, An earthquake occurrence prediction area A ₁ , A ₂ , A ₃ including these points P ₁ , P ₂ , P ₃ is set. Further, seismic observation points B ₁ and B ₂ between the prediction areas A ₁ , A ₂ and A ₃ and the assumed point Y are selected.

Then, the frequency transfer function F (f) of the ground motion between the earthquake observation points B ₁ and B ₂ and the assumed point Y with respect to these earthquake occurrence prediction areas A ₁ , A ₂ and A ₃ is obtained (FIG. 3). STEP1). Note that f is the frequency (Hz).
Here, when the assumed point Y is the ground surface Y ₁ of the building as shown in FIG. 1, the frequency transfer function F ₁ (f) is observed in the seismic observation network currently deployed throughout Japan. It can be created using seismic observation records and seismic motion waveforms created by theoretical ground motions by simulation.

For example, assuming that an observation point B ₁ , an assumed point Y ₁ and a ground motion waveform of an earthquake occurring in area A ₁ are x (t) and y (t) as functions of time t, the frequency transfer function is F _1. (F) can be obtained by the following Equation 1.

Here, Y (f) is the Fourier transform of the earthquake motion waveform y (t), and X (f) is the Fourier transform of the earthquake motion waveform x (t). The actual seismic motion waveform is a discrete value x _n , y _n (x _n = n · Δt, y _n = n · Δt: n = 0, 1, 2,..., N for each sampling time (Δt seconds). −1), the frequency transfer function F ₁ (f) is obtained by performing a discrete Fourier transform according to the following equation (2).

In addition, since seismic motion is affected by various mechanisms such as the failure mechanism of the fault, the deep underground structure that is the propagation path, the surface ground, etc., the observed seismic motion waveform differs to some extent even in the case of earthquakes of the same epicenter location and scale. It will be a thing. Therefore, it is more versatile to use an averaged frequency transfer function obtained for many earthquake motions than to use the frequency transfer function F ₁ (f) obtained for one earthquake motion. It is preferable.

Next, as shown in STEP 2 of FIG. 3, an approximate function Y (2πf · j) / X (2πf · j) = W (s) of the obtained frequency transfer function F ₁ (f) is obtained. Note that s = j · ω.
At this time, the orders n and m in the approximate function W (s) are orders sufficient to approximate the frequency transfer function F ₁ (f) and are selected as low as possible.

Then, by performing inverse Laplace transform on the approximate function W (s), a differential equation of time is obtained as shown in STEP 3.
As a result, the following differential equation is obtained in which the variable at the assumed point Y ₁ is y and the variable at the observation point B ₁ is x. Here, the superscript (n) represents the nth order differentiation.
^{y (n) (t) +} a 1 y (n-1) (t) + ... + a n-1 y (1) (t) + a n y (t)
= B ₁ x ^(m-1) (t) + ... + b _m-1 x ⁽¹⁾ (t) + b _m x (t)

And further, as shown in STEP4 in FIG. 3, the differential equation, by discretizing the time intervals Δt of data sampling in seismic stations B _1, and the ground motion waveforms of seismic stations B ₁ and the input data, assuming The following recurrence formula using the seismic motion response waveform at the point Y ₁ as output data can be derived.

y (k) = c ₁ y (k−1) +... + c _n y (k−n)
+ D ₁ x (k−1) +... + D _m x (k−m)
Here, k · Δt = t. Incidentally, at many seismic observation points B, the seismic motion is sampled at 200 Hz (200 times / second).

By using the recurrence formula obtained in this way, the seismic response waveform at the assumed point Y ₁ is delayed from the seismic observation waveform at the seismic observation point B ₁ by a discrete time step (Δt seconds). Can be estimated in real time.

Next, for other earthquake occurrence prediction areas A ₂ and A ₃ , frequency transfer functions F ′ (f), F ″ (f), etc. of the earthquake motion between the earthquake observation point B ₂ and the assumed point Y ₁ are obtained. 3, a recurrence formula is prepared in the same manner by discretizing at the time interval Δt.

Further, the assumed point Y is not limited to the above-mentioned point Y ₁ on the ground surface, but is installed in an arbitrary point Y ₂ of the structure 1 constructed on the ground or in the structure 1 as shown in FIG. It can also be set to an arbitrary point Y ₃ of the installed equipment 2.
When such assumed points Y ₂ and Y ₃ are selected, the frequency transfer functions F ₂ (f) and F ₃ (f) are similarly observed in the observation points B ₁ and B ₂ and the structure 1. It can be created using observation records of seismometers installed in the equipment 2 and a theoretical transfer function of the structure by simulation.

For example, the frequency transfer functions F ₂ (f) and F ₃ (f) may be directly obtained from the earthquake observation records of the observation point B ₁ and the assumed points Y ₂ and Y ₃ by the Fourier transform of Equation 2. Alternatively, as shown in FIG. 7, the theoretical transfer function D ₂ of the structure alone from the ground surface to the assumed point calculated separately is added to the frequency transfer function F ₁ (f) obtained for the assumed point Y ₁ on the ground surface. It can also be obtained by multiplying (f) and D ₃ (f).

Next, a method for estimating the earthquake response waveform at the assumed point Y ₁ or the like in real time at the time of the occurrence of an earthquake will be described using the many recurrence formulas prepared in advance in STEPs 1 to 4 above.
As shown in FIG. 4, first, from the information on hypocenter of real-time seismic information obtained by the P-wave indicating the initial tremor is detected when the earthquake occurred, among the vibration generating predictive area regions A _1, A _2, A ₃ In order to determine the nearest prediction area (for example, area A ₁ ) including the epicenter position, the recurrence formula created for the prediction area A ₁ is extracted and initialized.

Next, the seismic motion waveform obtained at the observation point (in this case, observation point B ₁ ) is acquired in real time at a time interval of Δt, and sequentially input to the above recurrence formula. Then, the value y (k) of the ground motion at the assumed point Y ₁ at a certain time k is the value of the ground motion waveform x (k−1), x (k−2) at the observation point B ₁ obtained before that time. sequentially calculated from x (k-m) and its value of previously obtained seismic motion waveform of supposition point Y ₁ is y (k-1) ... y (k-n).

As a result, as shown in FIGS. 5 and 6, before the ground motion of the earthquake reaches the assumed point Y _1, it is possible to estimate the seismic response waveform at the envisaged point Y ₁ in real time.
Accordingly, since a specific earthquake response waveform such as a change in ground motion at the assumed point Y ₁ , the arrival time of the peak, or the duration time can be obtained tens of seconds before the arrival of the earthquake, the assumed point Y ₁ The occurrence of earthquake damage can be suppressed with higher accuracy.

Next, analysis examples performed for verifying the usefulness of the present invention will be described below.
FIG. 8A shows an acceleration transfer function between the observation point B and the assumed point Y obtained from the observation record, and an approximation function obtained therefrom. In this analysis example, a recurrence formula for real-time prediction was created from the approximate function of this transfer function, and the predicted waveform of the assumed point Y by the real-time prediction system and the observed waveform were compared using the actual seismic motion waveform.

First, FIG. 8B shows the seismic observation waveform at observation point B. FIG. FIGS. 9A and 9B show a comparison between the predicted earthquake response waveform obtained step by step using the recurrence formula of the real-time prediction system and the actual observed waveform. .
As is clear from these results, both correspond well, and the validity of the estimation method according to the present invention could be confirmed.

  Note that the above method generally deals with other input multiple output (multiple observation points, multiple assumption points) systems, and in that case, transfer characteristics between each observation point and each assumption point. (If p inputs and q outputs, the transfer function is p × q), convert them into a state equation (differential equation), and discretize the state equation in time steps (Δt seconds) do it.

It is a schematic block diagram which shows the position of the assumption point which can be selected in one Embodiment of this invention. It is a top view which shows the positional relationship of the several earthquake occurrence prediction area at the time of calculating | requiring a transfer function, an earthquake observation point, and an assumption point. It is a flowchart until it obtains the recurrence formula discretized from the frequency transfer function. It is a flow figure for calculating an earthquake response waveform in an assumption point at the time of the occurrence of an earthquake by the above recurrence formula. It is a schematic diagram showing obtaining the seismic response waveform at an assumed point from the waveform of an observation point using this method. It is a schematic diagram showing estimating the earthquake response waveform in an assumption point in real time before the arrival of earthquake motion. It is a schematic diagram showing the calculation method of the transfer function at the time of setting the equipment in the structure or the equipment in a structure as an assumption point. FIG. 8A shows an analysis example according to the present invention, and FIG. 8A shows an acceleration transfer function between observation points obtained from observation records and assumed points, and an approximate function obtained therefrom. ) Shows the seismic waveform at the observation point. The results of the above analysis are shown. (A) is the actual observed waveform at the observation point, (b) is the predicted earthquake response waveform obtained step by step using the recurrence formula of the real-time prediction system, and This is a comparison with the observed values.

Explanation of symbols

1 Structure 2 Equipment A ₁ , A ₂ , A ₃ Earthquake Prediction Area B ₁ , B ₂ Earthquake Observation P ₁ , P ₂ , P ₃ Earthquake Prediction Y, Y ₁ , Y ₂ , Y ₃ Assumption

Claims (2)

When an earthquake occurs, before the seismic motion reaches a specific assumption point, a method for estimating the earthquake response waveform at the assumption point in real time,
The seismic motion transfer function between the predicted area and the estimated point for the predicted area and the estimated point for a plurality of predicted earthquake occurrence areas is obtained in advance, and the seismic position detected at the time of the earthquake is calculated. From the real-time earthquake information, extract the transfer function for the predicted earthquake occurrence area closest to the source location, then acquire the information of the seismic waveform obtained at the observation point in real time, and based on the transfer function A real-time earthquake response waveform estimation method using real-time earthquake information, characterized in that an earthquake response waveform at the assumed point is estimated in real time. The transfer function is the seismic motion waveform x (t) (t is time (seconds), the same applies hereinafter) at the seismic observation point with respect to the earthquake occurrence prediction region obtained by past earthquake observation records and / or theoretical simulations, and the above assumption. Frequency transfer function F (f) = Y (f) / X (f) (X (f) and Y (f) are Fourier transforms of x (t) and y (t), respectively, from the ground motion waveform y (t) at the point Where f is the frequency (Hz), and so on), an approximate function W (f) of the frequency transfer function F (f) is obtained, and this is converted into a differential equation of time by inverse Laplace transform, Furthermore, a recurrence formula obtained by discretizing the differential equation at a time interval Δt,
The real-time earthquake response waveform at the assumed point is calculated in real time by inputting the temporal information of the seismic motion waveform obtained at the observation point into the recurrence formula. Real-time earthquake response waveform estimation method using earthquake information.

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