JP6887630B2 - Seismic motion estimation method - Google Patents

Description

The present invention relates to a method for estimating ground motion.

For earthquake countermeasures, it is necessary to estimate how much seismic motion will occur in the event of an earthquake. Conventionally, as such a method for estimating ground motion, the geological characteristics of the surface layer existing between the underground base surface and the ground surface are grasped, and the seismic motion parameters on the ground surface are obtained from the ground data and the seismic waves calculated on the base surface. A method for estimating seismic motion to be calculated is known (for example, Non-Patent Document 1 and Non-Patent Document 2).

When performing wide-area seismic motion estimation using such a seismic motion estimation method, the target area is first divided into fixed sections (hereinafter referred to as "mesh"), and a ground model is created from the ground data inside and outside each mesh. However, in the above-mentioned conventional seismic motion estimation method, since the ground data in the same mesh is represented by a single ground model, the spatial distribution of the seismic motion parameters is ignored, and an accurate seismic motion estimation map cannot be created.

In order to solve this problem, the estimated specific point seismic motion parameter, which is an index of the seismic motion at the point where the ground data is collected, is calculated, and the interpolated seismic motion parameter interpolated at an arbitrary point or an arbitrary area by the kriging method, and its interpolation accuracy. A method for estimating ground motion has been proposed (Patent Document 1). According to this seismic motion estimation method, it is possible to estimate the distribution of seismic motion parameters in an arbitrary space and estimate the accuracy thereof. In addition, the seismic motion parameters measured in the actual earthquake that actually occurred and the seismic motion parameters reproduced from the records actually measured by the epicenter estimation of the earthquake, the engineering base surface, and the seismograph installed deeper than this. More significant statistical calibration is possible.

Japanese Unexamined Patent Publication No. 2005-156273

P. B. Schnabel, J. Lysmer and H. B. Seed: SHAKE a computer program for earthquake response analysis of horizontally layered site, EERC, 72-12,1 972. Shinta Sugito, Naoyoshi Goda, Tamio Masuda: A Study on Seismic Response Analysis Method of Ground by Equivalent Strain Considering Frequency Dependence, JSCE Proceedings, No.493 / II-27, pp.49-58, 1994

However, the seismic motion estimation method described in Patent Document 1 has the following problems 1) to 4). That is,
1) Since the target is earthquakes that will occur in the future, the epicenter of the estimated earthquake must be assumed.
2) Seismic waves propagating from the epicenter to the underground basement surface must be calculated.
3) In addition, there is a problem that the hypocenter assumption and the calculation of the seismic wave from the assumed epicenter to the basement surface are complicated and time-consuming.
"4) For this reason, compared to the case of estimating damage to an assumed earthquake that will occur in the future, the earthquake motion is estimated quickly and accurately immediately after the actual earthquake, and the damage is estimated for each building in detail. It was difficult to make assumptions. "
5) In addition, there is a possibility that a calculation error may occur in the process of calculating the seismic wave propagating from the epicenter to the underground basement surface.

The present invention has been made to solve the above problems, and 1) there is no need to assume the epicenter of an earthquake, 2) there is no need to calculate the seismic wave propagating from the epicenter to the underground basement surface, and 3) The issue to be solved is to provide a method that can quickly estimate the seismic motion based on the earthquake that is currently occurring.

The seismic motion estimation method of the first invention includes a seismic wave observation process for observing seismic waves at the time of an earthquake, an observation point seismic motion parameter calculation process for calculating seismic motion parameters at an observation point on the ground surface from the observed seismic waves, and observation of the ground surface. A ground surface space distribution calculation process that calculates the spatial distribution of the ground motion parameter from the seismic motion parameter at the point, and an arbitrary ground motion parameter calculation process that calculates the seismic motion parameter of the ground surface at an arbitrary point from the spatial distribution of the seismic motion parameter. It is characterized by comprising an arbitrary ground surface seismic motion calculation step of calculating the seismic motion of the arbitrary point from the seismic motion parameter on the ground surface of the arbitrary point.
The seismic motion parameters in the present invention include a Fourier amplitude spectrum, a power spectrum, a maximum acceleration, a maximum velocity, a measured seismic motion, a spectral strength, and the like.

According to the seismic motion estimation method of the first invention, since the seismic motion is estimated based on the seismic wave observed at the time of the occurrence of the earthquake, it is not necessary to assume the epicenter of the earthquake. In addition, it is not necessary to calculate the seismic waves propagating from the epicenter to the underground basement surface. Therefore, the spatial distribution of seismic motion can be estimated quickly.

In the seismic motion estimation method of the first invention, seismographs capable of observing earthquakes in and around the estimation target area are installed sufficiently densely with respect to the autocorrelation distance, and the seismic motion is measured by these seismographs. If possible, the seismic motion at any point can be estimated accurately.

However, if seismographs capable of observing earthquakes in and around the estimation target area are not installed sufficiently densely with respect to the autocorrelation distance, the estimation accuracy of seismic motion at arbitrary points may deteriorate. .. As a method of estimating the ground motion in such a case, the inventor considered using the distribution of the ground motion on the basement having a long autocorrelation distance as compared with the ground surface. The reason is as follows.

In order to estimate the ground motion at a certain point (strong ground motion estimation), it is necessary to consider the distance and direction from the epicenter to the estimated point and the characteristics of the surface layer near the ground surface. Among them, the surface ground has a large fluctuation in ground motion even in the same area as the basement deeper than it. This is because the surface layer near the ground surface is generally inhomogeneous compared to the basement, and the shaking transmitted to that point changes significantly even in a narrow area (see FIG. 1). For this reason, when estimating strong ground motion, the ground motion up to a place that is not significantly affected by the ground (that is, the basement surface) is first calculated from the seismic waves observed at the observation point, and the ground motion at the observation point is calculated. Next, the seismic motion of the basement surface of the observation point is calculated from the ground motion of the observation point using the transmission function of the surface layer ground (this is called the transmission function for inverse analysis of the surface layer ground) evaluated by another method. (This is called inverse analysis), then the spatial distribution of the seismic motion parameters on the basement surface is calculated from these calculated values, and then the seismic motion of the ground surface at the relevant arbitrary point is calculated from the basement surface at any point (this is called reverse analysis). It is rational to evaluate and use the transfer function of the surface ground (called the transfer function for forward analysis of the surface ground) by another method. This is because the seismic motion on the foundation surface is stable and does not change so much, so it is possible to accurately estimate the effect of the surface layer ground, and the estimation calculation can be done in a short time. In addition, this method does not need to calculate the seismic wave propagating from the epicenter to the underground basement surface, so that there is an advantage that the calculation time and the calculation error are greatly reduced.

That is, the seismic motion estimation method of the second invention is
A surface layer transfer function calculation process that calculates a transfer function that can perform forward and reverse analysis on the surface ground at the survey point from the seismic data and / or ground data at the survey point.
A surface ground transfer function spatial distribution calculation step for calculating the spatial distribution of the transfer function capable of performing forward and inverse analysis of the surface ground from the transfer function of the surface ground at the survey point.
From the spatial distribution of the transfer function of the forward and reverse analysis of the surface ground at the survey point and the transfer function of the forward and reverse analysis of the surface ground, the space of the transfer function that can perform the forward and reverse analysis of the surface ground at any point. Spatial interpolation function calculation process to calculate the interpolation value and
A database construction process for constructing a database of spatial interpolation functions for forward analysis and inverse analysis of the calculated transfer function of the surface layer, and
Seismic wave observation process for observing seismic waves at the time of an earthquake,
The seismic motion parameter calculation process for calculating the seismic motion parameters on the ground surface from the seismic waves at the time of the occurrence of the earthquake, and
The ground motion parameter calculation process for calculating the ground motion parameters of the basement surface from the database of the ground motion parameters on the ground surface and the spatial interpolation function of the transfer function for the inverse analysis of the surface layer constructed in the database construction process.
The base plane space distribution calculation process for calculating the spatial distribution of the seismic motion parameters of the base plane, and
Arbitrary basement surface seismic motion parameter calculation process for calculating the seismic motion parameter of the basement surface at an arbitrary point from the spatial distribution calculation of the seismic motion parameter of the basement surface,
From the database of the seismic motion parameters on the basement surface of the arbitrary point and the spatial interpolation function of the transfer function for forward analysis of the surface layer constructed in the database construction process, the seismic motion parameters on the ground surface of the arbitrary point are calculated. Arbitrary ground motion parameter calculation process and
It is characterized by including an arbitrary ground surface seismic motion calculation step for calculating the seismic motion of the arbitrary point from the seismic motion parameter on the ground surface of the arbitrary point.

The seismic motion estimation methods of the first invention and the second invention may further include a damage probability calculation step of calculating the damage probability of the building from the seismic motion and / or the seismic motion parameter of the arbitrary point calculated by the arbitrary ground surface seismic motion calculation step. .. This makes it possible to quickly determine the probability of damage to a building at any point in the event of an earthquake.

Furthermore, by utilizing the method of the second invention, particularly the database, it is possible to immediately calculate the seismic motion on the ground surface from the seismic waves on the basement calculated from the hypocenter assumption that may occur in the future. At the same time, it is possible to carry out the calibration shown in the background technology on the ground surface and the basement surface, and it is possible to improve the estimation accuracy of the seismic motion every time an earthquake occurs.

Further, it is also possible to provide an actual data correction step of correcting the damage probability of the building in the damage probability calculation step based on the actual data at the time of the occurrence of earthquake damage. By performing the actual data correction process, the reliability of the earthquake damage probability estimation can be further improved.

It is a schematic diagram showing how the ground motion from the epicenter is transmitted to the ground surface through the basement and the surface layer ground. It is a process diagram of the seismic motion estimation method of 1st invention. It is a process diagram of the seismic motion estimation method of the 2nd invention. It is a figure which shows the boring point (a to d) and the assumed seismograph installation point. It is a graph which shows the transfer function at a bowling point (a to d). It is a graph which shows the average value, the maximum value and the minimum value for each frequency of the transfer function at 748 boring points. It is a graph which shows the result of AIC modified kriging. It is a graph which shows the result of a range. It is a graph showing sill + calculation error variance. It is the figure which showed the transfer function at an arbitrary construction point in Owariasahi-shi about (a) 0.6012, (b) 1.001, (c) 2.038, (d) 4.065Hz. It is an acceleration Fourier amplitude spectrum of the seismic motion at four boring points in the city when the epicenter is the largest earthquake ever (direction EW). (a) The epicenter is the Sarutoshi-Takahama earthquake, (b) 2 interlocking earthquakes (direction NS), (c) the largest earthquake ever (direction EW) at 642 boring points in Owariasahi city. It is a graph which showed the scatter diagram of the pseudo-spectral intensity obtained from. It is a histogram with respect to the ratio of the estimated value of the pseudo-spectral intensity of the ground surface and the observed value (provisional) about the epicenter.

Hereinafter, embodiments that embody the seismic motion estimation method of the present invention will be described with reference to the drawings.

(Embodiment 1)
The first embodiment is the seismic motion estimation method of the first invention, and will be described with reference to the process diagram shown in FIG.

<Seismic wave observation process S1>
First, observe the seismic waves when an earthquake occurs. Here, the place where the seismic wave is observed is the observation point where the seismograph or the like is installed.

<Observation point seismic motion parameter calculation process S2>
Then, the seismic motion parameters at the observation points on the ground surface are calculated by performing spectral analysis of the seismic waves observed at the observation points. That is, the seismic motion parameters are calculated by Fourier analysis of seismic waves at observation points on the ground surface.

<Ground surface space distribution calculation step S3>
Furthermore, the spatial distribution of the seismic motion parameters is calculated from the calculated seismic motion parameters at the observation point.

<Arbitrary ground motion parameter calculation process S4>
Then, the seismic motion parameter of the ground surface at an arbitrary point is calculated from the spatial distribution of the seismic motion parameter at the observation point on the ground surface.

<Arbitrary ground motion calculation process S5>
Finally, the seismic motion at an arbitrary point is calculated from the seismic motion parameters on the ground surface at the arbitrary point.

In the seismic motion estimation method of the first embodiment, seismographs capable of observing earthquakes in and around the estimation target area are installed sufficiently densely with respect to the autocorrelation distance, and the seismic motion can be measured by these seismographs. In some cases, the seismic motion at any point can be estimated accurately.
However, if seismographs capable of observing earthquakes in and around the estimation target area are not installed sufficiently densely with respect to the autocorrelation distance, the estimation accuracy of seismic motion at arbitrary points may deteriorate. .. In such a case, it is preferable to estimate by the following seismic motion estimation method of the second embodiment.

(Embodiment 2)
The second embodiment is the seismic motion estimation method of the second invention, and will be described with reference to the process diagram shown in FIG.

<Surface ground transfer function calculation process S11>
First, the transfer function for forward analysis and inverse analysis of the surface layer ground at the survey point is calculated from the seismic data and / or the ground data at the survey point. Here, the seismic data means all the data related to the earthquake observed by the seismograph, the microtremor, etc. (for example, the acceleration waveform, the seismic motion parameter calculated from the acceleration waveform, the seismic source information data, etc.). In addition, the ground data means all the ground data having a correlation with the seismic motion, such as N value and boring data (type of stratum, layer thickness, unit volume weight, microtopography information, shear elastic wave velocity, etc.). .. Boring surveys are suitable as ground data because it is easy to collect information about the ground and the collected information is useful information for estimating seismic motion. Further, the N value, which is easy to measure, can be used for calculating the shear elastic wave velocity. Further, the ground data may be data by geophysical exploration method or sounding, data on microtopography, etc., in addition to boring survey and standard penetration test. It is also possible to adopt other ground data that the engineer deems appropriate. Seismic observation records (or artificial earthquake observation records) at each point are also included.

ここに、fはフーリエ振幅スペクトルの周波数、Ｚ(Ｓi)は特定地点Ｓiでの係数である。したがって、逆解析の伝達関数の空間補間値のデータベースは、順解析の伝達関数の空間補間値のデータベースから次式をもとに直ちに計算できる。

以下、順解析の伝達関数の空間分布を計算する方法のみを示す。すなわち、推定特定地点Ｓiと推定特定地点Ｓjとの２点間距離ｈijと、推定特定地点での表層地盤の伝達関数がの差の２乗の値(Ｚ(Ｓi)−Ｚ(Ｓj))²とを、全ての２地点の組み合わせについて算出する。そして、算出されたバリオグラムクラウドの２点間距離を適当な幅ｈで分割し、次式によってバリオグラムを算定する。 <Surface ground transfer function space distribution calculation step S12>
Then, the spatial distribution of the transfer function for the forward analysis and the inverse analysis of the surface layer is calculated from the transfer function for the forward analysis and the inverse analysis of the surface layer at the survey point. As for the spatial distribution and interpolation methods, in addition to the kriging method, a spline method, an inverse distance weighting method, and the like can be used in combination or independently. Here, as an example, a method using the kriging method is shown.
That is, here, as an example, when the seismic motion parameter is the Fourier amplitude spectrum, the Fourier amplitude spectrum of the ground surface is Gs (f), and the Fourier amplitude spectrum of the base surface is Bs (f), the transfer function of the forward analysis is as follows. It shall be possible to express it by an expression.

Here, f is the frequency of the Fourier amplitude spectrum, and Z (Si) is the coefficient at the specific point Si. Therefore, the database of the spatial interpolated values of the transfer function of the inverse analysis can be immediately calculated from the database of the spatial interpolated values of the transfer function of the forward analysis based on the following equation.

Below, only the method of calculating the spatial distribution of the transfer function of the forward analysis is shown. That is, the square value of the difference between the distance between the two points hij between the estimated specific point Si and the estimated specific point Sj and the transfer function of the surface layer ground at the estimated specific point (Z (Si) −Z (Sj)) ² And are calculated for the combination of all two points. Then, the calculated variogram cloud distance between two points is divided by an appropriate width h, and the variogram is calculated by the following equation.

Further, based on the variogram thus identified, the covariance function expressed by the function of the distance between two points h is identified by using the random field model. Here, the random field models include an exponential model, a Gaussian model, a spherical covariance model, a Hole-effect model, and a Nugget-effect model. ), Power model, Linear model, etc. can be used. AIC (Akaike Statistic Criterion), maximum likelihood method, etc. can be used to select the random field model and determine the parameters of each model.

<Spatial interpolation function calculation process S13>
Further, the spatial interpolation value of the transfer function of the surface layer at an arbitrary point is calculated from the spatial distribution of the transfer function of the surface layer at the survey point and the transfer function of the surface layer.
For example, the transfer function Z (S0) of the surface layer ground at an arbitrary point S0 is calculated by the weighted average of the transfer function Z (Si) of the surface layer ground at n estimated specific points Si. That is, a modified equation of the linear regression estimator Z (S0) represented by the following equation is introduced. Here, μ (S0) and μ (Si) are expected values of Z (S0) and Z (Si), respectively.

Further, λi is a weighting coefficient with respect to Z (Si) when Z (S0) is calculated by a weighted average, and the following equation is established.

At this time, based on the covariance function identified in the cytovariogram calculation step S2, the estimator Z (S0) satisfies the unbiasedness and the estimated error variance σ2 (S0) is minimized. λi is determined, and the expected value E [Z (S0)] of the estimator Z (S0) at the arbitrary point S0 and its estimated error variance σ2 (S0) are calculated. That is, under the condition of Eq. (4), λi is determined by minimizing Eq. (5).

At this time, the expected value E [Z (S0)] of the estimator calculated by substituting the determined λi into the following equation is used as the interpolated seismic motion parameter in S0, and the estimated error variance σ2 (5) of the minimized equation (5) is used. S0) can be the interpolation accuracy in S0.

Further, by extending the method of calculating the interpolated ground motion parameter and the interpolation accuracy at an arbitrary point, the interpolated ground motion parameter and the interpolation accuracy in an arbitrary region can be calculated.

The analysis can also be performed in consideration of the trend component. For example, simple (simple) kriging that analyzes the trend on the condition that it is constant and known, ordinary (normal) kriging that analyzes on the condition that the trend is unknown, and universal kriging that analyzes the trend as a linear combination of functions of position. , Non-linear (non-linear) and other methods can be used.

<Database construction process S14>
Then, the database of the calculated spatial interpolation function of the transfer function of the surface layer is stored in the storage unit of the computer.

<Seismic wave observation process S15>
Then, when an earthquake occurs, the seismic wave is observed.

<Ground motion parameter calculation process S16>
Further, as the ground surface seismic parameter calculation step S16, the seismic motion parameter (for example, the Fourier amplitude spectrum on the ground surface by performing spectral analysis of the seismic wave) is calculated from the observed seismic wave at the time of occurrence of the earthquake.

<Base surface seismic motion parameter calculation process S17>
Then, as the basement surface seismic motion parameter calculation step S17, the seismic motion parameter on the ground surface is subjected to inverse analysis using the database of the spatial interpolation function of the transfer function for inverse analysis of the surface layer constructed in the database construction step. By doing so, the seismic motion parameters of the basement surface are calculated. Here, the basement surface refers to a boundary surface that is not significantly affected by the surface layer ground near the ground surface, and is a concept including the basement surface and the earthquake basement surface shown in FIG. As described above, the seismic motion parameter on the basement surface can be obtained from the seismic motion parameter on the ground surface.

<Base surface space distribution calculation step S18>
Further, as the base surface spatial distribution calculation step S18, the spatial distribution of the seismic motion parameters is calculated from the seismic motion parameters of the base plane at the seismic wave observation point by using the kriging method or the like. In addition to the kriging method, the spline method, the inverse distance weighting method, and the like can be used in combination or independently for the spatial distribution calculation at this time.

<Arbitrary base surface seismic motion parameter calculation process S19>
Then, as the arbitrary base plane seismic motion parameter calculation step S19, the seismic motion parameter at the arbitrary base surface is calculated from the calculated seismic motion parameter on the base plane of the seismic wave observation point and the spatial distribution on the base plane calculated in the previous section. To do.

<Arbitrary ground motion parameter calculation process S20>
Further, as the arbitrary ground surface seismic motion parameter calculation step S20, from the seismic motion parameter on the base plane of the arbitrary point and the database of the spatial interpolation function of the transmission function for acclimatization of the surface layer constructed in the database construction process, the arbitrary point Calculate the seismic motion parameters on the ground surface.

<Arbitrary ground motion calculation process S21>
Finally, the seismic motion at the arbitrary point is calculated from the seismic motion parameters on the ground surface at the arbitrary point.

As described above, in the seismic motion estimation method of the second embodiment, 1) the transmission function of the surface layer ground at the observation point is calculated from the seismic data at the observation point, and 2) the seismic motion parameters and the surface layer calculated from the seismic waves observed on the ground surface. Inverse analysis using the spatial interpolation function database of the surface ground transmission function constructed in the database construction process from the ground transmission function was performed to calculate the seismic motion parameters of the basement surface, and 3) the basement from the seismic motion parameters of the basement surface. Calculate the spatial distribution of the seismic motion parameters on the surface and the seismic motion parameters at any point on the basement surface, and 4) calculate the seismic motion parameters at any point using the spatial interpolation function database of the surface ground transmission function constructed in the database construction process. The seismic motion is estimated by the feedback method of doing. Since the seismic motion on the foundation surface is stable and does not change so much, it is possible to accurately estimate the effect of the surface layer ground, and the estimation calculation can be done in a short time, so it is possible to quickly estimate the seismic motion at the time of an earthquake. Become. Moreover, it is not necessary to assume the epicenter of the estimated earthquake, and it is not necessary to calculate the seismic wave propagating from the epicenter to the underground basement surface. That is, the calculation error, calculation time, and calculation cost that occur when calculating the seismic wave propagating from the epicenter to the underground basement surface can be set to zero.

Furthermore, by using spatial statistical analysis, it is possible to objectively estimate at an arbitrary point in the analysis target area at low cost. Further, since the work in each process can be executed by processing the digitized data by a computer, there are few human errors and the labor cost is low. Furthermore, if the kriging method is used, it is possible to calculate the estimation result with accuracy.

In addition, each time a seismic wave is observed, and as the ground survey information in the surface layer is added, it becomes possible to estimate the situation in which the seismic motion is propagated in the surface layer with higher accuracy.

Furthermore, it is assumed that it will be applied when an earthquake is actually observed on the surface of the earth, and since it is not necessary to assume the epicenter or calculate from the epicenter to the basement surface, there will be no estimation error caused by these operations. Therefore, by grasping the state of earthquake propagation in the surface layer with high accuracy and in detail, it is possible to respond to the estimation of future earthquakes. For this reason, by using the calculation results of seismic waves that propagate through the assumed epicenter and the basement and reach the lower surface of the surface layer, as was conventionally done by the national government and local governments, on the ground surface, which is the final target. It is also possible to estimate the seismic motion of the earthquake with high accuracy and detail.

In addition, as the ground motion estimation on the ground surface becomes more accurate and detailed, the propagation status of the ground motion from the epicenter to the ground surface can also be estimated with higher accuracy and more detail. ..

(Embodiment 3)
In the third embodiment, after performing each step in the seismic motion estimation method of the second embodiment, a damage probability calculation step of calculating the damage probability of the building from the seismic motion at an arbitrary point calculated by the arbitrary ground surface seismic motion calculation step 20. I do. As a result, the probability of damage to a building due to earthquake motion can be quickly determined after an earthquake occurs.

(Embodiment 4)
In the fourth embodiment, after performing each step in the seismic motion estimation method of the first embodiment, an additional information correction step relating to the database of the database construction step S4 and the seismic response analysis method based on the additional ground information and the additional seismic observation information is further performed. Do. This makes it possible to further improve the reliability of seismic motion estimation.

(Embodiment 5)
In the fifth embodiment, after performing each step in the seismic motion estimation method of the second embodiment, an actual data correction step of correcting the damage probability of the building in the damage probability calculation step based on the actual data at the time of the occurrence of the earthquake damage is performed. As a result, the reliability of seismic motion estimation can be further improved.

(Embodiment 6)
In the sixth embodiment, when the seismic wave can be observed on the basement surface in the analysis region where the basement surface is exposed on the ground surface, the basement surface in the seismic motion estimation method of the second embodiment is used from the observed seismic wave. Seismic motion parameters can be calculated and used in subsequent processes. As a result, the reliability of seismic motion estimation can be further improved.

In the embodiment, the seismic motion was estimated by applying the seismic motion estimation method of the second embodiment described above in the Owariasahi city area of Aichi prefecture.
The transfer function at an arbitrary point was interpolated and estimated by applying the extended kriging method to the transfer function at the boring point. The transfer function at the boring point was evaluated by seismic response analysis (forward analysis) using seismic waves on the base surface of the assumed earthquake. The seismic motion parameter in the example was an acceleration Fourier amplitude spectrum. In other words, if the transfer functions of all building points and seismic observation points in the analysis target area are pre-amplituded and estimated and stored in a database, acceleration at the observation points will not be performed after an earthquake occurs. Immediately after the calculation of the Fourier amplitude spectrum, the acceleration Fourier amplitude spectrum of the seismic wave at an arbitrary point on the ground surface was calculated via the basement surface.
More specifically, the transfer function at the boring point using the assumed earthquake and the evaluation method of the same characteristic at any point using the extended kriging method are shown, and the target area is Owariasahi City, Aichi Prefecture (21.03 km2). Evaluation was performed. In addition, the pseudo-spectral strength obtained by using the seismic observation record was compared with the pseudo-spectral strength directly obtained by the response analysis at the boring point. It will be described in detail below.

(Analytical method)
1-1) Transfer function at the boring point As the surface layer ground transfer function calculation step, the transfer function at the boring point was obtained by the following method. As for the seismic response analysis method, various methods such as time history response analysis and equivalent linear analysis are used, but here, the equivalent linear analysis is used because it is necessary to return the observed seismic motion on the ground surface to the base.

Further, the following calculations were performed as a surface layer transfer function space distribution calculation step and a space interpolation function calculation step. That is, the acceleration Fourier amplitude spectrum on the ground surface at the relevant point calculated by equivalent linear analysis using the seismic waves on the basement surface by the assumed seismic source, and the provisional ground surface observation with a limited number of virtual seismographs placed at the ideal position. It is possible to compare the acceleration Fourier amplitude spectrum on the ground surface with the inverse analysis and forward analysis calculated from the record by the transfer function. However, this method is valid when the strain level of the ground is within the range of 0.1% ^1).

The desired acceleration Fourier amplitude spectrum A ^O (f) can be expressed by ^{Eq. (7) 2)} because the seismic wave on the base surface of the assumed earthquake is used.

Here, A ^E (f) is the seismic wave on the basement surface, and A ^G (f) is the transfer function of the observation point. From Eq. (1), A ^G (f) at an arbitrary point can be obtained by interpolation estimation by applying the extended kriging method based on the ratio of the acceleration Fourier amplitude spectrum on the base plane and the ground surface at the boring point. .. The acceleration Fourier amplitude spectrum on the ground surface at the boring point was calculated by equivalent linear one-dimensional seismic response analysis using seismic waves on the basement surface as input. At that time, frequency-dependent equivalent strain ³⁾ was used. Regarding the G-γ and h-γ relationships used in the ground model for response analysis, the soil classification of boring data was classified into three types: sand, cohesive soil, and gravel, ^{and set using the Imazu-Fukutake equation 4)} ((((). 8) Equation).

Here, G / G _max is the shear rigidity ratio, h is the damping constant, γ is the shear strain, and a, b, c, and d are the parameters ⁵⁾ for each soil shown in Table 1. The S wave velocity Vs (m / s) was calculated by ^{Eq. 6) (9).}

Here, N is the average N value for each layer, and e and f are the parameters for each soil type shown in Table 1. The acceleration Fourier amplitude spectra on the substrate surface and the ground surface were both smoothed using a Parzen window with a bandwidth of 0.4 Hz.

The above calculation results were stored in a computer storage unit and constructed as a database (database construction process).

Then, as a seismic wave observation process, the seismic wave at the time of the occurrence of the earthquake is observed, the Fourier amplitude spectrum on the ground surface is calculated from the data (ground surface Fourier amplitude spectrum calculation step), and the Fourier amplitude spectrum on the ground surface and the database construction are constructed. Calculate the Fourier amplitude spectrum of the base plane from the database of spatial interpolation values of the transfer function of the surface layer constructed in the process (base plane Fourier amplitude spectrum calculation step), and calculate the spatial distribution of the base plane Fourier amplitude spectrum (base). Plane space distribution calculation step), the Fourier amplitude spectrum of the base plane at an arbitrary point was calculated from the spatial distribution calculation of the Fourier amplitude spectrum of the base plane (arbitrary base plane Fourier amplitude spectrum calculation step). Hereinafter, it will be described in detail in 1-2).

1-2) Transfer function at an arbitrary point by the extended kriging method The transfer function at an arbitrary point was estimated for each frequency by the extended kriging method using the site transfer function at the boring point. The outline of the extended kriging method is shown below. In order to predict spatial data using the Kriging method, the most important analysis work is to identify the variogram function that defines the covariance matrix of the random field model and the trend function that represents the overall tendency in space ^{7). 8)} . The random field models (variogram function and trend function) for the spatial distribution of ground motion were identified by the criteria that minimize the ^{Akaike statistic AIC 9) based on the general maximum likelihood method shown in Eq. (10).}

_{Here, z is a variable vector composed of the seismic motion parameter z i} obtained at the observation point i in the analysis target area, and m is the number of explanatory variables of the random field in Eq. (4). p (z | ・) is a multivariate simultaneous probability density function of z, and when p (z | ・) is a lognormal distribution, it is expressed by Eq. (11).

Here, μ is the trend vector of ln (z). In this study, for the element μ _i = μ (u _i ) of μ, the n _t- dimensional trend function vector f (u _i ) and the coefficient vector based on the plane coordinates (x _i , y _{i ) of the position u i} at the point i. b of a polynomial of use ¹⁰⁾ that the the product ((12)).

_{The relationship between the dimension n t of} equation (11) and the number of elements m _t of b is shown in equation (13).

C is a covariance matrix of ln z determined by the explanatory variable θ, and the elements C (u _i , u _j ) that make up C depend only on the distance h between the two points _{u i} and u _j. Since it is a variance function, the general exponential model shown in Eq. (14) was used.

Here, σ ² and λ are parameters called sill and range (or autocorrelation distance), respectively. _{In general, C (u i} , u _j ) in Eq. (8) is expressed by Eq. (15) in relation to the variogram function γ (u _i , u _j).

Since _{the distance h between the two points u i} and u _j is known and C is defined by γ, all the elements of C are determined by ^{σ 2 and λ.}
From the above, m in Eq. (4) is _{the sum of the number m t of the parameters that determine μ and the number m c} of the parameters that determine the explanatory variable θ of C (m = m _c + m _t ).
In the case of general Kriging analysis, z is considered to be the realization value in the random field. However, when estimating seismic motion from a sample such as boring data, it is necessary to consider the estimation error at the estimation point.
Sugai, Mori et al., As a mathematical model of the calculation error σ _{i (hereinafter referred to as the calculation error standard deviation) of the element z i} of z, the calculation error in the diagonal term of the covariance matrix C as shown in Eq. (16). We proposed a method for estimating p (z | ·) using C'with the variance σ _i ^{2 as the covariance matrix 11)} .

Where σ _i ² = σ _c ² (i = 1, ..., n). At this time, the number m _c of the explanatory variables of C'is 3 because another explanatory variable σ _c ² is added to ^{the explanatory variables σ 2 and λ of C.}

Then, the Fourier amplitude spectrum on the ground surface of the arbitrary point is calculated from the Fourier amplitude spectrum on the base plane of the arbitrary point and the spatial interpolation value database of the transfer function of the surface layer constructed in the database construction process (arbitrary ground). Surface Fourier amplitude spectrum calculation step), the seismic motion of the arbitrary point was calculated from the Fourier amplitude spectrum of the arbitrary point on the ground surface (arbitrary ground surface seismic motion calculation step). Hereinafter, it will be described in detail in 1-3).

1-3) Acceleration Fourier amplitude spectrum of the ground surface at an arbitrary point The acceleration Fourier amplitude spectrum of the ground surface at an arbitrary point based on the seismograph observation record is estimated as follows using the transfer function at the arbitrary point estimated in Section 2.2. did.
1) The Fourier amplitude spectrum on the substrate surface was obtained by multiplying the acceleration Fourier amplitude spectrum on the ground surface at the same point obtained from the seismograph observation record by the reciprocal of the transfer function at that point.
2) Using the acceleration Fourier amplitude spectrum on the base plane at all seismograph points, find the curved surface of the base plane represented by Eq. (7), that is, the value of the parameter vector b in the same formula for each frequency by the least squares method. It was.
The transfer function at that point is applied to the acceleration Fourier amplitude spectrum on the base plane obtained by substituting the latitude and longitude at an arbitrary point into Eq. (6) using the values of the vectors b obtained in 1) and 2). By multiplying by, the acceleration Fourier amplitude spectrum on the ground surface at the same point can be obtained.
As a database construction process, the analysis time can be shortened by preparing the transfer functions at the seismic observation points and arbitrary points as a database in advance.

(Estimated results of earthquake motion in Owariasahi City, Aichi Prefecture)
The results of estimating the seismic motion in the Owariasahi city area of Aichi prefecture by the above analysis method are described below.
2-1) Target area and data The boring data used to evaluate the transfer function in Owariasahi City, Aichi Prefecture, which was the target area, was 676, which the city independently collected and organized in the 2013 project, and the surrounding cities. There are a total of 748 of the 72 provided by. As seismic motion data, the Sarutoshi-Takahama Fault Zone Earthquake (hereinafter referred to as the Sarutoshi-Takahama Earthquake), which the city made its own damage estimation in the damage estimation conducted by Owari Asahi City in 2014, and the Tokai / Tonankai earthquakes assumed by Aichi Prefecture. The source of the earthquake is the linked earthquake (hereinafter, 2 linked earthquakes), the Tokai, Tonankai, and Nankai 3 linked earthquakes (hereinafter, 3 linked earthquakes) envisioned by the national government, and the Nankai Trough envisioned by Aichi Prefecture based on the examination of the Cabinet Office. Three types of Nankai Trough giant earthquakes ²⁰⁾ (so-called "largest ever", "largest theoretical east side", "largest theoretical east side", hereafter the largest earthquake ever, eastern earthquake, land side earthquake) 250m A group of seismic waves (1 component for the Sarutoshi-Takahama earthquake and 2 horizontal components (NS, EW directions) for the other seismic sources) is used for each mesh (1 km mesh for 2-linked and 3-linked earthquakes). There was. Assuming that the seismic wave on the base plane calculated for each mesh is the seismic wave at the center point, the seismic wave on the base plane at each boring point is the acceleration Fourier amplitude of the seismic wave at the center points of the four meshes closest to the boring point. The spectrum was evaluated using the acceleration Fourier amplitude spectrum, which was weighted and averaged by the square of the inverse of the distance, and the phase of the seismic wave at the center point of the closest mesh.

2-2) Estimated result of transfer function
At each 748 boring point, based on the method described in "1-1) Transfer function at the boring point", the acceleration on the basement surface and the ground surface with respect to the 11 types of individual seismic waves described in "2-1 Target area and data". The ratio of the Fourier amplitude spectrum (this is called the spectral ratio) was obtained. As an example, Fig. 5 shows the spectral ratios of the seismic motions of each assumed earthquake at the four boring points (points marked with ● in FIGS. 4a to 4d), but the spectral ratios of all earthquakes excluding the Sanage-Takahama earthquake are almost the same. There is. Since the Saruto-Takahama earthquake has a higher seismic intensity than other epicenters (measured seismic intensity 6 upper, other epicenters 4-6 lower), we will confirm the effect of it on the spectral ratio. -The seismic wave of the Takahama earthquake was doubled and the spectral ratio was calculated in the same way as other earthquakes (thick solid line in Fig. 5), but (a) is 0.6 to 4 Hz, (b) is 0.3 to 6 Hz, In (c) 0.6 to 7 Hz and (d) 1 to 10 Hz, there were some differences from the spectral ratio values of the original Sarutoshi-Takahama earthquake. Since the purpose of this study is to propose a method using assumed earthquakes, it is a future task to consider the change in the spectral ratio value depending on the magnitude of the seismic intensity as shown in Fig. 5 in the transfer function. In Owariasahi City this time, the average value (logarithmic mean) of the spectral ratios obtained from 11 types of seismic wave groups at each boring point was used as the transfer function at that point.
FIG. 6 shows the average value, the maximum value, and the minimum value of the transfer function at the boring point 748 for each frequency. From Fig. 5, there is almost no difference in the magnitude of the transfer function at each boring point at low frequencies, but the difference between the maximum and minimum values gradually increases above 0.5 Hz, so Owariasahi City In this case, it is considered that the magnitude of the transfer function in the high frequency range differs depending on the point.

2-3) Analysis results on the variogram of the transfer function Here, the transfer function of 0.2 to 6.0 Hz (about 0.16 to 5 s) is targeted with the damage assumption of general structures in mind. Within this range, there are about 2000 data in 0.003052Hz increments, but this time, the transfer function at any point is used for the 313 frequencies extracted so that the data increments are about 0.01 seconds or less when the frequency is converted to a period. It was performed by Kriging analysis. The first term of Eq. (10) mentioned above becomes smaller as the dimension of the trend function of Eq. (12) becomes larger, while the second term becomes larger. Therefore, as the number of dimensions increases, the sum of the first and second terms of Eq. (10) decreases up to a certain dimension, but increases thereafter. Therefore, in this study, calculations were performed from 0 to 2 dimensions for all frequencies, and the value with the smallest AIC was judged to be the optimum value.

Figure 7 shows the AIC evaluated by Eqs. (a) and (10) for the transfer function in the frequency domain of 0.2 to 6.0 Hz, and 0-dimensional for the AIC of (b) and (a) when the trend function is one-dimensional or two-dimensional. Although the difference is shown (right axis in Fig. 7 (b)), the AIC value is the minimum when the trend function is 0-dimensional at all the target frequencies, and therefore in Owari Asahi City. The optimal probability field model can be represented by a zero-dimensional trend function. FIG. 8 shows the range, and FIG. 9 shows the sill + calculation error variance, but there is almost no difference in the values due to the trend function.
Figure 10 shows the transfer function at any construction site in Owariasahi City from the calculation results of the variogram using the 0-dimensional trend function (a) 0.6012, (b) 1.001, (c) 2.038, (d) 4.065Hz. It shows about. The transfer function of (a) frequency 0.6012Hz is distributed with values of 1.0 to 1.2, while (b) 1.001Hz is 1.0 to 1.4, (c) 2.038Hz is 1.0 to 2.0, and (d) 4.065Hz is. As the frequency increases from 0.6 to 2.6, the range of distributed values of the transfer function increases.

Calculation result of the acceleration Fourier amplitude spectrum of the ground surface at an arbitrary point Using the method explained in "2-3) Analysis result on the variogram of the transfer function", the ground surface at an arbitrary point using the transfer function and the virtual seismic observation record. The acceleration Fourier amplitude spectrum of was obtained. From the 748 boring points inside and outside Owariasahi City, reference ¹²⁾ , 20 seismograph installation points (13 points in the city) were selected as seismic observation points (Fig. 4). ▲), 642 points excluding 13 points in the city were used for verification. Assuming that the assumed earthquake described in "2-1) Target area and data" occurred and the seismic waves obtained by one-dimensional response analysis were observed at these 20 observation points, the proposed method was used to evaluate the seismic intensity. went. Regarding the dimension of the trend function, when the damage is estimated immediately after the occurrence of an earthquake, the number of elements of the parameter vector b of the curved surface is the seismograph, considering that it takes time to evaluate the seismic intensity in multiple dimensions. Only 3 dimensions less than the score.

FIG. 11 shows the acceleration Fourier amplitude spectrum estimated by the proposed method at four boring points in the city (same points as a to d in FIG. 5) when the epicenter is the largest earthquake ever (direction EW), and at each point. The acceleration Fourier amplitude spectrum of the seismic motion obtained by the one-dimensional response analysis of the assumed seismic motion on the base plane is shown, and the pseudo-spectral strength obtained by integrating each in the range of 0.1 to 2.5 s in the period is also shown. .. The acceleration Fourier amplitude spectrum at the same point has a slight difference when viewed at individual frequencies, but the values are about the same as a whole, and the pseudo-spectral intensity, which is the integrated value of this, is almost the same value. It has become.

Figure 12 shows the surface of the earth using the proposed method at 642 boring points in Owari Asahi City, where (a) the epicenter is the Sarutoshi-Takahama earthquake, (b) the two-linked earthquake (direction NS), and (c) the largest earthquake ever (direction EW). A scatter diagram of the pseudo-spectral strength (hereinafter "estimated value", vertical axis) and the pseudo-spectral strength obtained from the response analysis results (hereinafter "observed value (tentative)", horizontal axis) is shown. The coefficient of determination indicating the fit of the estimated value to the value (provisional) is 0.942 for the Sarutoshi-Takahama earthquake, 0.930 for the 2-linked earthquake NS direction, and 0.849 for the record maximum earthquake EW direction, which are close to 1 for all epicenters. Is shown. Fig. 13 shows a histogram of the ratio of the estimated value of the pseudo-spectral strength of the ground surface and the observed value (provisional) for the same source as in Fig. 12, but (a) the average value of the Sarutoshi-Takahama earthquake is 1.001 and the coefficient of variation. 0.020, (b) 2 interlocking earthquakes The average value in the NS direction is 1.002, the coefficient of variation is 0.064, (c) The average value in the EW direction of the largest earthquake in the past is 0.988, and the coefficient of variation is 0.045. It is distributed with close values. ^{Table 2 shows the coefficient of determination (R 2} ) for the ratio of pseudo-spectral intensity similar to that in FIG. 12, the mean value (mean) and the coefficient of variation (Cov) similar to those in FIG. 13, for all epicenters. The coefficient is close to 1 at all epicenters except for land-side earthquakes. In addition, the average value is close to 1, and the coefficient of variation is as small as 0.088 in the NS direction of the land-side earthquake, and the pseudo-spectral strength can be estimated with high accuracy by the proposed method.

The present invention is not limited to the embodiment of the above invention and the description of the examples. Various modifications are also included in the present invention as long as they do not deviate from the claims and can be easily conceived by those skilled in the art.

<References>
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The present invention assumes what kind of damage will occur in which district in the event of an earthquake in the future, examines the seismic design policy of buildings for each district, reduces damage caused by an earthquake, and takes emergency measures in the event of an earthquake. It can be used for planning.

S1 ... Seismic wave observation process, S2 ... Observation point seismic motion parameter calculation process, S3 ... Ground surface space distribution calculation process, S4 ... Arbitrary ground motion parameter calculation process, S5 ... Arbitrary ground motion parameter calculation process S11 ... Surface ground transmission function calculation process , S12 ... Surface ground transmission function calculation process, S13 ... Spatial interpolation function calculation process, S14 ... Database construction process, S15 ... Seismic wave observation process, S16 ... Ground surface seismic motion parameter calculation process, S17 ... Base surface seismic motion parameter calculation process, S18 ... Base surface space distribution calculation process, S19 ... Arbitrary base surface seismic motion parameter calculation process, S20 ... Arbitrary ground surface seismic motion parameter calculation process,
S21 ... Arbitrary ground motion calculation process

Claims (4)

A surface layer transfer function calculation process that calculates a transfer function that can perform forward and reverse analysis on the surface ground at the survey point from the seismic data and / or ground data at the survey point.
A surface ground transfer function spatial distribution calculation step for calculating the spatial distribution of the transfer function capable of performing the forward and reverse analysis of the surface ground from the transfer function of the forward and reverse analysis of the surface ground at the survey point.
From the spatial distribution of the transfer function of the forward and reverse analysis of the surface ground at the survey point and the transfer function of the forward and reverse analysis of the surface ground, the space of the transfer function that can perform the forward and reverse analysis of the surface ground at any point. Spatial interpolation function calculation process to calculate the interpolation value and
A database construction process for constructing a database of spatial interpolation functions for forward analysis and inverse analysis of the calculated transfer function of the surface layer, and
Seismic wave observation process for observing seismic waves at the time of an earthquake,
The seismic motion parameter calculation process for calculating the seismic motion parameters on the ground surface from the seismic waves at the time of the occurrence of the earthquake, and
The ground motion parameter calculation process for calculating the ground motion parameters of the basement surface from the database of the ground motion parameters on the ground surface and the spatial interpolation function of the transfer function for the inverse analysis of the surface layer constructed in the database construction process.
The base plane space distribution calculation process for calculating the spatial distribution of the seismic motion parameters of the base plane, and
Arbitrary basement surface seismic motion parameter calculation process for calculating the seismic motion parameter of the basement surface at an arbitrary point from the spatial distribution calculation of the seismic motion parameter of the basement surface,
From the database of the seismic motion parameters on the basement surface of the arbitrary point and the spatial interpolation function of the transfer function for forward analysis of the surface layer constructed in the database construction process, the seismic motion parameters on the ground surface of the arbitrary point are calculated. Arbitrary ground motion parameter calculation process and
An arbitrary ground surface seismic motion calculation process for calculating the seismic motion of the arbitrary point from the seismic motion parameters on the ground surface of the arbitrary point, and
A method for estimating ground motion, which comprises. The seismic motion estimation method according to claim 1 , wherein in the surface layer ground transfer function calculation step, the seismic data at the survey point includes seismic motion parameters on the basement surface and / or seismic motion parameters on the ground surface. The seismic motion estimation according to claim 1 or 2 , further comprising a damage probability calculation step of calculating the damage probability of the building from the seismic motion and / or the seismic motion parameter of the arbitrary point calculated by the arbitrary ground surface seismic motion calculation step. Method. The seismic motion estimation method according to claim 3 , further comprising an actual data correction step of correcting the damage probability of a building in the damage probability calculation step based on actual data at the time of occurrence of earthquake damage.

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