JP5638571B2 - Method for creating simulated seismic wave, simulated seismic wave creating program, and computer-readable recording medium recording simulated seismic wave creating program - Google Patents

Description

  The present invention relates to a method for creating a simulated seismic wave, a simulated seismic wave creating program, and a computer-readable recording medium that records the simulated seismic wave creating program. Specifically, a method for creating a simulated seismic wave incident on the ground surface from the engineering foundation surface in the target area, a simulated seismic wave creation program for causing a computer to function as means for realizing the method, and the simulated earthquake wave The present invention relates to a computer-readable recording medium on which a creation program is recorded.

When designing a structure to be constructed on the ground or in the ground, the structure is designed so that sufficient strength including toughness can be secured in the event of an earthquake. At this time, it has hitherto been performed to make a seismic response analysis of a structure by entering a simulated seismic wave using the structure as an analysis model.
As a technique for creating a simulated seismic wave incident on a structure, for example, a technique described in Patent Document 1 has been conventionally used. In this technology, a simulated seismic wave incident on a structure is created based on a simulated seismic wave incident on an engineering base plane and a ground property value of a ground in a construction area where the structure is constructed. Here, the simulated seismic wave incident on the engineering base plane is the historical earthquake parameter selected from the database by the engineer creating the simulated seismic wave, or the fault parameter of the active fault selected by the engineer from the database and Created based on destruction parameters.

JP-A-10-320450

By the way, historical earthquakes are earthquakes that occurred before modern observation facilities such as seismometers were installed, so the reliability of their parameters is low. In addition, it is very difficult to accurately estimate the fault parameter and the fracture parameter of the active fault, and the estimated values of the parameters are often different depending on engineers. For this reason, in the technique described in Patent Document 1, the reliability of the simulated seismic wave incident on the engineering base plane is lowered, and the reliability of the simulated seismic wave incident on the structure and the earthquake response analysis is lowered. There was a problem.
The present invention has been devised to solve the above problems. That is, the problem to be solved by the present invention is to create a simulated seismic wave incident on an engineering foundation surface using the ground characteristics of the surface ground (the ground existing between the ground surface and the engineering foundation surface). This eliminates the need to use parameters of historical earthquakes or active faults and improves the reliability of the generated simulated seismic waves.

In order to solve the above problems, the method of creating a simulated seismic wave and the simulated seismic wave creating program of the present invention take the following means.
First, the first invention is a method of creating a simulated seismic wave incident from the engineering base plane toward the ground surface in the target area. This method of creating a simulated seismic wave is based on the analysis parameters prepared from the ground characteristics of the surface ground of the target area existing between the ground surface of the target area and the engineering foundation surface of the target area. Inversion analysis of incident seismic waves that should be incident on the engineering foundation surface in the target area in order to cause the earthquake motion indicated in the analytical data prepared from the observation data of ground vibration on the surface The inversion step calculated by the above, the incident seismic wave amplitude deriving step for deriving the maximum amplitude of the incident seismic wave, which is a value determined independently from the vibration frequency in the incident seismic wave, and one in the simulated seismic wave independent from the vibration frequency The maximum amplitude of this simulated seismic wave is set to the maximum of the incident seismic wave with respect to the maximum amplitude of the simulated seismic wave set in advance as a value determined by An amplitude ratio calculating step of calculating a quotient obtained by dividing the width as the amplitude ratio, by amplifying or attenuating the amplitude of the incident seismic waves, the simulated maximum value of the amplitude is adjusted to be equal to the maximum amplitude of the simulated seismic wave And an amplitude adjustment step for making an amplitude adjustment seismic wave for outputting the seismic wave. In this amplitude adjustment step, a process of uniformly applying the amplitude magnification to the amplitude of the incident seismic wave regardless of the vibration frequency of the incident seismic wave is executed.
Seismic motion on the surface of the earth is characterized by the source characteristics (characteristics of the release of seismic waves at the source fault), propagation path characteristics (characteristics of the path from which the seismic waves propagate from the source to the engineering base of the target area), and point characteristics (of the target area). It is known that it is influenced by the ground characteristics of the surface layer between the engineering foundation surface and the ground surface). Since the surface ground is close to the ground surface, it is easy to conduct ground data surveys such as boring surveys, so that the point characteristics can be obtained with higher reliability than the seismic source characteristics and the propagation path characteristics.
Here, the present inventor has analyzed that the influence of the point characteristics on the ground motion on the ground surface by analyzing the measured data is so large that the influence of the source characteristics and the propagation path characteristics on the ground motion can be ignored. This is the headline and the present invention. That is, according to the first aspect of the present invention, the analysis using the highly reliable point characteristics is performed on the ground vibration on the ground surface in the target area, and the amplitude is adjusted to adjust the engineering basis of the target area. Create a simulated seismic wave incident on. As a result, it is possible to improve the reliability of the generated simulated seismic wave by eliminating the need for using a low-reliability historical earthquake or active fault parameter for generating the simulated seismic wave incident on the engineering base plane.

Next, in a second invention, in the first invention described above, a weak ground motion that can be regarded as a linear elastic body is selected as the ground vibration of the target region as the vibration of the ground, and the analysis data for the weak ground motion is selected. It is something to prepare. In the inversion step of the second aspect of the invention, the incident seismic wave is calculated by an inversion method on the premise that the surface ground in the target area is regarded as a linear elastic body. Furthermore, in the second aspect of the invention, when the simulated seismic wave is output, the correction of the influence that the dominant period of the seismic wave waveform is lengthened is an amplitude-adjusted seismic wave that is applied to the amplitude of the long-period component whose vibration frequency is a predetermined value or less. Prepare.
The above-mentioned weak ground motion is caused by a seismic wave whose amplitude is so small that the surface ground can be regarded as a linear elastic body. Here, weak earthquake motions can be easily distinguished from stronger earthquake motions when the maximum amplitude (that is, maximum acceleration) of the acceleration waveform is a predetermined value (for example, 0.3 [m / s ² ]) or less. In addition, weak ground motion has the property that the frequency of occurrence of ground motion is higher than that of stronger ground motion.
That is, according to the second aspect, since it is possible to calculate the incident seismic waves by inversion method that assumes that regard Surface Ground linear elastic body in inversion step, simplify this incident seismic Therefore, the reliability of the generated simulated seismic wave can be further improved. Furthermore, since the frequency of weak ground motions is higher than that of stronger ground motions, the ground motion observation period can be shortened. Furthermore, when the simulated seismic wave is output, by preparing an amplitude-adjusted seismic wave in which the amplitude of the long period component is corrected, the reliability of the created simulated seismic wave can be improved.

Furthermore, the third invention is the above-described first or second invention, in the first or second invention, a simulated earthquake source position setting step for setting the position of the simulated earthquake source serving as the simulated earthquake wave source as a simulated earthquake source position, and observation data A seismic source location step that secures the location of the observed earthquake source as the observed seismic source location as shown in Fig. 1. The observation data of the observed earthquake with a relatively short distance between the hypocenter and the simulated earthquake source location is selected, and the analysis data is prepared from this observation data.
According to the third aspect of the invention, the simulated earthquake wave of the simulated earthquake is created based on the observation data of the observed earthquake whose observed earthquake source position is relatively close to the simulated earthquake source position. Thereby, the difference in propagation path characteristics between the observed earthquake and the simulated earthquake can be reduced, and the reliability of the created simulated earthquake wave can be further improved.

Further, the fourth invention is selected in order to prepare analysis data in the above-described third invention, when there are a plurality of observed earthquakes, each of the observed earthquakes is classified by the above-mentioned seismic center distance classification. If multiple observed earthquakes are classified in the source distance category where the observed earthquakes should be classified, select the observed data of the observed earthquakes whose magnitude is closest to the magnitude of the simulated earthquake. The analysis data is prepared from this observation data.
It is generally known that there is a significant difference between a seismic wave generated by a strong earthquake having a large magnitude and a seismic wave generated by a weak earthquake having a small magnitude in a long period component having a relatively low vibration frequency. Here, in the fourth invention, a plurality of observed earthquakes whose observed earthquake source positions are relatively close to the simulated earthquake source positions can be identified by classifying the plurality of observed earthquakes according to the classification of the distance between the epicenters. If multiple observed earthquakes whose observed earthquake source locations are relatively close to the simulated earthquake source location are identified, based on the observed data of the observed earthquake whose magnitude is the closest to that of the simulated earthquake. A simulated earthquake wave of a simulated earthquake is created. Thereby, the influence by the difference in the long period component of the seismic wave between the observed earthquake and the simulated earthquake can be reduced, and the reliability of the created simulated earthquake wave can be further improved.

Furthermore, the fifth invention is a simulated seismic wave creating program for causing a computer to create a simulated seismic wave incident from the engineering base plane toward the ground surface in the target area. In this simulated seismic wave creation program, the observation data of ground vibration on the ground surface of the target area exists between the observation data input step input to the computer and the ground surface of the target area to the engineering base plane of the target area. The analysis parameter preparation step, in which the ground characteristics of the surface ground in the target area are input to the computer as analysis parameters, and the maximum amplitude of the simulated seismic wave, which is a single value independent of the vibration frequency in the simulated seismic wave An amplitude setting step that is set and input to the computer, an analysis data preparation step in which the computer creates and prepares analysis data from the observation data, and the computer determines the location of the target area based on the analysis parameters. In order to cause the earthquake motion indicated in the data for analysis above on the surface, The incident seismic wave to be incident on the engineering base surface, and inversion step of calculating the analysis using the inversion (Inversion), computer is the value determined in one independent from the vibration frequency in the incident seismic waves An incident seismic wave amplitude deriving step for deriving the maximum amplitude of the incident seismic wave, an amplitude multiplying step for calculating the quotient obtained by dividing the maximum amplitude of the simulated seismic wave by the maximum amplitude of the incident seismic wave, and a computer for calculating the incident seismic wave An amplitude adjustment step for calculating an amplitude-adjusted seismic wave by uniformly applying an amplitude magnification to the amplitude of the incident seismic wave regardless of the vibration frequency of the incident seismic wave, and an output step for the computer to output the amplitude-adjusted seismic wave as a simulated seismic wave This is a simulated seismic wave creation program to be executed.
According to the fifth aspect of the invention, the computer analyzes the analysis data obtained from the vibration of the ground on the ground surface in the target area using the analysis parameter of the highly reliable point characteristic, and the analysis result A simulated seismic wave incident on the engineering base plane in the target area is created by adjusting the amplitude of. As a result, it is possible to improve the reliability of the simulated seismic wave generated by the computer without the need to use a low-reliability historical earthquake or active fault parameter for generating the simulated seismic wave incident on the engineering base plane.

Furthermore, the sixth invention is a computer-readable recording medium that records a simulated seismic wave creating program for causing a computer to create a simulated seismic wave incident from the engineering base plane toward the ground surface in the target area. This computer-readable recording medium is composed of an observation data input step in which ground vibration observation data on the ground surface of the target area is input to the computer and the ground surface of the target area to the engineering foundation surface of the target area. Analysis parameter preparation step in which the ground characteristics of the surface layer ground in the target area existing in is input to the computer as analysis parameters, and the maximum of the simulated seismic wave that is a value determined independently from the vibration frequency in the simulated seismic wave Amplitude setting step in which amplitude is set and input to the computer, analysis data preparation step in which the computer creates and prepares analysis data from the observation data, and the computer determines the target area based on the analysis parameters To cause the ground motion indicated in the data for analysis above The incident seismic wave to be incident on the engineering base surface of the target area, and inversion step of calculating the analysis using the inversion (Inversion), computer, determined in one independent from the vibration frequency in the incident seismic waves An incident seismic wave amplitude deriving step for deriving the maximum amplitude of the incident seismic wave which is a value, an amplitude multiplying step for calculating the quotient by dividing the maximum amplitude of the simulated seismic wave by the maximum amplitude of the incident seismic wave, and a computer An amplitude adjustment step for calculating an amplitude-adjusted seismic wave by uniformly multiplying the amplitude of the incident seismic wave by the amplitude magnification without depending on the vibration frequency of the incident seismic wave; and an output step for the computer to output the amplitude-adjusted seismic wave as a simulated seismic wave , Recorded a simulated seismic wave creation program to run on a computer Computer is readable recording medium.
According to the sixth aspect of the invention, the computer that has read the simulated seismic wave generation program from the computer-readable recording medium has a high reliability with respect to the analysis data obtained from the vibration of the ground on the ground surface of the target area. Analyze using the characteristic analysis parameters, and adjust the amplitude of the analysis result to create a simulated seismic wave incident on the engineering base in the target area. As a result, it is possible to improve the reliability of the simulated seismic wave generated by the computer without the need to use a low-reliability historical earthquake or active fault parameter for generating the simulated seismic wave incident on the engineering base plane.

It is a flowchart which shows the method of producing the simulation seismic wave which concerns on the 1st Embodiment of this invention. It is a flowchart which shows the subroutine 1 of FIG. 3 is a flowchart showing a continuation of FIG. This is a map showing the location of the Hi-net Sendai station and the distribution of the epicenter of the earthquake that occurred around the Hi-net Sendai station. It is a spectrum distribution in Hi-net Sendai observation point of the earthquake shown by w1 in FIG. It is a spectrum distribution on the ground surface just above the Hi-net Sendai observation point of the earthquake indicated by w1 in FIG. This is the spectrum distribution at the Hi-net Sendai observation point of the earthquake indicated by w2 in FIG. It is the spectrum distribution on the ground surface just above the Hi-net Sendai observation point of the earthquake indicated by w2 in FIG. It is a spectrum distribution at Hi-net Sendai observation point of the earthquake indicated by w3 in FIG. Fig. 4 shows the spectral distribution of the earthquake indicated by w3 in Fig. 4 on the ground surface directly above the Hi-net Sendai station. It is a spectrum distribution at Hi-net Sendai observation point of the earthquake indicated by w4 in FIG. Fig. 4 shows the spectral distribution of the earthquake indicated by w4 in Fig. 4 on the ground surface directly above the Hi-net Sendai observation point. It is the spectrum distribution at the Hi-net Sendai observation point of the earthquake indicated by w5 in FIG. It is a spectrum distribution on the ground surface just above the Hi-net Sendai observation point of the earthquake indicated by w5 in FIG. It is a spectrum distribution at Hi-net Sendai observation point of the earthquake indicated by w6 in FIG. Fig. 4 shows the spectral distribution of the earthquake indicated by w6 in Fig. 4 on the ground surface directly above the Hi-net Sendai observation point. It is a spectrum distribution at Hi-net Sendai observation point of the earthquake indicated by w7 in FIG. It is a spectrum distribution on the ground surface just above the Hi-net Sendai observation point of the earthquake indicated by w7 in FIG. It is a spectrum distribution at Hi-net Sendai observation point of the earthquake indicated by w8 in FIG. Fig. 4 shows the spectral distribution of the earthquake indicated by w8 in Fig. 4 on the ground surface directly above the Hi-net Sendai observation point. It is a spectrum distribution in Hi-net Sendai observation point of the earthquake shown by w9 in FIG. Fig. 4 shows the spectrum distribution of the earthquake indicated by w9 in Fig. 4 on the ground surface directly above the Hi-net Sendai observation point. It is a spectrum distribution in Hi-net Sendai observation point of the earthquake shown by w10 in FIG. Fig. 4 shows the spectral distribution of the earthquake indicated by w10 in Fig. 4 on the ground surface directly above the Hi-net Sendai observation point. It is a spectrum distribution in Hi-net Sendai observation point of the earthquake shown as w11 in FIG. FIG. 4 is a spectrum distribution of the earthquake indicated by w11 in FIG. 4 on the ground surface directly above the Hi-net Sendai observation point. It is a flowchart which shows the method of creating the simulation seismic wave which concerns on the 2nd Embodiment of this invention. It is a flowchart which shows the method of producing the simulation seismic wave which concerns on the 3rd Embodiment of this invention. It is a flowchart which shows the subroutine 2 of FIG. It is a three-dimensional graph showing a part of unsteady spectrum of microtremor. This is the shear wave velocity structure around the observation point X. It is a response speed waveform of microtremors observed on the ground surface directly above observation point X. It is a response speed waveform of microtremor in the ground observed at the observation point X. 32 is a vibration characteristic around observation point X theoretically derived from the shear wave velocity structure of FIG. This is a response speed waveform of a body wave component of microtremor that reaches the ground surface directly above the observation point X. It is a response speed waveform of a surface wave component of microtremor that reaches the ground surface directly above the observation point X. FIG. 30 is a flowchart showing a subroutine 3 of FIG. 29. FIG. It is a flowchart which shows the subroutine 4 of FIG. FIG. 30 is a flowchart showing a subroutine 5 of FIG. 29. FIG. FIG. 40 is a flowchart showing a continuation of FIG. 39. FIG. FIG. 40 is a flowchart showing a subroutine 6 of FIG. 39. FIG. 42 is a flowchart showing a continuation of FIG. It is a flowchart which shows the subroutine 7 of FIG. It is a flowchart which shows the continuation of FIG. It is a flowchart which shows the subroutine 8 of FIG. It is a graph showing the frequency distribution of the maximum value and the first moving average in the spectral density of the analysis candidate spectrum. It is a graph showing the frequency distribution of the minimum value and the second moving average in the spectral density of the analysis candidate spectrum. It is the graph showing the distance attenuation | damping formula with respect to the earthquake of the moment magnitude 7. It is the graph showing the distance attenuation | damping formula with respect to the earthquake of the moment magnitude 6. This is the spectral distribution obtained from the velocity waveform data in the north-south direction in the seismometer on the surface side of the KIK-net Hachioji observation station in the western Kanagawa earthquake. Relative spectral distribution of FIG. 5 0, a spectral distribution obtained by amplifying the long-period components. This is the spectral distribution obtained from the velocity waveform data in the north-south direction of the seismometer at the underground side of the KIK-net Hachioji observation station for the Tohoku Earthquake. This is the spectral distribution obtained from the velocity waveform data in the north-south direction in the seismometer on the surface side of the KIK-net Hachioji observation station in the Miyagi-oki earthquake. This is a map showing the location of the KIK-net Hachioji station and the epicenter distribution of earthquakes observed at the KIK-net Hachioji station. It is the spectrum distribution of the velocity waveform of the north-south direction in the incident seismic wave calculated | required from the earthquake motion corresponding to the spectrum distribution of FIG. It is the spectrum distribution of the velocity waveform of the north-south direction in the incident seismic wave calculated | required from the earthquake motion corresponding to the spectrum distribution of FIG.

EMBODIMENT OF THE INVENTION Below, the form for implementing this invention is demonstrated using drawing. Note that in the following, detailed description of ancillary steps such as an error detection step of detecting an error contained in input or calculated data and outputting an error message will be omitted.
<First Embodiment>
First, a method for creating a simulated seismic wave according to the first embodiment will be described with reference to the flowcharts of FIGS. 1 and 2. In this method of creating a simulated seismic wave, an engineer who creates a simulated seismic wave (hereinafter also simply referred to as “engineer”) uses a simulated earthquake wave creating program and data in a known database to create a computer (this embodiment). This is a method of creating a simulated seismic wave by letting a personal computer) create a simulated seismic wave that is incident from the engineering base to the ground surface in the target area.

The simulated earthquake wave creation program is recorded on a computer-readable recording medium (CD-ROM in the present embodiment), and is read by the computer and executed, thereby causing the computer to function as a simulated earthquake wave creation means. Be able to. The known database includes the position information of a plurality of observation points, the ground data such as the seismic velocity structure in the ground located below each observation point, the arrival times of earthquake waves of a plurality of earthquakes observed at each observation point, and The acceleration waveform and the earthquake data of these earthquakes (for example, the moment magnitude and mechanism solution of the earthquake and the position of the epicenter) are input to the computer in advance (see step S1 in FIG. 1).
In the present embodiment, the database corresponds to a weak ground motion whose maximum acceleration is 0.3 [m / s ² ] or less among the ground motions observed by K-NET of the National Research Institute for Earth Science and Disaster Prevention. Use a database from which only data is extracted. This weak ground motion corresponds to “ground vibration” in the present invention. Since weak ground motions have a higher frequency of ground motions than stronger ground motions, the ground motion observation period required to obtain the same amount of data can be shortened.

When the engineer creates a simulated seismic wave using the simulated earthquake wave creation program, the engineer first inputs the maximum amplitude of the simulated earthquake wave to be created into the computer (step S2), and the earthquake that generates the simulated seismic wave. Set earthquake data. Here, step S2 corresponds to the “amplitude setting step” in the present invention. Next, the engineer inputs the position and range of the target area and the earthquake data extraction period to the computer (step S3).
In contrast to the above steps S2 and S3, a computer executing a simulated seismic wave generation program (hereinafter also simply referred to as “computer”) is an observation point where weak ground motion is observed during the input earthquake data extraction period. Among them, the observation point closest to the target area is extracted as the nearest point (step S4). Here, if the computer cannot automatically extract the nearest point, such as when there are multiple observation points within the target area, the computer outputs a message telling the technician to that effect. Allows a person to select an observation point to be extracted as the nearest point.

The computer that has executed step S4 extracts weak ground motion data during the earthquake data extraction period of the nearest point from the database described above (step S5), and acquires the ground data of the nearest point as an analysis parameter of the target area. Prepare (step S6). This step S6 corresponds to the “analysis parameter preparation step” in the present invention.
Subsequently, the computer determines whether or not there are a plurality of weak earthquake motion data extracted in step S5 (step S7). If the determination result in step S7 is “No” (that is, only one weak ground motion data is extracted in step S5), the computer analyzes the weak ground motion data extracted in step S5 in the target area. Prepared as data for use (step S8), and prepared by extracting the earthquake data of the weak ground motion from the above-mentioned database. Here, step S8 corresponds to the “analysis data preparation step” in the present invention.

On the other hand, when the determination result in step S7 is “Yes” (that is, a plurality of weak ground motion data is extracted in step S5), the computer selects each weak ground motion among the plurality of weak ground motions extracted in step S5. One weak ground motion that best reflects the characteristics of is extracted.
Specifically, the computer first calculates a Fourier amplitude spectrum for each of the plurality of weak ground motions extracted in step S5 (step S9). Next, the computer stacks each Fourier amplitude spectrum calculated in step S9 to calculate a representative Fourier amplitude spectrum (step S10). Further, the computer calculates the value of the cross-correlation function between each Fourier amplitude spectrum and the representative Fourier amplitude spectrum when the delay amount between each Fourier amplitude spectrum calculated in step S9 and the representative Fourier amplitude spectrum is zero. Calculate and obtain (step S11). Then, the computer extracts one weak ground motion with the largest cross-correlation function value obtained in step S11 (step S12).

The weak ground motion extracted in steps S9 to S12 is prepared as analysis data in step S8 described above, and the earthquake data of this weak ground motion is extracted from the database described above and prepared.
Then, the computer that has prepared the analysis data in step S8 calculates and outputs a simulated seismic wave using the analysis data and the analysis parameter prepared in step S6 (step S13).

Details of step S13 will be described with reference to the flowchart of FIG. 3 and the graphs of FIGS. The computer that has executed step S13 first acquires the maximum amplitude of the simulated seismic wave, the analysis parameter of the target area, and the analysis data of the target area (step S14).
Subsequently, based on the analysis parameter acquired in step S14, the computer is incident to be incident on the engineering base plane of the target area in order to cause the earthquake motion indicated in the analysis data on the ground surface of the target area. The seismic wave is calculated and obtained by inversion (step S15). This step S15 corresponds to an “inversion step” in the present invention.

In the present embodiment, in step S15, the surface ground between the engineering foundation surface and the ground surface in the target area is regarded as a one-dimensional stratified structure model, and inversion based on the double reflection theory is executed. Inversion based on this double reflection theory is a known inversion method that assumes that the target ground is regarded as a linear elastic body, and has the advantage that the inversion result can be easily calculated by linear analysis. ing.
By the way, in step S13, only the data corresponding to the small and small earthquake motion whose maximum acceleration is 0.3 [m / s ² ] or less is handled. For this reason, in the above-mentioned weak ground motion, the surface layer ground in the target area can be regarded as a linear elastic body. Thereby, the incident seismic wave can be calculated easily and accurately, and the reliability of the created simulated seismic wave can be improved.

The computer that executed Step S15 described above calculates and obtains the maximum amplitude of the incident seismic wave obtained in Step S15 (Step S16). Subsequently, the computer calculates a quotient obtained by dividing the maximum amplitude of the simulated seismic wave acquired in step S14 described above by the maximum amplitude of the incident seismic wave calculated in step S16 as an amplitude magnification (step S17). Then, the computer calculates the amplitude-adjusted seismic wave by uniformly applying the amplitude magnification calculated in step S17 to the amplitude of the incident seismic wave obtained in step S15 (step S18).
The step S16 corresponds to the “incident seismic wave amplitude derivation step” in the present invention, the step S17 corresponds to the “amplitude magnification calculation step” in the present invention, and the step S18 corresponds to the “amplitude adjustment step” in the present invention. To do.

The computer that has calculated the amplitude-adjusted seismic wave in step S18 outputs the calculated spectrum distribution of the amplitude-adjusted seismic wave together with the analysis parameters of the target area, and determines whether or not the nonlinear response of the surface ground can be ignored in creating the simulated seismic wave. The engineer is determined (step S19). If the determination result in step S19 is “Yes” (that is, the nonlinear response of the surface ground can be ignored), the computer outputs the amplitude-adjusted seismic wave as a simulated earthquake wave created as it is (step S20). This step S20 corresponds to an “output step” in the present invention.
On the other hand, if the determination result in step S19 is “No” (that is, the nonlinear response of the surface ground cannot be ignored), the computer corrects the amplitude-adjusted seismic wave calculated in step S18 (step S21) and corrects it. The amplitude adjusted seismic wave is output as the created simulated seismic wave (step S20).

In step S21, the computer calculates the long-period component of the amplitude-adjusted seismic wave so that a distance attenuation formula is established between the epicenter distance and the maximum value of the spectral density in the long-period component of the Fourier amplitude spectrum of the seismic wave. Correction to adjust the amplitude of the.
Here, the long period component is extracted on the basis that the vibration frequency is a predetermined value (0.5 [Hz] in the present embodiment) or less. The epicenter distance is obtained from the relative position between the epicenter and the target area. The distance attenuation formula is set in advance for each earthquake type and moment magnitude based on the earthquake database observed by the earthquake observation network (in this embodiment, KIK-net of the National Research Institute for Earth Science and Disaster Prevention). (See, for example, distance attenuation formula 10 for intraplate earthquakes and distance attenuation formula 11 for interplate earthquakes shown in FIGS. 48 and 49). The type of earthquake is determined as an intraplate earthquake or an interplate earthquake depending on the mechanism solution of the earthquake and the location of the epicenter.

When the maximum amplitude of the corrected amplitude-adjusted seismic wave does not coincide with the maximum amplitude of the simulated seismic wave created in step S21, the computer performs the processing performed on the incident seismic wave in steps S17 and S18 described above. The same process is performed on the amplitude-adjusted seismic wave, and the maximum amplitude of the amplitude-adjusted seismic wave is made to coincide with the maximum amplitude of the simulated seismic wave.
With the above-described correction, the computer can improve the reliability of the generated simulated seismic wave. Here, since the correction is performed on the long-period component of the seismic wave, it is possible to more accurately reflect the effect of extending the dominant period of the seismic wave waveform due to the nonlinear response of the surface layer ground.

According to each step described above, the computer that has read the simulated seismic wave generation program from the computer-readable recording medium uses the point characteristics (of the target area) for the analysis data obtained from the ground vibration on the ground surface of the target area. Analyzes using the analysis parameters of the ground characteristics of the surface layer between the engineering foundation surface and the ground surface) and adjusting the amplitude of the analysis results to simulate simulated earthquake waves incident on the engineering foundation surface in the target area Create For this reason, in the creation of simulated seismic waves incident on the engineering foundation surface, the source characteristics of historical earthquakes or active faults (the characteristics of seismic wave release at the source fault) and propagation path characteristics (from the source to the engineering foundation surface of the target area) There is no need to consider the characteristics of the path of propagation of seismic waves. This presupposes the knowledge that the influence of the site characteristics on the ground motion on the ground surface is so large that the effects of the source characteristics and propagation path characteristics on the ground motion can be ignored.
In addition, the surface ground is close to the ground surface and it is easy to conduct ground data surveys such as drilling surveys. For this reason, the said point characteristic can be calculated | required with high reliability compared with the hypocenter characteristic and propagation path characteristic of a historical earthquake or an active fault. Thereby, the reliability of the simulated seismic wave created by the computer can be improved.

The knowledge that the influence of the site characteristics on the ground motion on the ground surface is so great that the effects of the source characteristics and propagation path characteristics on the ground motion can be ignored is a knowledge newly discovered by the present inventor by analyzing the measured data. is there. In the following, the analysis on which the inventor has discovered the above findings will be described with reference to FIGS.
In the following, observation data at Hi-net Sendai station (see Hi-net Sendai station V shown in Fig. 4) is used. The seismometer at this Hi-net Sendai station is used for ground surveys by boring. By being put in a hole formed in the trace, it is installed at a depth of 1200 [m] underground. For this reason, the seismic waves observed by the seismometers at the Hi-net Sendai Station reflect the seismic waves incident from the engineering base to the ground surface in the area surrounding the Hi-net Sendai Station. Can be considered.

The present inventor observed 11 earthquakes (see Fig. 4) around Miyagi Prefecture at the Hi-net Sendai station and the ground surface directly above the Hi-net Sendai station. We analyzed the data corresponding to the earthquake observation data. Specifically, an analysis was performed to compare the spectrum distribution of the Fourier amplitude spectrum of the ground motion observed as observation data for the above 11 earthquakes (see FIGS. 5 to 26).
Here, Table 1 shows the parameters of each earthquake to be analyzed.

なお、「震源位置」は、地震の震源が図４に示した各震源ｗ１、ｗ２、・・・、ｗ１１のうちどれであるかを示す符号である。この各震源ｗ１、ｗ２、・・・、ｗ１１は、防災科学技術研究所のHi-netのデータベースから検索したものであり、ｗ１ないしｗ５はプレート内地震の、ｗ６ないしｗ１１はプレート間地震の震源である。「地震発生年月日」は、地震が発生した年月日を気象庁の地震のデータベースから検索したものである。「震源深さ」は、地震の震源の深さをHi-netのデータベースから検索したものである。「Ｍｊ」は、地震の気象庁マグニチュードを気象庁の地震のデータベースから検索したものである。「地表面応答加速度」は、Hi-net仙台観測点の真上の地表面で観測された地震動の水平動成分に対して、応答加速度波形の最大振幅を抽出したものである。上記各データベースの検索は、２０１２年１月に行った。

The “seismic source position” is a code indicating which of the seismic sources w1, w2,..., W11 shown in FIG. These epicenters w1, w2,..., W11 are retrieved from the Hi-net database of the National Research Institute for Earth Science and Disaster Prevention. It is. “Earthquake date” is a search for the date of earthquake occurrence from the earthquake database of the Japan Meteorological Agency. “Source depth” is a search of the depth of the earthquake from the Hi-net database. “Mj” is obtained by searching the Meteorological Agency magnitude of the earthquake from the earthquake database of the Meteorological Agency. “Surface response acceleration” is the maximum amplitude of the response acceleration waveform extracted from the horizontal motion component of the ground motion observed on the ground surface directly above the Hi-net Sendai station. The above database was searched in January 2012.

Now, comparing the graphs of FIGS. 5 to 26 in correspondence, the spectral distribution of the seismic motion observed with the seismometer at the Hi-net Sendai station is that the magnitude (amplitude) of the spectral density and the dominant vibration frequency are earthquakes. It can be seen that they are greatly different. On the other hand, the spectral distribution of the ground motion observed on the ground surface directly above the Hi-net Sendai observation point, although the magnitude of the spectral density is different, the dominant vibration frequency is about 0.9 [Hz] regardless of the earthquake. It can be seen that 2 [Hz] and approximately 6 [Hz] are almost the same. This means that even if any seismic wave is incident on the ground surface from the engineering foundation surface, similar characteristics are given to the seismic wave that reaches the ground surface.
Here, the seismic wave incident from the engineering foundation surface toward the ground surface reflects the seismic source characteristics and propagation path characteristics among the effects on the ground motion. The seismic wave that reaches the ground surface reflects all of the site characteristics, the source characteristics, and the propagation path characteristics among the effects on the ground motion. For this reason, ground motions caused by seismic waves that reach the ground surface have such a large impact that the effects of the source and propagation path properties on the ground motion are negligible. it can.

<Second Embodiment>
Next, a method for creating a simulated seismic wave according to the second embodiment will be described with reference to the flowchart of FIG. The method for creating a simulated seismic wave according to the second embodiment is a modified embodiment of the method for creating a simulated seismic wave according to the first embodiment. Therefore, the steps common to the steps of the method for creating a simulated seismic wave according to the first embodiment are the same as the symbols attached to the steps of the method for creating the simulated seismic wave according to the first embodiment. The detailed explanation is omitted.
The method for creating a simulated seismic wave according to the second embodiment is a simulated earthquake wave creating program (hereinafter simply referred to as “simulated seismic wave creation program”) based on the assumption that data of a known database is used in the method of creating a simulated seismic wave according to the first embodiment. Instead of “simulated seismic wave creation program according to the first embodiment”), a weak earthquake motion (corresponding to “ground vibration” in the present invention) and a target area obtained in advance by an engineer. A simulated seismic wave creation program (hereinafter also simply referred to as “simulated seismic wave creation program according to the second embodiment”) based on the use of analysis parameters is used.

The analysis parameter is the ground data of the target area acquired by the engineer by performing the ground survey of the target area (see step S22 in FIG. 27), and is prepared by being input to the computer in advance. That is, step S22 corresponds to the “analysis parameter preparation step” in the present invention.
In addition, the above-described weak ground motion is a ground motion in which the engineer performs seismic observation of the target area on three axes, and the observed value of the maximum acceleration is equal to or less than a predetermined value (0.3 [m / s ² ] in the present embodiment). Are obtained by observing one or more of them (see step S23 in FIG. 27). Here, since the weak ground motion has a higher frequency of occurrence of the ground motion than the stronger ground motion, the observation period of the weak ground motion in step S23 is relatively short.

In addition, earthquake data of an earthquake (hereinafter also referred to as “observed earthquake”) that is a source of the above-mentioned weak ground motion is input to a computer and prepared in advance by an engineer (see step S120 in FIG. 27). In step S120, the engineer first secures the following data for each weak ground motion observed in step S23.
(A) Triaxial acceleration waveform and maximum value of amplitude of each acceleration waveform (maximum acceleration) and amplitude of initial motion of each acceleration waveform (b) Seismic wave arrival time and dominant vibration frequency of dense wave and shear wave

Next, the engineer extracts the earthquake corresponding to each of the weak ground motions from the database of earthquakes observed by the seismic observation network (in this embodiment, the Hi-net of the National Research Institute for Earth Science and Disaster Prevention). In other words, the engineer calculates an earthquake corresponding to the seismic wave arrival time of the dense wave (b) described above from the earthquake database and the distance from the earthquake source to the target area. The operation of extracting in consideration of the above is executed for each weak ground motion. Thereby, the engineer can use the highly accurate observation result obtained by the earthquake observation network only by performing the earthquake observation of the target area.
In this embodiment, when an engineer cannot extract an earthquake corresponding to a weak earthquake motion from the earthquake database, the engineer determines that the weak earthquake motion for which the corresponding earthquake could not be extracted is a misrecognized noise. Thus, it is excluded from the acquisition result of step S23. Thus, when all the weak ground motions acquired in step S23 are excluded, the engineer re-executes step S23 to acquire the weak ground motions again, and extracts the earthquake corresponding to the weak ground motions.

Then, the engineer secures the extracted moment magnitude, mechanism solution, and location of the epicenter of each earthquake, and the three-axis acceleration waveform of (a) and the dense and shear waves of (b) above. Along with the arrival time of each seismic wave, it is input to the computer as seismic data for each observed earthquake.
Here, the position of the epicenter input as the earthquake data of the observed earthquake corresponds to the “observed earthquake source position” in the present invention, and step S120 corresponds to the “observed earthquake source position securing step” in the present invention. For this reason, hereinafter, the position of the above-mentioned epicenter is also referred to as “observed seismic epicenter position”.

When the engineer creates a simulated seismic wave using the simulated earthquake wave creation program, the engineer first inputs the maximum amplitude of the simulated earthquake wave to be created into the computer (step S2). Next, the engineer sets the earthquake data of the simulated earthquake that generates the simulated earthquake wave and inputs it to the computer (step S121).
Here, in this embodiment, the earthquake data of the simulated earthquake includes the moment magnitude of the simulated earthquake, the mechanism solution of the simulated earthquake, and the location of the simulated earthquake (the location of the simulated earthquake). That is, the step S2 corresponds to an “amplitude setting step” in the present invention, and the step S121 corresponds to a “simulated earthquake source position setting step” in the present invention.

In step S2, the computer determines whether or not there are a plurality of weak ground motion data observed in step S23 based on the number of observed earthquakes in which the earthquake data is input to the computer in step S120. Step S25). If the determination result in step S25 is “No” (that is, only one observed earthquake), the computer prepares the weak ground motion data extracted in step S23 as analysis data for the target area (step S26), acquiring and preparing earthquake data of this weak and small earthquake motion. Here, step S26 corresponds to the “analysis data preparation step” in the present invention.
On the other hand, when the determination result in step S25 is “Yes” (that is, there are a plurality of observed earthquakes), the computer selects each observed earthquake among the observed earthquakes corresponding to the plurality of weak ground motions observed in step S23. One observed earthquake whose epicenter position is relatively close to the simulated seismic hypocenter position is selected, and weak ground motion corresponding to this observed earthquake is extracted.

Specifically, the computer first acquires the observed earthquake source position and simulated earthquake source position of each observed earthquake input in step S121 (step S122). Next, the computer calculates the distance between the hypocenters from the simulated seismic source position for each observed seismic source position acquired in step S122 (step S123). Further, the computer classifies each observed earthquake based on the pre-set seismic source distance classification based on the respective interseismic distances calculated in step S123 (step S124). Then, the computer selects one observed earthquake classified into the category with the shortest epicenter distance from among the seismic source distance categories in which one or more observed earthquakes are classified, and the weak ground motion corresponding to this observed earthquake is selected. Is extracted (step S125).
In addition, in this embodiment, the division | segmentation for every 100 [km] of 0-99 [km], 100-199 [km] ... is used as a division | segmentation of the said epicenter distance. In addition, when a plurality of observed earthquakes are classified in the category in which the observed earthquake is to be selected in step S125, the computer selects the simulated earthquake whose moment magnitude is input in step S121 described above from the plurality of observed earthquakes. Select the observed earthquake closest to the moment magnitude.

The computer that has performed the extraction prepares the extracted weak earthquake motion data as analysis data for the target area (step S27), and acquires and prepares the weak earthquake motion data. Here, step S27 corresponds to the “analysis data preparation step” in the present invention. Then, the computer that has prepared the analysis data in step S26 or step S27 calculates and outputs a simulated seismic wave using the analysis data and the analysis parameter prepared in step S22 (step S13). Here, step S13 is the same step as step S13 in the simulated seismic wave generation program according to the first embodiment, and therefore detailed description thereof is omitted.
According to each of the above procedures, a simulated seismic wave of a simulated earthquake is created based on observation data of an observed earthquake whose observed seismic source location is relatively close to the simulated seismic source location. Thereby, the difference in propagation path characteristics between the observed earthquake and the simulated earthquake can be reduced, and the reliability of the created simulated earthquake wave can be further improved. Moreover, by classifying a plurality of observed earthquakes according to the classification of the distance between the epicenters, it is possible to identify a plurality of observed earthquakes whose observed earthquake source positions are relatively close to the simulated earthquake source positions. If multiple observed earthquakes whose observed seismic source positions are relatively close to the simulated seismic source position are identified, among these observed earthquakes, the moment magnitude is the observation data of the observed earthquake closest to the simulated earthquake moment magnitude. Based on this, a simulated earthquake wave of the simulated earthquake is created. Thereby, the influence by the difference in the long period component of the seismic wave between the observed earthquake and the simulated earthquake can be reduced, and the reliability of the created simulated earthquake wave can be further improved.

Here, the verification result of the effectiveness of the method of creating a simulated seismic wave according to the second embodiment will be described with reference to FIGS. The above verification results reproduce the earthquake data on the engineering foundation surface of the huge earthquake observed in the target area using the earthquake data on the ground surface of the weaker earthquake, and this reproduction result and the earthquake data of the huge earthquake are It was obtained by comparison. In addition, the above-described reproduction is performed for each of the earthquake Y that is relatively close to the epicenter of the huge earthquake and the earthquake Z that is relatively far from the epicenter, so that the distance between the hypocenters (see step S123 in FIG. 27) is a large earthquake. The effect on the reproduction results was also verified.
Here, the Tohoku-Pacific Ocean Earthquake (Meteorological Agency magnitude 9.0) which occurred on March 11, 2011 was used as a huge earthquake. As the earthquake Y, the Miyagi-ken Oki earthquake (Meteorological Agency magnitude 7.2) which occurred on August 16, 2005 was used. As the earthquake Z, in the Kanagawa western earthquake (JMA magnitude 4.1) that occurred on July 11, 2003, the vibration frequency of the velocity amplitude Fourier amplitude spectrum (see FIG. 50) is 2.5 [Hz] or less. Synthetic earthquakes were used in which the long-period components of were amplified by assuming a stronger earthquake. As the earthquake data of each earthquake used for the reproduction and comparison, a Fourier amplitude spectrum obtained from the velocity waveform data in the north-south direction was used (see FIGS. 51 to 53).

Further, as the target area, the KIK-net Hachioji observation point (see KIK-net Hachioji observation point V ′ in FIG. 54) of the National Research Institute for Earth Science and Disaster Prevention was used. This KIK-net Hachioji observation point is inserted into a hole formed in the site of a ground survey by boring, and an underground seismometer installed at a depth of 147 [m] underground, And a seismometer on the surface side installed on the surface of the ground located directly above the seismometer. In addition, the ground motion observed by the seismometer on the underground side of the KIK-net Hachioji observation station is directly reflected by the seismic wave incident from the engineering base to the ground surface in the surrounding area of the KIK-net Hachioji observation station. Can be considered. Therefore, in this verification, the seismometer on the underground side of the KIK-net Hachioji observation point is regarded as the seismometer installed on the engineering base of the target area, and the seismometer on the ground side is also installed on the ground surface of the target area. Was considered a seismometer.
FIG. 54 shows the positional relationship between the KIK-net Hachioji observation point V ′ and the epicenters w12, w13, and w14. Here, the epicenter w12 is the epicenter of the off the Pacific coast of Tohoku Earthquake (big earthquake) (depth 24 [km]), the epicenter w13 is the epicenter of the Miyagi Prefecture offshore earthquake (earthquake Y) (depth 42 [km]), the epicenter w14 Is the epicenter of the Kanagawa Seibu Earthquake and Earthquake Z (depth 21 [km]). The Miyagi-oki earthquake is stronger than the Kanagawa-ken Seibu earthquake and earthquake Z (the maximum amplitude of the acceleration waveform is larger), but the maximum response acceleration of horizontal motion in the seismometer on the surface side of the KIK-net Hachioji station Was 0.106 [m / s ² ] equal to the Kanagawa west earthquake and earthquake Z by three significant figures due to the difference in propagation path characteristics. From this, in this verification, each ground motion due to earthquakes Y and Z can be regarded as weak ground motions that can ignore the non-linearity of the surface ground.

Each Fourier amplitude spectrum of the incident seismic wave (see step S15 in FIG. 3) obtained from the earthquake data on the ground surface of each of the earthquakes Y and Z is shown in FIGS. From FIG. 55 and FIG. 56, each dominant vibration frequency of the incident seismic wave of earthquake Y is an error of about ± 0.1 [Hz] with respect to each dominant vibration frequency (see FIG. 52) of the incident seismic wave of the huge earthquake. In addition, it can be read that each dominant vibration frequency of the incident seismic wave of earthquake Z corresponds well with an error of about ± 0.3 [Hz].
From this, it can be said that the method of creating a simulated seismic wave according to the second embodiment has shown its effectiveness. In addition, it can be seen that the earthquake Y that is relatively close to the epicenter of the giant earthquake can reproduce the seismic waves of the giant earthquake more accurately than the earthquake Z that is relatively far from the epicenter of the giant earthquake.

52 and 55, focusing on the shape of the spectral distribution, the incident seismic wave of earthquake Z has a spectral distribution in a long-period component with an oscillation frequency of 1 [Hz] or less compared to the incident earthquake wave of a huge earthquake. It can be seen that the shapes are different. On the other hand, when FIG. 52 and FIG. 56 are compared by paying attention to the shape of the spectrum distribution, it can be seen that the incident seismic wave of earthquake Y has almost the same shape of the spectrum distribution as compared to the incident earthquake wave of the giant earthquake.
Here, the amplitude in the amplitude adjusting step (see step S1 8 in FIG. 3) of the present embodiment is adjusted uniformly. Here, corrected for the vibration frequency 1 [Hz] or less long period components for the amplitude controller seismic wave seismic Z obtained in Step S1 8 (see step S21 in FIG. 3) While it is necessary, as well it can be seen that there is no need to correct the above step S21 for the amplitude controller seismic waves earthquakes Y obtained in step S1 8. From here, when creating a seismic wave of a huge earthquake as a simulated seismic wave, if an earthquake with the location of the epicenter relatively close to the huge earthquake and the maximum amplitude of the acceleration waveform is relatively close, nonlinearity of the surface ground It can be seen that a simulated seismic wave having a relatively small response effect can be obtained without correction for the amplitude adjusted seismic wave.

<Third Embodiment>
Next, a method for creating a simulated seismic wave according to the third embodiment will be described with reference to the flowchart of FIG. The method of creating a simulated seismic wave according to the third embodiment is a modified embodiment of the method of creating a simulated earthquake wave according to the first embodiment. Therefore, the steps common to the steps of the method for creating a simulated seismic wave according to the first embodiment are the same as the symbols attached to the steps of the method for creating the simulated seismic wave according to the first embodiment. The detailed explanation is omitted.
The method of creating a simulated seismic wave according to the third embodiment is a method of creating a microtremor of a target area obtained in advance by an engineer (a weakly acting constant ground) instead of the simulated seismic wave creating program according to the first embodiment. Vibration (corresponding to "ground vibration" in the present invention)) From the observation data of the ground in the target area, we estimate the vibration characteristics (amplitude of amplitude with respect to vibration) and artificially generate weak earthquake motion for creating simulated seismic waves. A simulated earthquake wave creation program to be created (hereinafter also simply referred to as “simulated earthquake wave creation program according to the third embodiment”) is used. In the following, detailed description of the incidental steps such as the step of preparing various parameters necessary for creating the simulated seismic wave from the vibration characteristics of the ground will be omitted.

The observation data of the above-mentioned microtremor is obtained by the engineer observing the microtremor in the target area on three axes for a predetermined time (in this embodiment, 5 minutes) (see step S29 in FIG. 28). Here, since the fine movement is constantly acting on the ground, the engineer can finish the step S29 in a short time (5 minutes). This microtremor observation data is prepared by inputting to the computer in advance for each microtremor direction component.
When the engineer creates a simulated seismic wave using the simulated earthquake wave creation program, the engineer first inputs the maximum amplitude of the simulated earthquake wave to be created into the computer (step S2), and the earthquake that generates the simulated seismic wave. Set earthquake data. Here, step S2 corresponds to the “amplitude setting step” in the present invention.

Subsequently, the computer estimates and prepares the vibration characteristics of the ground in the target area as analysis parameters from observation data of microtremors (step S30), and sets various parameters necessary for creating a simulated seismic wave from the estimated vibration characteristics. . Further, the computer sets vibration frequency characteristics and phase characteristics in weak ground motion for generating simulated seismic waves (step S31), and creates earthquake motion having the set vibration frequency characteristics and phase characteristics by calculation processing in the frequency domain. The computer applies an envelope shape with respect to the amplitude of the seismic waveform to the generated seismic motion to convert it into a weak seismic motion waveform in the time domain, and creates and prepares the weak seismic motion data as analysis data ( Step S32). The step S30 corresponds to the “analysis parameter preparation step” in the present invention, and the step S31 and the step S32 correspond to the “analysis data preparation step” in the present invention.
In the present embodiment, the vibration frequency characteristic is set to coincide with the vibration characteristic estimated in step S30 described above. The phase characteristic is set by a random number. The envelope shape is a shape created by an engineer so that the maximum acceleration of seismic motion is a predetermined value (0.3 [m / s ² ]) or less, and is input to the computer in advance.

And the computer which prepared the data for analysis by said step S31 and said step S32 calculates and outputs a simulated seismic wave using this analysis data and the analysis parameter prepared by step S30 (step S13).
Here, step S13 is the same step as step S13 in the simulated seismic wave generation program according to the first embodiment, and therefore detailed description thereof is omitted.

Details of step S30 will be described using the flowchart of FIG. 29 and the three-dimensional graph of FIG. The computer that has executed step S30 acquires the above-described observation data of microtremors in three axes (step S33), and obtains the nonstationary spectrum of microtremors from the acquired observation data, and the spectral density and vibration of this nonstationary spectrum. It is calculated as a three-dimensional function with frequency and time as variables (step S34). The unsteady spectrum is always prepared for each direction component of fine movement by a computer executing a known program.
In this embodiment, the operation for plotting the non-stationary spectrum of the microtremor on the graph is not performed. However, when the non-stationary spectrum of the microtremor is plotted on the three-dimensional graph, for example, the nonstationary spectrum partially shown in FIG. A three-dimensional graph such as spectrum 1 is obtained for each direction component of the observation data.

When the computer calculates the unsteady spectrum of microtremors in three axes in step S34, each calculated unsteady spectrum is discretized at a predetermined sampling frequency (100 [Hz] in this embodiment), and is calculated for each discrete time domain. A two-dimensional function with the spectral density and vibration frequency of the unsteady spectrum as variables is calculated (step S35). This corresponds to obtaining a plurality of time sections 3 where the unsteady spectrum 1 and a plurality of planes 2 perpendicular to the time axis intersect in the unsteady spectrum 1 shown in FIG.
Subsequently, the computer creates an array of two-dimensional functions having all of the discretized non-stationary spectra (that is, time sections of the non-stationary spectra) as array elements (step S36). Then, the computer calculates the spectral intensity by integrating the array elements with the vibration frequency of the fine movement at all times (step S37).

Subsequently, the computer rearranges each array element of the array created in step S36 in ascending order of the spectrum intensity calculated in step S37, and sets the analysis order in ascending order of the spectrum intensity (step S38). Then, the computer extracts an analysis candidate spectrum from the array elements whose spectrum intensity is equal to or lower than a predetermined reference value (step S39). Further, the computer determines the natural frequency and non-resonant frequency of the ground from the analysis candidate spectrum, and outputs the result as an estimation result of the vibration characteristics of the ground in the estimation target area (step S40).
According to each step described above, the computer that has read the simulated seismic wave generation program from a computer-readable recording medium uses, as an analysis candidate spectrum, a time section of an unsteady spectrum with a relatively small spectrum intensity from an unsteady spectrum of microtremors. Extract and estimate the vibration characteristics of the ground. For this reason, the analysis candidate spectrum for the computer to estimate the vibration characteristics reflects only data that is relatively weakly influenced by the surface wave component of the microtremor. As a result, the noise due to the surface wave component of the fine movement can be reduced, and the accuracy of estimating the vibration characteristics of the ground from the fine movement can be improved.

Here, the inventor has found that the influence of the surface wave component of microtremor is relatively weak on the time section of the nonstationary spectrum having a relatively small spectral intensity among the nonstationary spectrum of microtremor. It is a knowledge newly discovered through analysis. In the following, the analysis on which the present inventor has discovered the above findings will be described with reference to FIGS.
In the following, observation data of observations made by the present inventor at observation point X will be used. The seismometer at observation point X is inserted into a hole formed in the site of a ground survey by boring, so that It is installed at a depth of .52 [m]. Further, in the vicinity of the observation point X, the physical properties and the shear wave velocity structure (see FIG. 31) of the ground from the ground surface to the depth of 280 [m] underground are found by the above ground survey.

The present inventor has made microtremors in the ground at observation point X (see the horizontal motion north-south component of the response speed shown in FIG. 32) and microtremors on the ground surface directly above observation point X (shown in FIG. 33). (See the horizontal dynamic north-south component of the response speed) and the same time.
Here, it can be considered that only the body wave transmitted from the deeper ground reaches the underground observation point X. Moreover, on the ground surface directly above the observation point X, a body wave transmitted from the underground ground through the underground observation point X, a surface wave transmitted along the ground surface from the surrounding area, Both can be considered to reach. In addition, from the fact that the distance from the underground observation point X to the ground surface is 208.52 [m] and the shear wave velocity structure shown in FIG. 32 and 33 can be considered to be negligibly small with respect to the time scale of FIGS.

32 and 33 are compared, the response speed waveform based only on the body wave shown in FIG. 32 has a smaller amplitude variation over time than the response speed waveform based on both the surface wave and the body wave shown in FIG. This is presumed to be due to the fact that the surface wave component varies more with time than the body wave component and is non-stationary during constant tremor.
Therefore, in order to support the above estimation, the inventor conducted an analysis for separating the surface wave component and the body wave component from the response speed waveform shown in FIG. That is, the present inventor firstly made a fine movement from the observation point X to the ground surface directly above the observation point X based on the physical properties of the ground around the observation point X and the shear wave velocity structure of the ground shown in FIG. The vibration characteristic around the observation point X when the wave is transmitted (see FIG. 34) was derived. Next, the present inventor uses the vibration characteristics around the observation point X shown in FIG. 34 and the response speed waveform based only on the body wave shown in FIG. 32 to cause the seismic wave shown in FIG. The response speed waveform of microtremor when transmitted to the ground surface (see FIG. 35) was calculated by analysis in the frequency domain. This response speed waveform (see FIG. 35) can be considered as a body wave component of fine movement on the ground surface directly above. Therefore, the present inventor subtracts the response speed waveform of the body wave component of the continuous fine movement shown in FIG. 35 from the response speed waveform of the continuous fine movement shown in FIG. The response speed waveform of the wave component (see FIG. 36) was calculated.

35 is compared with FIG. 36, the response speed waveform of the body wave component of continuous fine movement shown in FIG. 35 has a time variation in amplitude compared to the response speed waveform of the surface wave component of continuous fine movement shown in FIG. small. In other words, it can be said that the surface wave component is non-stationary and has a larger fluctuation with time than the body wave component in the constant tremor.
By the way, the non-stationary spectrum is a spectrum that represents the spectrum of the non-stationary signal as a function having at least time as a parameter for a signal having non-stationarity with respect to time (unsteady signal). Here, the spectrum intensity of the unsteady spectrum becomes stronger as the influence of the unsteady signal becomes larger. In other words, the influence of the non-stationary signal is relatively small in a time zone in which the spectrum intensity of the non-stationary spectrum is relatively small. For this reason, out of the non-stationary spectrum of microtremors, the influence of the relatively unsteady surface wave component is relatively weak on the time section of the unsteady spectrum with a relatively small spectral intensity, and the stationary wave is relatively stationary. It can be said that the influence of the components is relatively strong.

Here, the details of step S39 described above will be described using the flowchart of FIG. The computer that has executed step S39 first acquires the array created in step S36 described above and rearranged in step S38 and set in the analysis order together with the number of array elements f of this array (step S41).
Subsequently, the computer sets parameter variables g and i to be used for an after-mentioned iterative process (step S43) (step S42). Here, g is the analysis order of the array elements currently analyzed, and g = 1 is set in step S42. Further, i is the total number of extracted analysis candidate spectra, and i = 0 is set in step S42.

The computer that has initially set the parameters g and i in step S42 repeatedly performs a routine shown in steps S44 to S48 described later (step S43). This step S43 is repeatedly executed while the condition of g ≦ f is satisfied while increasing g (see step S46 and step S48). If g> f is satisfied in step S43, the computer terminates the above iterative process and terminates step S39 for extracting an analysis candidate spectrum.
In the routine repeated in step S43, the computer first acquires the spectral intensity of the g-th array element in the analysis order (step S44). This spectral intensity is calculated in step S37 (see FIG. 29) described above. Then, the computer determines whether or not the spectrum intensity acquired in step S37 is relatively large according to a predetermined criterion set in advance, and whether or not the spectrum intensity is greater than a preset reference value. (Step S45).

Here, in step S45, when the determination result is “No” (that is, the spectrum intensity is equal to or less than the reference value), the influence of the surface wave component of fine movement is relatively weak on the g-th array element in the analysis order. It can be considered that the data is reflected.
Therefore, when the determination result of step S45 is “No”, the computer executes step S47 of outputting an analysis candidate spectrum from the g-th array element in the analysis order. Then, after executing step S47, the computer adds 1 to g (step S48) and repeats the routine in order to execute analysis on the next array element in the analysis order.

On the other hand, when the determination result is “Yes” in Step S45 (that is, the spectrum intensity is larger than the reference value), the influence of the surface wave component of microtremor is relatively small on the g-th array element in the analysis order. It can be considered that strong data is reflected. In addition, since the analysis order of each array element is set in the above-described step S38 in ascending order of the spectrum intensity of each array element, all the array elements whose analysis order is the g-th and after are always subjected to surface waves of fine movement. It can be considered that data with a relatively strong influence of the component is reflected.
For this reason, when the determination result in step S45 is “Yes”, the computer substitutes a value larger than f (f + 1 in the present embodiment) for g (step S46) and terminates the iterative process of step S43. Then, step S39 for extracting the analysis candidate spectrum is ended. In other words, the computer omits step S45 and step S47 in the subsequent analysis order when the spectral intensity becomes larger than the reference value.

By the way, in step S47, the computer discriminates only the unsteady spectrum having relatively small noise (for example, the surface wave component of constantly fine movement) from the assumed steady wave body wave component and outputs it as an analysis candidate spectrum. To do. Here, the above-mentioned discrimination is the value of the cross-correlation function in a state where there is no delay between the hypothetical non-stationary spectrum derived from the hypothetical value and each array element (hereinafter also simply referred to as “cross-correlation value”) h. It is determined by the size of That is, in step S47, the computer converts the non-stationary spectrum of the array element whose cross-correlation value h is less than the predetermined value k, regardless of the magnitude relationship between the spectrum intensity of the non-stationary spectrum and the reference value described above. Exclude from analysis candidate spectrum.
According to the above-described method, the unsteady spectrum having relatively large noise with respect to the assumed body wave component of microtremor is excluded from the analysis candidate spectrum because the cross-correlation value h is smaller than the predetermined value k. . Thereby, the data with comparatively large noise can be removed from the analysis candidate spectrum, and the estimation accuracy of the vibration characteristics of the ground can be improved. For unsteady spectra that are not clearly extracted as analysis candidate spectra due to the magnitude of the spectrum intensity, the calculation of the cross-correlation value h, which requires a large amount of calculation, and the comparison of the magnitude relationship between the spectrum intensity and the reference value are omitted. Is done. Thereby, the amount of calculation in estimating the vibration characteristics of the ground can be reduced, and the vibration characteristics of the ground can be estimated more quickly.

Here, the details of step S47 described above will be described using the flowchart of FIG. Note that the predetermined value k to be compared with the cross-correlation value h is set in advance by the above-described engineer and input to the computer (step S52).
Further, the above-described hypothetical unsteady spectrum is calculated in advance by the engineer before the execution of step S47 based on the assumed vibration characteristic value of the ground and the actual body wave component assumed value of microtremor (step S51). ). The assumed vibration characteristic assumed value of the ground is a value set in advance by the engineer assuming the vibration characteristic of the ground in the estimation target area (step S49). The always fine body wave component assumed value is a value set in advance by the engineer assuming the always fine body wave component incident on the estimation target area (step S50).

After the preprocessing of steps S49 to S52 is performed, the computer that executed step S47 first acquires the above-described parameters g and i (step S53), and then acquires the g-th array element in the analysis order. (Step S54). Then, the computer calculates a cross-correlation function between the array element acquired in step S54 and the assumed unsteady spectrum calculated in step S51 described above as a function of the delay amount (step S55). Further, the computer substitutes 0 for the delay amount of the cross-correlation function calculated in step S53, so that the value of the cross-correlation function in a state where there is no delay between the hypothetical non-stationary spectrum and the array element is calculated. The correlation value h is calculated (step S56).
Subsequently, the computer determines whether or not the cross-correlation value h calculated in step S56 is greater than or equal to the predetermined value k set in advance in step S52 by comparing the magnitude relationship between the cross-correlation value h and the predetermined value k. Determination is made (step S57).

Here, when the determination result is “Yes” (ie, h ≧ k) in step S57, the array element in the g-th analysis order reflects data with relatively small noise with respect to the constantly moving body wave component. Can be considered. For this reason, when the determination result in step S57 is “Yes”, the computer adds 1 to i (step S58), and then analyzes the array element in the g-th analysis order extracted i-th. A candidate spectrum is output together with i (step S59), and step S47 is terminated. In addition, by sequentially outputting i in step S59, the calculation process for deriving the total number i of analysis candidate spectra extracted after the end of step S47 can be omitted.
On the other hand, when the determination result is “No” (that is, h <k) in step S47, the g-th array element in the analysis order reflects data with relatively large noise for the body wave component of constantly fine movement. Can be considered. Therefore, when the determination result of step S57 is “No”, the computer ends the step S47 as it is. Thereby, the non-stationary spectrum of the array element whose cross-correlation value h is less than the predetermined value k can be excluded from the analysis candidate spectrum.

Details of step S40 described above will be described with reference to the flowcharts of FIGS. Here, the natural frequency of the ground determined in step S40 and the maximum order b of the non-resonant frequency are set in advance by the above-described engineer and input to the computer (step S60).
In the following description, it is assumed that b = 3 is set in step S60 unless otherwise specified.

The computer that has executed Step S40 first acquires the total number i of analysis candidate spectra extracted in Step S39 and each analysis candidate spectrum (Step S61). If the value of i acquired in step S61 is 0 (that is, there is no analysis candidate spectrum to be analyzed), the computer outputs an error message indicating that “analysis candidate spectrum extraction has failed”. To forcibly terminate the simulated seismic wave creation program.
Subsequently, the computer sets parameter variables j and l used for repetitive processing (step S63) described later (step S62). Here, j is an argument indicating which analysis candidate spectrum is currently analyzed, and j = 1 is set in step S62. Further, l is an argument indicating which analysis candidate spectrum is the analysis candidate spectrum for which the natural frequency of the ground can be clearly identified, and l = 0 is set in step S62.

The computer that has initialized the parameters j and l in step S62 repeatedly performs routines shown in steps S64 to S69 described later (step S63). This step S63 is repeatedly executed while the condition of j ≦ i is satisfied while increasing j (see step S68 and step S69). When j> i is satisfied in step S63, the computer ends the above repeating process and executes step S70 described later.
In the routine repeated in step S63, the computer first acquires the jth analysis candidate spectrum and sets it as an analysis target spectrum (step S64). Then, the computer determines whether or not the natural frequency of the ground can be clearly determined in the spectrum to be analyzed set in step S64 (step S65), and performs conditional branching (step S66).

In the conditional branch of step S66, if the determination result of step S65 is “No” (that is, the natural frequency of the ground cannot be clearly determined in the analysis target spectrum), the computer analyzes the next analysis candidate. In order to perform analysis on the spectrum, 1 is added to j (step S69), and the routine is repeated.
On the other hand, in the conditional branch of step S66, when the determination result of step S65 is “Yes” (that is, the natural frequency of the ground can be clearly determined in the analysis target spectrum), the computer sets j to l. Is substituted (step S67). By using the parameter l, the computer can store the number of analysis candidate spectra that can be clearly discriminated from the natural frequency of the ground. Subsequently, the computer substitutes a value larger than i (i + 1 in the present embodiment) for j (step S68), and ends the repetition process of step S63. In other words, when an analysis candidate spectrum that can clearly discriminate the natural frequency of the ground is found, the computer omits subsequent analysis on the analysis candidate spectrum.

The computer that has completed the repetitive processing in step S63 can clearly determine the natural frequencies of the ground among the total number i of the analysis candidate spectra (that is, each natural frequency of the ground can be estimated with high accuracy). Whether or not it exists is determined by whether or not l = 0 (step S70).
Here, in step S70, when the determination result is “No” (that is, l ≠ 0), the computer can clearly determine the natural frequency of the ground in at least the l-th analysis candidate spectrum. It will be judged. Therefore, when the determination result in step S70 is “No”, the computer calculates the natural frequency and the non-resonant frequency of the l-th analysis candidate spectrum to the b-th order, and the natural frequency of the ground in the estimation target area. And it outputs as a non-resonant frequency estimation result (step S71). And a computer complete | finishes step S40 which outputs the estimation result of the vibration characteristic of the ground in an estimation object area.

On the other hand, when the determination result is “Yes” (ie, l = 0) in step S70, the computer determines that there is no analysis candidate spectrum that can clearly determine the natural frequency of the ground. It will be. For this reason, when the determination result of step S70 is “Yes” and i ≧ 2 (that is, when a plurality of analysis candidate spectra are extracted in step S39), the computer performs the operations from the first to the i-th. A spectrum obtained by geometrically averaging all analysis candidate spectra is calculated, this spectrum is set as an analysis target spectrum (step S72), and the natural frequency of the ground is clearly discriminated in the analysis target spectrum set in step S72. Is determined (step S73), and conditional branching is performed (step S74).
Here, step S73 is exactly the same processing as step S65 described above, and the same subroutine (see subroutine 6 in FIGS. 41 and 42) is used in the simulated seismic wave creation program of the present embodiment. Therefore, in the following, with regard to step S65 and step S73, the description and the flowchart are represented by the description of step S65 and the flowchart, and the description of step S73 and the flowchart are omitted.

According to each step described above, the influence of noise included in a plurality of analysis candidate spectra on the analysis target spectrum can be reduced by geometric averaging, and the accuracy of estimating the vibration characteristics of the ground from the analysis target spectrum can be improved. . In other words, according to step S72, an analysis target spectrum that can more clearly discriminate the natural frequency of the ground can be prepared from a plurality of analysis candidate spectra. Thereby, even if there is no analysis candidate spectrum that can clearly determine the natural frequency of the ground, there is a possibility that the vibration characteristics of the ground can be estimated with high accuracy.
When the determination result in step S70 is “Yes” and i = 1 (that is, only one analysis candidate spectrum is extracted in step S39), the vibration of the ground is determined by the analysis after step S72. The estimation accuracy of characteristics cannot be improved. For this reason, when the determination result in step S70 is “Yes” and i = 1, the computer outputs an error message stating that “estimation of the vibration characteristics of the ground has failed” and generates a simulated seismic wave generation program Is forcibly terminated.

In the conditional branch of step S74, if the determination result of step S73 is “Yes” (that is, the natural frequency of the ground can be clearly determined in the analysis target spectrum), the computer The natural frequency and non-resonant frequency of the spectrum are calculated up to the b-th order, and are output as estimation results of the natural frequency and non-resonant frequency of the ground in the estimation target area (step S75). And a computer complete | finishes step S40 which outputs the estimation result of the vibration characteristic of the ground in an estimation object area.
On the other hand, in the conditional branch of step S74, when the determination result of step S73 is “No” (that is, the natural frequency of the ground cannot be clearly determined in the analysis target spectrum), the computer starts from the first. Step S76 is executed in which the natural frequency and non-resonant frequency of the ground are determined and output from the frequency distribution of each extreme value of each i-th candidate analysis spectrum. And a computer complete | finishes step S40 which outputs the estimation result of the vibration characteristic of the ground in an estimation object area.

Next, details of step S65 described above will be described using the flowcharts of FIGS. Here, the maximum order b set in step S60 and input to the computer is acquired in advance by the computer (step S78). Further, a predetermined value m (where m> 0) whose magnitude relation is compared in step S90 described later is set in advance by an engineer and input to the computer (step S80). Furthermore, the condition D that is established for each natural frequency below the b-th order due to the physical properties of the ground in the estimation target area is set by the engineer before the execution of step S65 (step S79). The physical properties of the ground are assumed by the engineer in advance and set in the computer (step S77).
In the following description, unless otherwise stated, it is assumed that the engineer assumes that “the physical properties of the ground are relatively small in the region where the vibration characteristics are estimated”. That is, the above-mentioned condition D is that the quotient obtained by dividing the value of the c-order natural frequency by the value of the primary natural frequency with respect to the natural number c of “b (= 3) or less is 1 if c = 1, c = 2 is 2.7 to 3.3, and c = 3 is 4.5 to 5.5 ".

After the preprocessing of step S77 to step S80 is performed, the computer that executed step S65 first obtains the analysis target spectrum set and prepared in step S64 or step S72 described above (step S81).
Next, the computer sets each maximum value and each minimum value of the spectral density of the analysis target spectrum acquired in step S81 to a predetermined vibration frequency range (in this embodiment, 0.1 [Hz] or more and 100 [Hz]). All are calculated and extracted in the following range) (step S82).

Subsequently, the computer extracts the maximum value of the spectral density calculated and extracted in step S82, with the vibration frequency value being a predetermined value (1 [Hz] in this embodiment) or more (step S83). . In step S83, the computer can generally remove the influence of relatively large low-frequency noise from the determination result in step S65.
Then, the computer determines a local maximum value having the maximum spectral density among the local maximum values extracted in step S83, and adds the number 1 to the local maximum value (step S84).

Subsequently, the computer sets parameter variables c and n to be used for an after-mentioned iterative process (step S86) (step S85). Here, c is an argument indicating the number of the extreme value analyzed at the present time, and c = 1 is set in step S85. In addition, n is a Boolean argument, and is associated with 0 if the natural frequency of the ground can be clearly identified, and 1 if the natural frequency of the ground cannot be clearly identified. Yes. This n is set to n = 0 in the above step S85.
The computer that has initially set the parameters c and n in step S85 repeatedly performs a routine shown in steps S87 to S95 described later (step S86). This step S86 is repeatedly executed while the condition of c ≦ b is satisfied while increasing c (see step S91 and step S95). If c> b is satisfied in step S86, the computer ends the repetitive processing and executes step S96 described later.

In the routine repeated in step S86, the computer first extracts a minimum value of the spectral density extracted in step S82 that has a vibration frequency greater than the vibration frequency at the c-th maximum value (step S87). If the extraction of the minimum value fails in step S87, the computer substitutes 1 for n. Then, the computer substitutes a value larger than b (b + 1 in the present embodiment) for c, and finishes the iterative process of step S86. According to the above processing, the computer can clearly determine the natural frequency of the ground from the analysis target spectrum when the analysis of at least one of the minimum values from No. 1 to b cannot be performed. It can be determined that it is not possible.
Next, the computer determines a minimum value that minimizes the vibration frequency from among the minimum values extracted in step S87, and adds the number c to the minimum value (step S88). Subsequently, the computer calculates and obtains a difference p between the c-th maximum value and the c-th minimum value (step S89), and the difference p is equal to or larger than the predetermined value m set and input in step S80. Is determined by comparing the magnitude relationship between the difference p and the predetermined value m (step S90).

Here, in Step S90, when the determination result is “No” (that is, p <m), the difference p between the c-th local maximum value and the c-th local minimum value is relatively small that appears in the analysis target spectrum. It can be considered that noise is reflected. That is, when the determination result in step S90 is “No”, it can be considered that the natural frequency of the ground cannot be clearly determined from the analysis target spectrum.
Therefore, when the determination result in step S90 is “No”, the computer substitutes 1 for n, substitutes a value larger than b (b + 1 in this embodiment) for c (step S91), The repeating process of step S55 is terminated. In other words, when the computer determines that the natural frequency of the ground cannot be clearly determined from the analysis target spectrum, the computer repeats the subsequent iterative process.

On the other hand, when the determination result is “Yes” (ie, p ≧ m) in step S90, the computer assumes that the vibration frequency at the c-th maximum value is equal to the c-order natural frequency of the ground. It is determined whether or not the c-th natural frequency of the ground is satisfied when the condition D set in step S79 is satisfied (step S92).
In step S92, when the determination result is “not established”, at least one of the c-th local maximum value and the c-th local minimum value reflects the local maximum value or local minimum value of noise appearing in the analysis target spectrum. You can think of it as something. That is, when the determination result in step S92 is “not established”, it can be considered that the natural frequency of the ground cannot be clearly determined from the analysis target spectrum. For this reason, when the determination result of step S92 is “not established”, the computer executes step S91 described above and ends the repetition process of step S86.

If the determination result is “Established” in step S92, the computer prepares for the next iterative process in step S86. That is, the computer first extracts a maximum value of the spectral density extracted in step S82 that has a vibration frequency greater than the vibration frequency at the c-th maximum value (step S93). Here, when the extraction of the maximum value fails in step S93, the computer determines whether c ≠ b, and substitutes 1 for n only when c ≠ b. Then, the computer substitutes a value larger than b (b + 1 in the present embodiment) for c, and finishes the iterative process of step S86.
According to the above processing, the computer can clearly determine the natural frequency of the ground from the analysis target spectrum when the analysis of at least one of the maximum values from 1 to b cannot be performed. It can be determined that it is not possible. In addition, when the computer can analyze all the local maximum values from No. 1 to No. b, the computer can analyze from the spectrum to be analyzed regardless of whether or not the local maximum values after (b + 1) can be analyzed. It can be determined whether or not the natural frequency of the ground can be clearly identified.

Next, the computer determines the local maximum value at which the vibration frequency is minimum among the local maximum values extracted in step S93, and adds the number (c + 1) to the local maximum value (step S94).
And the computer which performed step S93 and step S94 adds 1 to c (step S95), and repeats routine.

When n = 0 at the time when the repetitive processing in step S86 is completed, the difference between the maximum value of the c-th spectral density and the minimum value of the c-th spectral density with respect to an arbitrary natural number c equal to or less than b is A first condition that the value is greater than or equal to a predetermined value m, and a second condition that the vibration frequency at the maximum value of the c-th spectral density satisfies the physical property of the ground assumed in the physical property assumption step and the predetermined condition D derived from c. Both of these conditions are satisfied. That is, it can be said that the estimation accuracy of the natural frequency of the ground in the analysis target spectrum is high.
For this reason, the computer that has finished the repetitive processing in step S86 determines whether or not the natural frequency of the ground can be clearly determined in the analysis target spectrum by determining whether n = 0 (step S96).

Here, when the determination result is “Yes” (ie, n = 0) in Step S96, the computer determines that “the natural frequency of the ground can be clearly determined from the analysis target spectrum”. Are output (step S97).
On the other hand, if the determination result is “No” (ie, n = 1) in step S96, the computer determines that “the natural frequency of the ground cannot be clearly determined from the analysis target spectrum” and is output. (Step S98).

Then, the computer that has executed either step S97 or step S98 ends step S65 for determining whether or not the natural frequency of the ground can be clearly determined in the analysis target spectrum.
According to each of the above steps, in the analysis target spectrum prepared from each analysis candidate spectrum, the difference between the maximum value and the minimum value of the spectral density is large, and the predetermined property determined by the physical properties of the ground and the order of the natural frequency An analysis target spectrum that satisfies the condition D is extracted. As a result, when there is an analysis target spectrum in which each natural frequency of the ground is estimated with high accuracy, each natural frequency of this analysis target spectrum is determined as the natural frequency of the ground in the estimation target area. The estimation accuracy of the natural frequency can be improved.

Next, details of step S76 described above will be described using the flowcharts of FIGS. 43 to 45 and the graphs of FIGS. 46 and 47. FIG.
The computer that has executed step S76 first acquires the maximum order b of the natural frequency and non-resonant frequency of the ground to be determined and the total number i of analysis candidate spectra (step S99).

Next, the computer calculates each spectral density of each of the first to i-th analysis candidate spectra in a predetermined vibration frequency range (in the present embodiment, a range of 0.1 [Hz] to 100 [Hz]). All local maximum values and local minimum values are acquired and prepared (step S100).
By the way, in the above-described step S65, when the analysis candidate spectrum is analyzed as it is as the analysis target spectrum, step S82 for calculating and extracting each maximum value and each minimum value of the analysis target spectrum is executed. For this reason, the extraction result of step S82 in step S65 can be used for each local maximum value and local minimum value acquired in step S100.

The computer that has acquired each local maximum value of the spectral density of each analysis candidate spectrum in step S100 creates a frequency distribution of the number of appearances of each local maximum value as a discrete function with respect to a predetermined range of vibration frequencies (step S100). S101) A moving average (in this embodiment, a simple moving average of 15 sections including the preceding and succeeding data for 7 sections) is calculated and obtained as the first moving average (step S101). S102).
In this embodiment, the operation of plotting the frequency distribution of each local maximum value and the first moving average on the graph is not performed, but the frequency distribution of each local maximum value and the first moving average are plotted on the graph. For example, the graph of the frequency distribution of the local maximum data points 4 and the first moving average 5 shown in FIG. 46 is obtained.

In addition, the computer that has acquired each minimum value of the spectral density of each analysis candidate spectrum in step S100 obtains the frequency distribution of the number of occurrences of each minimum value as a discrete function with respect to a predetermined range of vibration frequencies. (Step S103) A moving average with respect to the vibration frequency of the obtained frequency distribution (in this embodiment, a simple moving average of 15 sections including preceding and subsequent data for 7 sections) is calculated and obtained as a second moving average. (Step S104).
In the present embodiment, the frequency distribution of each local minimum value and the second moving average are not plotted on a graph, but the frequency distribution of each local minimum value and the second moving average are plotted on a graph. For example, a graph of the frequency distribution of the minimum value data points 6 and the second moving average 7 shown in FIG. 47 is obtained.

Now, the computer that has obtained the first moving average in step S102 determines from this first moving average a vibration frequency (hereinafter referred to as “natural frequency”) that is likely to have a natural frequency that maximizes the spectral density in the analysis candidate spectrum. Also referred to as “frequency candidate”). That is, the computer extracts a local maximum value in which the value of the vibration frequency is equal to or higher than a predetermined value o (1 [Hz] in the present embodiment) among the local maximum values in the first moving average. The vibration frequency in the value is extracted as a natural frequency candidate (step S105). This step S105 corresponds to extracting a maximum value at which the vibration frequency is equal to or higher than the predetermined value o from the maximum value of the first moving average 5 shown in FIG.
In step S105 described above, by excluding the natural frequency candidates from which the vibration frequency value is less than the predetermined value, the computer can generally detect relatively large low-frequency noise from the determination results in steps S107 to S112 described later. Can be removed.

In addition, the computer that has obtained the second moving average in step S104 determines from this second moving average a vibration frequency (hereinafter referred to as “a resonance frequency that is likely to have a non-resonant frequency that minimizes the spectral density in the analysis candidate spectrum”). Also called “non-resonant frequency candidate”). That is, the computer extracts a local maximum value in which the value of the vibration frequency is equal to or higher than a predetermined value q (1 [Hz] in the present embodiment) among the local maximum values in the second moving average, and the extracted local maximums. The vibration frequency in the value is extracted as a non-resonant frequency candidate (step S106). This step S106 corresponds to extracting a local maximum value at which the vibration frequency is equal to or higher than the predetermined value q from the local maximum value of the second moving average 7 shown in FIG.
In step S106, by excluding those whose vibration frequency values are less than a predetermined value from the non-resonant frequency candidates, the computer can generally detect a relatively large low frequency from the determination results in steps S107 to S112 described later. The influence of noise can be removed.

The computer that has performed the extraction and setting of the natural frequency candidate and the non-resonant frequency candidate in Steps S105 and S106, respectively, selects the natural frequency candidate having the highest spectral density with respect to the vibration frequency as the primary natural frequency r of the ground. ₁ (see FIG. 46) and output (step S107).
Subsequently, the computer sets a parameter a to be used for an after-mentioned iterative process (step S110) (step S108). Here, a is an argument indicating the order of the natural frequency and the non-resonant frequency currently analyzed, and a = 1 is set in step S108.

The computer that performed the initial setting of the parameter a in step S108 compares the magnitude relationship between a and b acquired in step S99 described above, and determines whether b> a is satisfied (step S109).
Here, in the above-described step S109, when the determination result is “No” (that is, b = a = 1), if the primary non-resonant frequency of the ground is determined, the estimation of the vibration characteristics is completed. Therefore, when the determination result is “No” in step S109, the computer extracts a non-resonant frequency candidate that is larger than the b (= 1) -order natural frequency of the ground from the non-resonant frequency candidates (step S111). ), It determines that the smallest one of the extracted non-resonant frequency candidates is the b (= 1) -order non-resonant frequency u _b (see FIG. 47) of the ground and outputs it (step S112). Then, the computer ends the step S76 of determining and outputting the natural frequency and non-resonant frequency of the ground from the frequency distribution of each extreme value of each of the first to i-th analysis candidate spectra.

On the other hand, when the determination result is “Yes” (ie, b> a = 1) in step S109, the computer determines and outputs the natural frequency of the ground and the non-resonant frequency in ascending order. Execute. In step S110, the computer first acquires a and b described above (step S113).
Next, the computer repeatedly performs a routine shown in steps S115 to S119 described later (step S114). This step S114 is repeatedly executed while a is increased by 1 (see step S119) while the condition of a <b is satisfied. If a ≧ b is satisfied in step S114, the computer ends the above repeating process.

In the routine repeated in step S114, the computer first extracts a non-resonant frequency candidate that is larger than the a-order natural frequency of the ground (step S115), and selects the smallest one of the extracted non-resonant frequency candidates as the ground a. it is determined that the next non-resonant frequency _{u a} (see FIG. 47) and outputs (step S116).
Subsequently, the computer extracts natural frequency candidates larger than the a-order non-resonant frequency of the ground (step S117), and the smallest one of the extracted natural frequency candidates is the (a + 1) -th natural frequency frequency r _{( a + 1)} (see FIG. 46) and output (step S118).

Then, the computer that has executed the above-described steps S114 to S118 adds 1 to a (step S119) and repeats the routine in order to execute the determination for the next-order nonresonant frequency and natural frequency.
In addition, in the first moving average described above, there may be a local maximum value due to the influence of the dominant vibration frequency of noise in addition to the influence of the natural frequency of the ground (for example, vibration around 2 [Hz] in FIG. 46). See candidate natural frequency 8 in frequency). Here, by alternately determining the natural frequency and the non-resonant frequency of the ground in order of decreasing order, it is possible to reduce errors in estimation of vibration characteristics due to the influence of the dominant vibration frequency.

By the way, in the routine repeated by step S114 mentioned above, a repetition process is complete | finished before determining the b-order non-resonance frequency of a ground. For this reason, the computer that has performed the repetitive processing in step S114 extracts non-resonant frequency candidates larger than the b-th natural frequency of the ground from the non-resonant frequency candidates (step S111), and the extracted non-resonant frequency candidates The smallest one of them is determined to be the b-th order non-resonant frequency u _b (see FIG. 47) of the ground and output (step S112).
Then, the computer ends the step S76 of determining and outputting the natural frequency and non-resonant frequency of the ground from the frequency distribution of each extreme value of each of the first to i-th analysis candidate spectra.

According to each step described above, in the analysis candidate spectrum that is a non-stationary spectrum in a plurality of time sections of microtremors, vibration frequencies having a high appearance ratio of the maximum value and the minimum value of the spectral density are respectively the natural frequency of the ground and It determines with corresponding to each non-resonance frequency. Thereby, even if data with relatively large noise is mixed in the analysis candidate spectrum, each natural frequency and each non-resonant frequency of the ground can be estimated from another analysis candidate spectrum with relatively small noise.
Further, the vibration frequency corresponding to the maximum value of the spectral density maximum in the analysis candidate spectrum (that is, the maximum value of the spectral density) is determined as the primary natural frequency r _1, and each natural frequency and each non-resonant frequency of the ground is determined. By determining in ascending order, the order of each natural frequency and each non-resonant frequency can be easily determined.

The present invention is not limited to the appearance and configuration described in the first and second embodiments described above, and various modifications, additions, and deletions can be made without changing the gist of the present invention. For example, the following various forms can be implemented.
(1) The method of creating a simulated seismic wave according to the present invention is not limited to a method in which a technician reads a simulated seismic wave creating program from a computer-readable recording medium and creates a simulated seismic wave. That is, the simulated seismic wave creation program can be read and executed by a computer through information transmission means that does not use a recording medium such as the Internet. In addition, the engineer can create a simulated seismic wave without using a simulated seismic wave creating program by executing each step of the present invention using an appropriately selected calculation means.
(2) The analysis parameter preparation step is not limited to the method of each of the above embodiments. That is, for example, it is possible to prepare H / V spectrum ratio data of microtremors in the target area, and to estimate the ground characteristics of the ground in the target area from the H / V spectrum ratio data, and prepare analysis parameters.
(3) The inversion in the inversion step is not limited to the inversion based on the double reflection theory for the one-dimensional stratified structure model. That is, for example, a ground model such as a two-dimensional or three-dimensional finite element model can be selected to perform inversion. In addition, a known method such as waveform inversion can be selected and used as the inversion method, and it can be appropriately changed whether the calculation process in the time domain or the frequency domain is performed. .
(4) Amplitude adjustment The method for determining whether or not to correct the amplitude of the long-period component of the seismic wave and the correction method can be changed as appropriate. It is also possible to employ a method that always corrects the amplitude of the long-period component of the amplitude-adjusted seismic wave or a method that does not perform the above correction at all. It is also possible to employ a method in which the correction of the amplitude of the long-period component is applied not to the amplitude-adjusted seismic wave but to the weak ground motion.
(5) In the simulated seismic wave creation program according to the first embodiment, a method of extracting one weak ground motion when a plurality of weak ground motion data is extracted from the database is not limited to the above embodiment. That is, by setting each earthquake that generated each weak ground motion as an observed earthquake, data for analysis is prepared by comparing each observed earthquake with the simulated earthquake, similar to the simulated seismic wave creation program according to the second embodiment. It is possible to select observed earthquakes and weak ground motions.
(6) In the simulated seismic wave creation program according to the second embodiment, the earthquake data of the observed earthquake can be estimated only from the data obtained from the earthquake observation of the target area. That is, it is possible to secure the following data (A) to (D) and set the seismic data of the observed earthquake by seismic observation of the target area.
(B) The magnitude of the observed earthquake. This is obtained from the arrival time of each seismic wave of the dense wave and the shear wave or the dominant vibration frequency of the dense wave.
(B) Epicenter direction of the observed earthquake and incident angle of the seismic wave. These are obtained from triaxial acceleration waveforms.
(C) Source distance of observed earthquakes. This can be obtained from the arrival times of the seismic waves of the dense wave and the shear wave, or the magnitude of the observed earthquake and the amplitude of the initial motion of the acceleration waveform obtained in (a) above.
(D) Location of the epicenter of the observed earthquake. This is obtained from the epicenter distance of the observed earthquake obtained in (c) above, the epicenter direction of the observed earthquake and the incident angle of the seismic wave obtained in (b) above.
In addition, each of the above data (a) to (d) improves the accuracy of the extraction when the earthquake corresponding to the earthquake observed in the target area is extracted from the earthquake database observed by the earthquake observation network. Can also be used.
(7) In the simulated seismic wave creation program according to the second embodiment, the method of selecting an observation earthquake for preparing analysis data from a plurality of observation earthquakes is not limited to the above embodiment. That is, when a plurality of observed earthquakes are classified into the category in which the observed earthquake is to be selected, the magnitude to be compared for selecting one observed earthquake from each observed earthquake is changed to an arbitrary magnitude such as, for example, the Japan Meteorological Agency magnitude. Can be changed. In addition, by comparing the observed earthquakes with simulated earthquakes by comparing the parameters indicating the earthquake source characteristics, such as the earthquake mechanism solution, the differences in the source characteristics between the observed earthquakes and the simulated earthquakes are reduced. A method of selecting observed earthquakes can be used. Further, similarly to the simulated seismic wave creation program according to the first embodiment, it is possible to extract one observed earthquake and weak earthquake motion that best reflects the characteristics of the weak earthquake motion of each observed earthquake.
(8) Each time section prepared in the simulated seismic wave creation program according to the third embodiment is not limited to the one obtained by discretizing a non-stationary spectrum of constant tremor at a predetermined sampling frequency. That is, the position on the time axis of each time section can be set to one or more arbitrary positions where the data of the unsteady spectrum of microtremor is always present. In addition, a non-stationary spectrum of microtremor is calculated as a discrete function with respect to time, and each time section is prepared by extracting a discrete time domain that satisfies a predetermined condition from each discrete time domain in which this discrete function has a value. Can do.
(9) In the simulated seismic wave creation program according to the third embodiment, the standard of the spectrum intensity for extracting the analysis candidate spectrum from each time section is whether or not the spectrum intensity of each time section is a predetermined reference value or less. It is not limited to the standard. That is, for example, each time section can be extracted as a candidate analysis spectrum by extracting a predetermined number (or a predetermined ratio with respect to the total number of time sections) in ascending order of spectrum intensity.
(10) The method of preparing analysis target spectra using a plurality of analysis candidate spectra in the simulated seismic wave creation program according to the third embodiment is not limited to the method of geometrically averaging all analysis candidate spectra. That is, an analysis target spectrum can be prepared by taking an arbitrary average that can reduce the influence of noise, such as an arithmetic average or an ensemble average, for an arbitrary combination of a plurality of analysis candidate spectra. .
(11) The execution order of each step is not limited to the order of the above embodiments. That is, the execution order of each step can be changed as appropriate, for example, the amplitude setting step is executed immediately before the amplitude magnification calculation step.

DESCRIPTION OF SYMBOLS 1 Unsteady spectrum 2 Plane 3 Time section 4 Local maximum data point 5 First moving average 6 Local minimum data point 7 Second moving average 8 Natural frequency candidate 9 Nonresonant frequency candidate 10 Intraplate earthquake distance attenuation formula 11 Plate Inter-earthquake distance attenuation equation o Predetermined value q Predetermined values r ₁ , r ₂ , r ₃ natural frequencies u ₁ , u ₂ , u ₃ non-resonant frequencies V Hi-net Sendai observation point V 'KIK-net Hachioji observation point w1, w2, ..., w14 epicenter

Claims (6)

A method of creating a simulated seismic wave incident from the engineering foundation surface toward the ground surface in the target area,
Based on the analysis parameters prepared from the ground characteristics of the surface ground of the target area existing between the ground surface of the target area and the engineering foundation surface of the target area, Inversion is used to analyze the incident seismic waves that should be incident on the engineering foundation surface in the target area in order to cause the earthquake motion indicated in the analysis data prepared from the ground vibration observation data. An inversion step calculated by
An incident seismic wave amplitude deriving step for deriving a maximum amplitude of the incident seismic wave which is a value determined independently from the vibration frequency in the incident seismic wave;
In the simulated seismic wave, the quotient obtained by dividing the maximum amplitude of the simulated seismic wave by the maximum amplitude of the incident seismic wave with respect to the maximum amplitude of the simulated seismic wave set in advance as a value determined independently from the vibration frequency as an amplitude magnification Amplitude magnification calculation step for calculating,
By amplifying or attenuating the amplitude of the incident seismic waves, the amplitude adjusting step to amplitude adjustment seismic waves for maximum value of the amplitude outputs the adjusted the simulated seismic wave to be equal to the maximum amplitude of the previous SL simulated seismic wave and, with a,
Wherein the amplitude adjusting step, a method of creating a simulated seismic wave, characterized that you perform a process of applying uniformly the amplitude ratio to the amplitude of the incident seismic wave regardless of the vibration frequency of the incident seismic wave. A method of creating a simulated seismic wave according to claim 1,
Select the weak ground motion that can be regarded as a linear elastic body of the surface ground of the target area as the vibration of the ground, prepare the analysis data of the weak ground motion ,
In the inversion step, the incident seismic wave is calculated by an inversion method on the premise that the surface ground of the target area is regarded as a linear elastic body,
Further, when the simulated seismic wave is output, the amplitude-adjusted seismic wave that is subjected to the correction of the influence that the dominant period of the seismic wave waveform is extended is applied to the amplitude of the long-period component whose vibration frequency is a predetermined value or less is prepared. How to create a simulated seismic wave. A method of creating a simulated seismic wave according to claim 1 or 2,
A simulated earthquake source position setting step for setting the location of the simulated earthquake source as the simulated earthquake wave source as a simulated earthquake source position;
An observed earthquake source position securing step for securing the position of the observed earthquake source as the observed earthquake source position, which is a source of vibration of the ground indicated in the observed data,
When there are a plurality of the observed earthquakes, the observation data of the observed earthquake with a relatively short source distance between the observed earthquake source position and the simulated earthquake source position is selected, and the analysis is performed from the observed data. A method of creating a simulated seismic wave characterized by preparing data for use. A method of creating a simulated seismic wave according to claim 3,
When there are a plurality of observed earthquakes, classify each observed earthquake according to the classification of the distance between the epicenters, and the distance between the epicenters where the observed earthquakes to be selected to prepare the analysis data are classified. When a plurality of the observed earthquakes are classified in the category, the observed data of the observed earthquake whose magnitude is closest to the magnitude of the simulated earthquake is selected from the observed earthquakes, and the analysis is performed from the observed data. A method of creating a simulated seismic wave characterized by preparing data for use. A simulated seismic wave creation program for causing a computer to create a simulated seismic wave incident from the engineering base to the ground surface in the target area,
Observation data input step in which observation data of ground vibration on the ground surface of the target area is input to the computer;
An analysis parameter preparation step in which the ground characteristics of the surface ground of the target area existing between the ground surface of the target area and the engineering foundation surface of the target area are input to the computer and prepared as an analysis parameter When,
An amplitude setting step in which the maximum amplitude of the simulated seismic wave, which is a value determined independently from the vibration frequency in the simulated seismic wave, is set and input to the computer;
The computer prepares analysis data from the observation data and prepares the analysis data preparation step;
Based on the analysis parameter, the computer generates an incident seismic wave to be incident on the engineering base plane of the target area to cause the ground motion indicated in the analysis data on the ground surface of the target area. An inversion step calculated by analysis using inversion,
An incident seismic wave amplitude deriving step in which the computer derives the maximum amplitude of the incident seismic wave, which is a value determined independently from the vibration frequency in the incident seismic wave;
An amplitude factor calculating step in which the computer calculates, as an amplitude factor, a quotient obtained by dividing the maximum amplitude of the simulated seismic wave by the maximum amplitude of the incident seismic wave;
An amplitude adjustment step in which the computer calculates an amplitude-adjusted seismic wave by uniformly applying the amplitude magnification to the amplitude of the incident seismic wave without depending on the vibration frequency of the incident seismic wave ;
A simulated seismic wave creation program for causing the computer to execute an output step in which the computer outputs the amplitude-adjusted seismic wave as the simulated seismic wave. A computer-readable recording medium that records a simulated seismic wave creation program for causing a computer to create a simulated seismic wave incident on the ground surface from an engineering foundation surface in a target area,
Observation data input step in which observation data of ground vibration on the ground surface of the target area is input to the computer;
An analysis parameter preparation step in which the ground characteristics of the surface ground of the target area existing between the ground surface of the target area and the engineering foundation surface of the target area are input to the computer and prepared as an analysis parameter When,
An amplitude setting step in which the maximum amplitude of the simulated seismic wave, which is a value determined independently from the vibration frequency in the simulated seismic wave, is set and input to the computer;
The computer prepares analysis data from the observation data and prepares the analysis data preparation step;
Based on the analysis parameter, the computer generates an incident seismic wave to be incident on the engineering base plane of the target area to cause the ground motion indicated in the analysis data on the ground surface of the target area. An inversion step calculated by analysis using inversion,
An incident seismic wave amplitude deriving step in which the computer derives the maximum amplitude of the incident seismic wave, which is a value determined independently from the vibration frequency in the incident seismic wave;
An amplitude factor calculating step in which the computer calculates, as an amplitude factor, a quotient obtained by dividing the maximum amplitude of the simulated seismic wave by the maximum amplitude of the incident seismic wave;
An amplitude adjustment step in which the computer calculates an amplitude-adjusted seismic wave by uniformly applying the amplitude magnification to the amplitude of the incident seismic wave without depending on the vibration frequency of the incident seismic wave ;
A computer-readable recording medium recording a simulated seismic wave creation program for causing the computer to execute an output step in which the computer outputs the amplitude-adjusted seismic wave as the simulated seismic wave.

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