JP6559579B2 - Method for estimating distance parameter of observed earthquake, distance parameter estimation program, and computer-readable recording medium recording distance parameter estimation program - Google Patents

Description

  The present invention records a method for estimating a distance parameter corresponding to the distance from the epicenter of the observed earthquake based on observation data of the observed earthquake observed at the observation point, a program for realizing the method, and the program. The present invention relates to a computer-readable recording medium.

  In general, in strong ground motion (strong ground motion that causes damage), after the initial microtremor, which is relatively weak, starts, the main motion, which is relatively strong, begins. Therefore, by detecting and analyzing the beginning of the initial tremor when an earthquake occurs, the earthquake warning system that obtains information about the earthquake that occurred before the main motion starts and issues a warning of the main motion based on this information. It has been used for some time. This earthquake warning system is a wide-area earthquake warning system that issues a more accurate alarm by using multiple observation points, and an early warning while sacrificing accuracy by using only a single observation point. There are roughly two types: an on-site type earthquake warning system.

  Of the above-mentioned “information about the earthquake that occurred”, one of the most important is the magnitude of the earthquake that occurred. Generally, the magnitude of this earthquake depends on the amplitude of the initial tremor and the epicenter of the earthquake. It is estimated from the value of the distance parameter that is a parameter corresponding to the distance. For this distance parameter, for example, a source distance 90B, which is a linear distance from the earthquake source 90A to the observation point 10, or a straight line from the epicenter 91A to the observation point 10 located on the ground surface 91 directly above the earthquake source 90A. The epicenter distance 91B (see FIG. 1), which is the distance, is used.

  As a research on the estimation of the distance parameter in the on-site type earthquake warning system, for example, a research described in Non-Patent Document 1 below is known. In this study, an attempt was made to estimate the epicenter distance of an earthquake using the ratio of the acceleration amplitude with a frequency of 0.5 [Hz] and the acceleration amplitude with a frequency of 30 [Hz] in the vertical motion component of the initial tremor of the earthquake. It is carried out. In this study, it was shown that the epicenter distance of the earthquake could be estimated with high accuracy by using the ratio of the amplitude of the earthquake motion at the low frequency to the amplitude at the high frequency. In addition, the research of the said nonpatent literature 1 shows that it is also possible to estimate an epicenter distance from the ratio of the said amplitude.

Ministry of Education, Culture, Sports, Science and Technology, Research and Development Bureau, National Institute for Disaster Prevention Science and Technology. Science and Technology Promotion Expenditures Research and development project for revitalizing the economy. May 2008

  By the way, it is known that the observation data of seismic motion is data in which the amplitude is amplified with a different amplification factor for each frequency under the influence of the point characteristics which are the ground characteristics of the ground around the observation point. Here, in the research of the said nonpatent literature 1, since the influence of a point characteristic was not considered when estimating the epicenter distance of an earthquake from the ratio of the said amplitude, the epicenter distance of an earthquake was not able to be estimated accurately.

  The present invention sets a range of low and high frequencies based on past data when estimating a distance parameter of an earthquake from a ratio of an amplitude at a low frequency to an amplitude at a high frequency. This makes it possible to improve the estimation accuracy of.

  In order to solve the above-described problems, a method for estimating a distance parameter of an observation earthquake, a distance parameter estimation program, and a computer-readable recording medium recording the distance parameter estimation program according to the present invention employ the following means.

  First, in the first invention, an observation point where earthquake vertical motion waveforms of a plurality of earthquakes having different distance parameter values corresponding to the distance from the epicenter are recorded in the past is observed at this observation point. This is a method to estimate the distance parameter of the observed earthquake based on the observed data of the observed earthquake. The method includes an extraction step, a setting step, a spectral intensity ratio derivation step, a correlation coefficient derivation step, a frequency range setting step, a distribution derivation step, a first spectral intensity derivation step, a second spectral intensity derivation step, and And having a plurality of steps including an estimation step. Here, in the extraction step, for one of a plurality of seismic vertical motion waveforms recorded in the past, waveform data including the initial fracture phase of the initial tremor in the seismic vertical motion waveform is obtained by using the spectral density of the amplitude in the frequency domain. Extracted as extracted data that is a discrete function of. In the setting step, the first frequency range that is a relatively low frequency range and the second frequency range that is a relatively high frequency range are set so that the frequency ranges do not overlap each other. . Further, in the spectral intensity ratio deriving step, the extracted spectral data extracted in the extracting step is integrated with the extracted spectral data in the first frequency range, and the extracted data is integrated in the second frequency range. The ratio of the measured spectral intensity value to the amplitude is obtained as the spectral intensity ratio. Further, in the correlation coefficient deriving step, the extraction step and the spectral intensity ratio deriving step are executed for each of a plurality of earthquake vertical motion waveforms recorded in the past, and an earthquake corresponding to each earthquake vertical motion waveform is obtained. The correlation coefficient between each distance parameter and each spectral intensity ratio is derived. In the frequency range setting step, the correlation coefficient deriving step is repeatedly executed while changing the first frequency range and the second frequency range set in the setting step, and in the correlation coefficient deriving step, A combination of the first frequency range and the second frequency range in which the derived correlation coefficient is closest to 1 is obtained, and the first frequency range and the second frequency range are determined as the low frequency range and the high frequency range, respectively. Determine as In the distribution derivation step, the distribution of the spectral density of the amplitude in the frequency domain of the vertical motion component in the waveform data including the initial fracture phase of the initial tremor of the observed earthquake is derived. In the first spectral intensity deriving step, the amplitude spectral intensity value obtained by integrating the distribution of the spectral density of the amplitude derived in the distribution deriving step in the low frequency range determined in the frequency range setting step is set as the first spectral intensity deriving step. Derived as spectral intensity. In the second spectral intensity deriving step, the amplitude spectral intensity value obtained by integrating the distribution of the spectral density of the amplitude derived in the distribution deriving step in the high frequency range determined in the frequency range setting step is set as the second spectral intensity deriving step. Derived as spectral intensity. Further, in the estimation step, the distance parameter of the observed earthquake is estimated on the assumption that the distance parameter of the observed earthquake can be obtained by a linear expression of the spectral ratio obtained by dividing the first spectral intensity by the second spectral intensity.

  In the first invention, when estimating the distance parameter of the observed earthquake from the ratio of the amplitude at the low frequency and the amplitude at the high frequency of the ground motion, the distance parameter and the spectral intensity ratio of the plurality of earthquakes recorded in the past are estimated. The combination of low and high frequencies with the highest correlation is used. Here, since the distance parameters of the plurality of earthquakes are different from each other, the combination of the low frequency and the high frequency to be set is relatively strongly influenced by the common point characteristics regardless of the location of the epicenter. Reflected. That is, according to the first aspect, the distance parameter of the earthquake is estimated by estimating the distance parameter of the earthquake from the ratio of the amplitude at the low frequency and the amplitude at the high frequency, in which the influence of the point characteristic is reflected relatively strongly. The estimation accuracy can be increased. According to the first aspect of the invention, the low frequency and the high frequency are each set as a frequency range having a frequency range, and the estimation is performed based on the spectrum intensity of the amplitude in each frequency range. It is possible to suppress an error that occurs when only the amplitude of the frequency is greatly amplified. In addition, according to the method of extracting the waveform data of the initial tremor as a discrete function of the spectral density in the frequency domain, it is necessary to obtain the correlation with the distance parameter while giving the frequency width to the low frequency range and the high frequency range. The number of combinations in each frequency range can be finite.

  Next, the second aspect of the present invention is an observation point where a plurality of earthquake vertical motion waveforms having different distance parameter values corresponding to the distance from the epicenter are recorded in the past. This is a distance parameter estimation program for causing a computer to estimate the distance parameter of an observed earthquake based on the observed data of the observed earthquake. The distance parameter estimation program stores an extraction step, a setting step, a spectral intensity ratio derivation step, a correlation coefficient derivation step, a frequency range setting step, a distribution derivation step, a first spectral intensity derivation step, a second A plurality of steps including a spectral intensity derivation step and an estimation step are executed. Here, in the extraction step, for one of a plurality of seismic vertical motion waveforms recorded in the past, waveform data including the initial fracture phase of the initial tremor in the seismic vertical motion waveform is obtained by using the spectral density of the amplitude in the frequency domain. Extracted as extracted data that is a discrete function of. In the setting step, the first frequency range that is a relatively low frequency range and the second frequency range that is a relatively high frequency range are set so that the frequency ranges do not overlap each other. . Further, in the spectral intensity ratio deriving step, the extracted spectral data extracted in the extracting step is integrated with the extracted spectral data in the first frequency range, and the extracted data is integrated in the second frequency range. The ratio of the measured spectral intensity value to the amplitude is obtained as the spectral intensity ratio. Further, in the correlation coefficient deriving step, the extraction step and the spectral intensity ratio deriving step are executed for each of a plurality of earthquake vertical motion waveforms recorded in the past, and an earthquake corresponding to each earthquake vertical motion waveform is obtained. The correlation coefficient between each distance parameter and each spectral intensity ratio is derived. In the frequency range setting step, the correlation coefficient deriving step is repeatedly executed while changing the first frequency range and the second frequency range set in the setting step, and in the correlation coefficient deriving step, A combination of the first frequency range and the second frequency range in which the derived correlation coefficient is closest to 1 is obtained, and the first frequency range and the second frequency range are determined as the low frequency range and the high frequency range, respectively. Determine as In the distribution derivation step, the distribution of the spectral density of the amplitude in the frequency domain of the vertical motion component in the waveform data including the initial fracture phase of the initial tremor of the observed earthquake is derived. In the first spectral intensity deriving step, the amplitude spectral intensity value obtained by integrating the distribution of the spectral density of the amplitude derived in the distribution deriving step in the low frequency range determined in the frequency range setting step is set as the first spectral intensity deriving step. Derived as spectral intensity. In the second spectral intensity deriving step, the amplitude spectral intensity value obtained by integrating the distribution of the spectral density of the amplitude derived in the distribution deriving step in the high frequency range determined in the frequency range setting step is set as the second spectral intensity deriving step. Derived as spectral intensity. Further, in the estimation step, the distance parameter of the observed earthquake is estimated on the assumption that the distance parameter of the observed earthquake can be obtained by a linear expression of the spectral ratio obtained by dividing the first spectral intensity by the second spectral intensity.

  According to the distance parameter estimation program according to the second aspect of the present invention, the same effect as that of the above-described first aspect can be obtained using a computer.

  Furthermore, the third aspect of the present invention is an observation point where a plurality of earthquakes having different distance parameter values corresponding to the distance from the epicenter are recorded in the past, and observed at this observation point. This is a computer-readable recording medium recording a distance parameter estimation program for causing a computer to estimate the distance parameter of the observed earthquake based on the observed data of the observed earthquake. The distance parameter estimation program stores, in a computer, an extraction step, a setting step, a spectral intensity ratio deriving step, a correlation coefficient deriving step, a frequency range setting step, a distribution deriving step, a first spectral intensity deriving step, a second A plurality of steps including a spectral intensity derivation step and an estimation step are executed. Here, in the extraction step, for one of a plurality of seismic vertical motion waveforms recorded in the past, waveform data including the initial fracture phase of the initial tremor in the seismic vertical motion waveform is obtained by using the spectral density of the amplitude in the frequency domain. Extracted as extracted data that is a discrete function of. In the setting step, the first frequency range that is a relatively low frequency range and the second frequency range that is a relatively high frequency range are set so that the frequency ranges do not overlap each other. . Further, in the spectral intensity ratio deriving step, the extracted spectral data extracted in the extracting step is integrated with the extracted spectral data in the first frequency range, and the extracted data is integrated in the second frequency range. The ratio of the measured spectral intensity value to the amplitude is obtained as the spectral intensity ratio. Further, in the correlation coefficient deriving step, the extraction step and the spectral intensity ratio deriving step are executed for each of a plurality of earthquake vertical motion waveforms recorded in the past, and an earthquake corresponding to each earthquake vertical motion waveform is obtained. The correlation coefficient between each distance parameter and each spectral intensity ratio is derived. In the frequency range setting step, the correlation coefficient deriving step is repeatedly executed while changing the first frequency range and the second frequency range set in the setting step, and in the correlation coefficient deriving step, A combination of the first frequency range and the second frequency range in which the derived correlation coefficient is closest to 1 is obtained, and the first frequency range and the second frequency range are determined as the low frequency range and the high frequency range, respectively. Determine as In the distribution derivation step, the distribution of the spectral density of the amplitude in the frequency domain of the vertical motion component in the waveform data including the initial fracture phase of the initial tremor of the observed earthquake is derived. In the first spectral intensity deriving step, the amplitude spectral intensity value obtained by integrating the distribution of the spectral density of the amplitude derived in the distribution deriving step in the low frequency range determined in the frequency range setting step is set as the first spectral intensity deriving step. Derived as spectral intensity. In the second spectral intensity deriving step, the amplitude spectral intensity value obtained by integrating the distribution of the spectral density of the amplitude derived in the distribution deriving step in the high frequency range determined in the frequency range setting step is set as the second spectral intensity deriving step. Derived as spectral intensity. Further, in the estimation step, the distance parameter of the observed earthquake is estimated on the assumption that the distance parameter of the observed earthquake can be obtained by a linear expression of the spectral ratio obtained by dividing the first spectral intensity by the second spectral intensity.

  According to the computer-readable recording medium on which the distance parameter estimation program according to the third aspect of the invention is recorded, the same operational effects as those of the first aspect described above can be obtained using a computer.

It is explanatory drawing for demonstrating the epicenter distance and epicenter distance of an earthquake. It is explanatory drawing showing the schematic structure for implement | achieving the method of estimating the distance parameter of the observation earthquake concerning one Embodiment of this invention. It is a flowchart showing the method of estimating the distance parameter of the observation earthquake concerning one Embodiment of this invention. It is a flowchart showing the subroutine 1 of FIG. 5 is a flowchart showing a subroutine 2 of FIG. It is a graph showing an example of the vertical motion response acceleration waveform 20 input in step S20 of FIG. It is a figure showing an example of the arrangement | sequence arranged in step S140 of FIG. It is a graph showing an example of the spectral density of amplitude. It is a graph showing an example of the primary formula 22 produced in step S60 of FIG.

  Hereinafter, a method for estimating a distance parameter of an observed earthquake according to an embodiment of the present invention will be described with reference to the drawings. The method for estimating the distance parameter of this observed earthquake is that the epicenter distance 91B of this observed earthquake is obtained from the observed data of the observed earthquake at the single observation point 10 (see FIG. 1) on the ground surface 91 by the computer 11 ( This is a method of estimation using FIG. Here, the epicenter distance 91 </ b> B corresponds to a “distance parameter” in the present invention. In addition, at the observation point 10, the seismic vertical motion waveform (that is, the vertical motion component of the seismic waveform; specifically, the vertical motion component of the earthquake waveform of A times (A is a natural number of 2 or more, for example, A = 17) having different epicenter distances 91B. For example, the vertical motion response acceleration waveform 20) shown in FIG. 6 has been recorded in the past. The computer 11 is specifically a display-integrated laptop computer, for example.

  As shown in FIG. 2, the computer 11 is installed in the observation point 10 in a state where a recording medium 11 </ b> A (specifically, for example, a USB memory) and the seismometer 10 </ b> A at the observation point 10 are connected. Here, the seismometer 10A accumulates the data while measuring the ground motion at the observation point 10 in three axes, and outputs the observation data of the detected observation earthquake to the computer 11 in real time when the earthquake is detected. It is supposed to be. In addition, a distance parameter estimation program for realizing the method for estimating the distance parameter of the observed earthquake is recorded on the recording medium 11A so as to be readable by a computer. This distance parameter estimation program realizes a method for estimating the distance parameter of the observed earthquake by causing the computer 11 to function as an estimation means for the epicenter distance 91B (see FIG. 1) of the observed earthquake.

  Here, with respect to a series of steps executed when an engineer (not shown) tries to implement the above-described method for estimating the distance parameter of the observed earthquake, mainly the flowcharts shown in FIGS. 3 to 5 are used. I will explain. Note that, in the following, when the sampling frequency of the input data is not compatible with the processing of the distance parameter estimation program, details of ancillary steps such as a resampling step for converting the input data so as to conform to this processing will be described in detail. The detailed explanation is omitted.

  When the engineer causes the computer 11 to execute the distance parameter estimation program, the processing by the computer 11 first proceeds to step S10.

  In step S <b> 10, the computer 11 performs initial settings necessary for executing each step described later. The initial setting includes a process in which the computer 11 recognizes the connection of the seismometer 10A and acquires a sampling frequency (for example, 100 [Hz]) for measuring the seismic motion in the seismometer 10A. Then, the computer 11 advances the process to step S20.

  In step S20, the computer 11 displays a message on the display requesting the input of earthquake data recorded in the past at the observation point 10, and until the input of the earthquake data to the computer 11 is completed. stand by. On the other hand, the engineer inputs the data of A earthquakes recorded in the past at the observation point 10 to the computer 11 one by one, and then inputs a data input completion command to the computer 11. Here, when a data input completion command is input, the computer 11 advances the process to step S30.

  It should be noted that the earthquake data input to the computer 11 in step S20 includes the vertical motion response acceleration waveform 20 (see FIG. 6) of the earthquake, the epicenter distance of this earthquake, and the time when the earthquake motion started at the observation point 10 (see FIG. 6). It is the data associated with the illustrated earthquake arrival time 20A). Here, the epicenter distance of the earthquake is the distance between the epicenter of the earthquake determined from the seismic observation data by the seismic observation network (not shown) that exists independently of the observation point 10 and the position of the observation point 10. The linear distance of The vertical motion response acceleration waveform 20 corresponds to the “earthquake vertical motion waveform” in the present invention.

  In step S30, the computer 11 performs a repetitive process of performing the process of step S40 described later once for all the earthquake data input to the computer 11 in step S20. In addition, if the computer 11 performs the process of step S40 about all the earthquake data in step S30, it will complete | finish the repetition process of this step S40, and will advance the process to step S50.

  In step S40, the computer 11 selects one piece of earthquake data that has not yet been processed in step S40, and prepares waveform data including the initial failure phase of the initial tremor. Specifically, the computer 11 has a waveform of an extraction range 20B that is a predetermined time range (for example, 1 [second]) starting from the landing time 20A in the vertical motion response acceleration waveform 20 of the earthquake (see FIG. 6). ) Are extracted and prepared at the same sampling frequency (for example, 100 [Hz]) as that of the seismometer 10A.

  Here, the “initial failure phase” refers to an earthquake waveform of a portion corresponding to the earthquake motion of the initial failure that triggers the main failure that generates the main motion following the initial tremor among the initial tremors of the earthquake. This initial failure phase has the property that there is less difference in the seismic waveform depending on the type of earthquake compared to the portion other than the initial failure phase in the seismic waveform.

  The nature of the initial fracture phase will be described in more detail with reference to FIG. The earthquake is a phenomenon in which the energy accumulated in the asperity 92, which is a region spreading in a plane in the ground 90, is released while destroying the rocks existing in the asperity 92. Here, when the asperity 92 causes an earthquake that causes strong ground motion, the asperity 92 has accumulated a source region 92A existing around the earthquake source 90A and energy that causes strong ground motion. It is known to have a large destruction area 92B.

  When such an asperity 92 causes an earthquake that causes strong ground motion, first, an initial failure occurs in which the destruction of rocks existing in the hypocenter region 92A starts from the epicenter 90A. In this initial failure, a seismic wave including a shear strain wave is generated, and this seismic wave is propagated around the hypocenter region 92A. When this seismic wave reaches the ground surface 91, it appears as an initial failure phase of ground motion. Further, when the shear strain wave reaches the large fracture area 92B of the asperity 92, it becomes a trigger for causing a main fracture in which the rock is destroyed in the large fracture area 92B. This main destruction releases the energy accumulated in the asperity 92, thereby causing strong ground motion on the ground surface 91 and stopping the initial destruction.

  That is, the extent of the rock failure in the hypocenter area 92A at the initial failure is the speed at which the rock fracture spreads at the initial failure and the shear strain wave generated by the initial failure reaches the large fracture area 92B from the hypocenter area 92A. Time. For this reason, the seismic waveform of the initial failure phase has less difference in the seismic waveform due to the type of earthquake than the seismic waveform of the portion other than the initial failure phase.

  In step S50, the computer 11 executes the process of subroutine 1 shown in FIG. 4, and advances the process to step S60. The processing of this subroutine 1 obtains a combination of a low frequency and a high frequency that has the highest correlation with the epicenter distances of a plurality of earthquakes recorded in the past in the ratio of the amplitude at the low frequency of the earthquake motion to the amplitude at the high frequency. It is processing. Here, in the processing of the subroutine 1, the low frequency and the high frequency are set to a low frequency range and a high frequency range, which are frequency ranges each having a width in frequency. For this reason, step S50 is also referred to as a “frequency range setting step” in this specification.

  In the processing of the subroutine 1, as shown in FIG. 4, the processing by the computer 11 first proceeds to step S140.

  In step S140, the computer 11 makes initial settings necessary for executing each step of subroutine 1 described later, and then advances the process to step S150.

  The initial setting includes a process for obtaining a frequency distribution range and a distribution interval for a frequency domain discrete function obtained by performing discrete Fourier transform on the waveform data prepared in step S40. The frequency distribution range and the distribution interval are calculated from the sampling frequency in the waveform data and the time length of the extraction range 20B so that the frequency distribution range includes at least four frequency components. Specifically, for example, when the sampling frequency is 100 [Hz] and the time length of the extraction range 20B is 1 [second], the frequency distribution range is 1 [Hz] to 50 [Hz]. The frequency distribution interval is calculated as 1 [Hz].

In addition, the initial setting includes a process of counting up a combination pattern for selecting four different frequencies from each frequency included in the frequency distribution range and collecting them in an array. This array is declared with a number of elements that is one greater than the total number of combinations of frequencies given as elements, so that the last element is a missing value. Specifically, for example, when the frequency distribution interval is 1 [Hz] and the frequency distribution range is 1 [Hz] to 50 [Hz], as shown in FIG. The number is declared in a range of 1 to 230, 301 (= ₅₀ C ₄ +1). In addition, in each of the elements having pattern numbers 1 to 230 and 300 in the above array, four frequencies F ₁ , F ₂ , F ₃ , and F ₄ (where F ₁ <F ₂ <F ₃ <F _{4) are selected.} ) Are assigned one by one. In addition, elements having pattern numbers 230 and 301 in the above array are regarded as missing values because there are no four frequencies to be substituted.

  In step S150, the computer 11 first sets the pattern number of the array to be processed to 1 in the repetitive processing of step S160 described later, and advances the processing to step S160.

  In step S160, the computer 11 repeatedly executes a series of processes from step S170 to step S240 described later. This series of processing is repeatedly executed until a missing value is handled in step S170 ("setting step" shown in FIG. 4) described later. Note that when a missing value is handled in step S170, which will be described later, the computer 11 stops the repetition process of step S160 and advances the process to step S250.

In step S170, the computer 11 refers to the above-described array (see FIG. 7), and combines the _four frequencies F ₁ , F ₂ , F ₃ , and F ₄ corresponding to the current pattern number in this array. Extract. Here, if the current pattern number is the maximum (ie, the last) pattern number in the above array, the element corresponding to this pattern number is a missing value, and therefore the process of step S170 is the iterative process of step S160. Trigger to stop.

Subsequently, the computer 11 sets a relatively low frequency range from the frequency F ₁ to the frequency F ₂ as the first frequency range, and a relatively high frequency range from the frequency F ₃ to the frequency F ₄ as the second frequency range. The frequency range is set, and the process proceeds to step S180. Here, in the initial setting in step S140, the frequencies F ₁ , F ₂ , F ₃ , and F ₄ are substituted so that F ₁ <F ₂ <F ₃ <F _4. The range is set as a frequency range lower in frequency than the second frequency range so that the frequency ranges do not overlap each other. For this reason, step S170 is also referred to as a “setting step” in this specification.

  In step S180, the computer 11 executes the process of subroutine 2 shown in FIG. 5, and advances the process to step S190. The processing of this subroutine 2 is to calculate the correlation coefficient between the spectral intensity ratio obtained from each vertical motion response acceleration waveform 20 input in step S20 and the epicenter distance of the earthquake corresponding to each vertical motion response acceleration waveform 20. This is a process to derive. For this reason, step S180 is also referred to as a “correlation coefficient deriving step” in this specification.

  Here, in the processing of the subroutine 2, the “spectral intensity ratio” means a ratio between the spectral intensity of the amplitude in the first frequency range and the spectral intensity of the amplitude in the second frequency range. The “amplitude spectral intensity” is a value obtained by integrating the spectral density of the amplitude, which is a function representing the amplitude component for each frequency, in a predetermined frequency range. That is, for example, when the amplitude spectral density 21 is given as shown in FIG. 8, the “amplitude spectral intensity in the first frequency range” is a region obtained by cutting the amplitude spectral density 21 in the first frequency range 21A. This is the total amount of amplitude components included in 21B. The “amplitude spectral intensity in the second frequency range” is the total amount of amplitude components included in the region 21D obtained by cutting the amplitude spectral density 21 in the second frequency range 21C. In the process of subroutine 2, the obtained spectral intensity ratio is archived in the computer 11 in a state associated with the epicenter distance of the earthquake.

  In the processing of the subroutine 2, as shown in FIG. 5, the processing by the computer 11 first proceeds to step S260.

  In step S260, the computer 11 performs initial settings necessary for executing each step of subroutine 2 described later. This initial setting includes processing for acquiring the first frequency range and the second frequency range set in the setting step (step S170) executed immediately before as arguments. Then, the computer 11 advances the process to step S270.

  In step S270, the computer 11 sets the value of a that functions as a counter variable to 1 in the repetitive processing in step S280 described later, and advances the processing to step S280.

  In step S280, the computer 11 repeatedly executes a series of processes from step S290 to step S330 described later. This series of processes is repeatedly executed while increasing a that functions as a counter variable (see step S330) until this a becomes larger than the number A of earthquakes for which data was input in step S20. . Note that when the value a is greater than the number A of earthquakes, the computer 11 stops the repeated process of step S280 and advances the process to step S340.

  In step S290, the computer 11 extracts and acquires the a-th earthquake data input from the A-time earthquake data input in step S20. Then, the computer 11 advances the process to step S300.

  In step S300, the computer 11 uses the earthquake data acquired in step S290 executed immediately before the waveform data including the initial fracture phase of the initial fine movement in the vertical motion response acceleration waveform 20 (see FIG. 6). Extracted as extracted data that is a discrete function of the spectral density of the amplitude in the frequency domain. Specifically, the computer 11 first generates a waveform in a predetermined time range (for example, 1 [second]) starting from the earthquake landing time 20A in the vertical motion response acceleration waveform 20 of the earthquake, using the seismometer 10A. The sampling processing is performed at the same sampling frequency (for example, 100 [Hz]). Next, the computer 11 performs a discrete Fourier transform on the extracted waveform to derive a discrete function in the frequency domain, and performs processing for using the derived discrete function as the extracted data. This step S300 is also referred to as an “extraction step” in this specification. In addition, when the computer 11 completes the process of step S300, the process proceeds to step S310.

  In step S310, the computer 11 integrates the extracted data in the first frequency range with respect to the extracted data extracted in the immediately preceding extraction step (step S300), so that the amplitude in the first frequency range is obtained. Is obtained. Subsequently, the computer 11 obtains the spectral intensity of the amplitude in the second frequency range by integrating the extracted data in the second frequency range. Then, the computer 11 obtains the ratio of the spectral intensity value of the amplitude in the first frequency range and the spectral intensity value of the amplitude in the second frequency range as a spectral intensity ratio, and the process is performed in step S320. Proceed. For this reason, step S310 is also referred to as a “spectral intensity ratio deriving step” in this specification. In the process of step S310, the computer 11 sets the first frequency range and the second frequency range set in the most recently executed setting step (step S170) as the first frequency range and the second frequency range. Use the frequency range.

  In step S320, the computer 11 extracts the epicenter distance of this earthquake as a distance parameter from the earthquake data acquired in step S290 executed most recently. Subsequently, the computer 11 archives in the computer 11 the spectral intensity ratio derived in the spectral intensity ratio deriving step (step S310) executed immediately before in association with the extracted distance parameter. Then, the computer 11 advances the process to step S330.

  In step S330, the computer 11 performs a process of adding 1 to a described above. Then, the computer 11 ends the process of one time in step S280 described above. If a ≦ A, the process returns to step S290, and if a> A, the process proceeds to step S340. Here, in step S270 executed immediately before the repetitive processing in step S280, a indicating the number of the input earthquake data is set to 1. For this reason, in the iterative process of step S280, the process is executed in the order in which the data is input with respect to the A-time earthquake data input in step S20.

  In step S340, the computer 11 acquires all data archived in the computer 11 in the repetitive processing of step S280 executed immediately before. Subsequently, the computer 11 derives a correlation coefficient between the spectrum intensity ratio and the distance parameter in the acquired data. Then, the computer 11 ends the processing of the subroutine 2 using the derived correlation coefficient as a return value, and advances the processing to step S190 shown in FIG.

  That is, in the processing of the subroutine 2 described above, the computer 11 performs the extraction step (step S300) and the spectral intensity ratio derivation step (step S310) for each vertical motion response acceleration waveform 20 in the A times of earthquakes recorded in the past. Run against. Then, the computer 11 derives a correlation coefficient between the earthquake distance parameter corresponding to each vertical motion response acceleration waveform 20 and each spectral intensity ratio.

  In step S190, as shown in FIG. 4, the computer 11 stores the correlation coefficient closest to 1 among the correlation coefficients obtained in step S180 repeated in step S160 on the recording medium 11A (see FIG. 2). The correlation coefficient stored value that is the stored value is acquired. Then, the computer 11 advances the process to step S200.

  Note that the computer 11 stores the dummy data of the correlation coefficient storage value in the recording medium 11A in the initial setting in step S140. Thereby, even when step S180 is executed for the first time in the processing of subroutine 1, the computer 11 does not generate an error in step S190.

  In step S200, the computer 11 uses the correlation coefficient derived in step S180 executed most recently as the closest correlation coefficient among the correlation coefficients obtained in step S180 repeated in step S160. It is determined whether or not there is. This determination is based on whether or not the expression “| 1- (correlation coefficient) | ≦ | 1- (correlation coefficient storage value) |” holds for the correlation coefficient and the correlation coefficient storage value. Is determined by If the result of the determination is “Yes” (that is, | 1- (correlation coefficient) | ≦ | 1- (correlation coefficient stored value) |), the computer 11 advances the process to step S210. If the result of the determination is “No” (that is, | 1- (correlation coefficient) |> | 1- (correlation coefficient stored value) |), the computer 11 advances the process to step S240.

  Note that the computer 11 sets the dummy data of the correlation coefficient storage value stored in the initial setting in step S140 as a value (for example, 4) that satisfies the inequality | 1- (dummy data) |> 2. Thereby, when step S200 is executed for the first time in the process of subroutine 1, the computer 11 ensures that the determination result of step S200 is “yes”. In addition, the engineer can clearly distinguish the correlation coefficient that always takes a value between −1 and 1 and the dummy data.

  In step S210, the computer 11 updates the correlation coefficient derived in the most recently executed step S180 as a correlation coefficient storage value, and overwrites and stores this correlation coefficient storage value in the recording medium 11A (see FIG. 2). To do. Then, the computer 11 advances the process to step S220.

  In step S220, the computer 11 stores the first frequency range and the second frequency range set in the most recently executed setting step (step S170) in the recording medium 11A (see FIG. 2). Here, when the data of the first frequency range and the second frequency range are already stored in the recording medium 11A, the computer 11 erases the data stored in the recording medium 11A and then stores the data. I do. Then, the computer 11 advances the process to step S230.

  In step S230, the computer 11 stores the data archived in the computer 11 in the correlation coefficient derivation step (step S180) executed most recently in the recording medium 11A (see FIG. 2). Then, the computer 11 advances the process to step S240.

  In step S240, the computer 11 performs a process of adding 1 to the pattern number described above. Then, the computer 11 ends the process for one time in step S160 described above, and returns the process to step S170. Here, the pattern number is set to 1 in step S150 executed immediately before the repetitive processing in step S160. For this reason, in the iterative process of step S160, the process is executed in ascending order of pattern numbers for all the patterns (see FIG. 7) in the combination of frequencies described above.

  In step S250, the computer 11 acquires the first frequency range currently stored in the recording medium 11A, and sets the first frequency range as the low frequency range described above. In addition, the computer 11 acquires the second frequency range currently stored in the recording medium 11A, and sets the second frequency range as the above-described low frequency range. Then, the computer 11 ends the processing of the subroutine 1 by using the first frequency range and the second frequency range as return values, and advances the processing to step S60 shown in FIG.

  That is, in the processing of the subroutine 1 described above, the computer 11 changes the first frequency range and the second frequency range set in the setting step (step S170) in the correlation coefficient derivation step (step S180). Execute repeatedly. Then, the computer 11 obtains a combination of the first frequency range and the second frequency range in which the correlation coefficient derived in the correlation coefficient deriving step is closest to 1, and determines the first frequency range and the first frequency range. Two frequency ranges are defined as a low frequency range and a high frequency range, respectively.

  In step S60, the computer 11 acquires the data stored in the recording medium 11A (see FIG. 2) in the most recently executed step S230 (see FIG. 3). Further, the computer 11 extracts the epicenter distance and the spectral intensity ratio of the earthquake corresponding to each vertical motion response acceleration waveform 20 input in step S20 from the acquired data, and the epicenter distance and the spectral intensity ratio are used as axes. A scatter diagram (see FIG. 9) is created. Then, the computer 11 derives a linear expression 22 (ie, a linear expression of a regression line) that best approximates the epicenter distance and the spectral intensity ratio distribution in the created scatter diagram, and advances the processing to step S70.

  In step S <b> 70, the computer 11 stops the processing until the observation data of the observed earthquake is input from the seismometer 10 </ b> A at the observation point 10. When the observation data of the observed earthquake is input from the seismometer 10A (see FIG. 2) at the observation point 10, the computer 11 advances the process to step S80. Here, in the routine shown in FIG. 3, step S70 is a repetitive process of “doing nothing” under the condition that “observation data of the observed earthquake is input”. However, the process of step S70 may be a sleep process of the computer 11 that is triggered by the fact that the observation data of the observed earthquake is output from the seismometer 10A to the computer 11.

  In step S80, the computer 11 acquires observation data of the observed earthquake input from the seismometer 10A, and extracts waveform data including the initial fracture phase of the initial tremor of the observed earthquake from this observed data. Specifically, the computer 11 includes waveform data in a predetermined time range (for example, 1 [second]) starting from the landing time of the observed earthquake among the vertical motion response acceleration waveforms included in the observed data of the observed earthquake. Extract. Then, the computer 11 advances the process to step S90.

  In step S90, the computer 11 derives a distribution of amplitude spectral density in the frequency domain by performing Fourier transform on the waveform data of the vertical motion response acceleration waveform extracted in step S80 executed immediately before. Then, the computer 11 advances the process to step S100. Here, step S90 corresponds to the “distribution derivation step” in the present invention.

  In step S100, the computer 11 derives an amplitude spectral intensity value by integrating the amplitude spectral density distribution derived in step S90 executed immediately before in the low frequency range set in step S50. The process proceeds to step S110. Here, step S100 is also referred to as “first spectral intensity derivation step” in the present specification, and the spectral intensity of the amplitude derived in step S100 is also referred to as “first spectral intensity” in this specification. .

  In step S110, the computer 11 derives the value of the spectral intensity of the amplitude by integrating the distribution of the spectral density of the amplitude derived in step S90 executed most recently in the high frequency range set in step S50, The process proceeds to step S120. Here, step S110 is also referred to as a “second spectral intensity derivation step” in the present specification, and the spectral intensity of the amplitude derived in step S110 is also referred to as a “second spectral intensity” in the present specification. .

  In step S120, the computer 11 acquires the linear equation 22 (see FIG. 9) derived in the most recently executed step S60 in the form of a binary primary indefinite equation based on the epicenter distance and the spectral intensity ratio. To do. Subsequently, the computer 11 uses the first spectrum intensity derived in the most recently executed first spectrum intensity deriving step (step S100) as the most recently executed second spectrum intensity deriving step (step S110). To obtain the spectral ratio divided by the second spectral intensity derived in. Then, the computer 11 substitutes the obtained spectral ratio value into the element of the spectral intensity ratio in the primary expression 22 to create a single linear equation of the epicenter distance, and obtains the epicenter distance by solving the single linear equation. The process proceeds to step S130.

  Here, since the primary equation 22 is an equation that approximates the epicenter distance and the spectral intensity ratio distribution of the earthquake observed at the observation point 10, the epicenter distance obtained in step S120 is the epicenter distance 91B (Fig. 1)). That is, in step S120, the computer 11 estimates the epicenter distance 91B on the assumption that the epicenter distance 91B, which is the distance parameter of the observed earthquake, can be obtained from the linear expression of the spectral ratio. For this reason, step S120 is also referred to as an “estimation step” in this specification.

  In step S130, the computer 11 outputs the estimation result of the epicenter distance 91B obtained in step S120 to the display. Then, the computer 11 ends a series of steps executed in the above-described method for estimating the distance parameter of the observed earthquake.

  According to each step described above, when estimating the epicenter distance of the observed earthquake from the ratio of the amplitude at the low frequency and the amplitude at the high frequency of the earthquake motion, the epicenter distance and the spectral intensity ratio of the A earthquake recorded in the past are recorded. The combination of low frequency and high frequency with the highest correlation with is used. Here, since the A earthquakes have different epicenter distances, the combination of the low frequency and high frequency to be set reflects the influence of the common point characteristics relatively strongly regardless of the location of the epicenter. Is done. That is, according to each step described above, the epicenter distance of the earthquake is estimated by estimating the epicenter distance of the earthquake from the ratio of the amplitude at the low frequency and the amplitude at the high frequency, in which the influence of the site characteristics is reflected relatively strongly. Accuracy can be increased. Also, according to each step described above, the low frequency and the high frequency are set as frequency ranges each having a width in frequency, and estimation is performed based on the spectrum intensity of the amplitude in each frequency range. Thereby, the error which arises only by the amplitude of a specific frequency greatly amplified by point characteristics can be suppressed. In addition, according to the method of extracting the initial tremor waveform data as a discrete function of the spectral density in the frequency domain, it is necessary to obtain the correlation with the epicenter distance while giving the frequency range to the low frequency range and the high frequency range described above. There can be a finite number of combinations of each frequency range. Further, according to the method in which the waveform data of the initial tremor includes the initial fracture phase of the initial tremor, the influence of the difference in the seismic waveform due to the type of earthquake on the estimation result of the epicenter distance 91B is reduced. The accuracy of estimation can be improved.

  The engineer can cause the computer 11 to execute the above-described distance parameter estimation program again after confirming the estimation result of the epicenter distance 91B output in step S130. In this case, the engineer re-estimates the vertical motion response acceleration waveform 20 of the observed earthquake for which the epicenter distance 91B was previously estimated in step S20 to be executed again, and estimates the seismic time 20A and the previous epicenter distance 91B. In association with the result, additional data may be input as the above-described earthquake data. According to this method, the number of earthquake data for determining the primary equation 22 used for the estimation of the epicenter distance 91B can be increased every time an observed earthquake occurs, and the accuracy of the estimation of the epicenter distance 91B can be improved. .

  The present invention is not limited to the above-described embodiments using flowcharts and the like, and various changes, additions, and deletions can be made without changing the gist of the present invention. For example, the following various forms can be implemented.

(1) In the present invention, instead of the epicenter distance 91B of the observed earthquake, a method of estimating the epicenter distance 90B, which is a different distance parameter from the epicenter distance, and outputting the epicenter distance 90B as an estimation result is adopted. can do. In the present invention, it is also possible to adopt a method of estimating both the epicenter distance 91B and the epicenter distance 90B of the observed earthquake and estimating the epicenter depth 90C of the observed earthquake from this estimation result. Here, as shown in FIG. 1, the epicenter depth 90C is a linear distance from the epicenter 90A to the epicenter 91A, and can be calculated from the epicenter distance 91B and the epicenter distance 90B.

(2) In the present invention, instead of the vertical motion response acceleration waveform of the earthquake, the vertical parameter of the earthquake is estimated using the vertical motion velocity waveform which is a different type of earthquake vertical motion waveform from this vertical motion response acceleration waveform. The technique to do can be adopted. Here, the vertical motion velocity waveform of an earthquake has the property of being less affected by relatively high-frequency noise that is unlikely to be generated by an earthquake than the vertical motion response acceleration waveform of an earthquake. For this reason, when the earthquake distance parameter is estimated using the earthquake vertical motion velocity waveform, the earthquake distance parameter is estimated using the earthquake vertical motion response acceleration waveform. The influence of noise in this estimation can be reduced.

10 observation point 10A seismometer 11 computer 11A recording medium 20 vertical motion response acceleration waveform (earthquake vertical motion waveform)
20A Landing time 20B Extraction range 21 Amplitude spectral density 21A First frequency range 21B Region 21C Second frequency range 21D Region 22 Primary equation 90 Ground 90A Earthquake source 90B Earthquake source distance 90C Earthquake source depth 91 Distance parameter)
92 Asperity 92A Hypocenter area 92B Large destruction area F ₁ frequency F ₂ frequency F ₃ frequency F ₄ frequency

Claims (3)

Based on observation data of observation earthquakes observed at the observation point where the vertical motion waveforms of multiple earthquakes with different distance parameter values corresponding to the distance from the epicenter are recorded. In the method of estimating the distance parameter of the observed earthquake,
For one of the plurality of seismic vertical motion waveforms recorded in the past, waveform data including the initial fracture phase of the initial tremor in the seismic vertical motion waveform is extracted as a discrete function of the spectral density of the amplitude in the frequency domain An extraction step to extract as data;
A setting step of setting a first frequency range that is a relatively low frequency range and a second frequency range that is a relatively high frequency range so that the frequency ranges do not overlap each other;
For the extracted data extracted in the extraction step, a value of an amplitude spectrum intensity obtained by integrating the extracted data in the first frequency range, and an amplitude spectrum obtained by integrating the extracted data in the second frequency range. A spectral intensity ratio deriving step for obtaining a ratio of the intensity value as a spectral intensity ratio;
The extraction step and the spectral intensity ratio derivation step are performed for each of the plurality of earthquake vertical motion waveforms recorded in the past, and the distance parameter of the earthquake corresponding to each earthquake vertical motion waveform and each of the earthquake vertical motion waveforms A correlation coefficient deriving step for deriving a correlation coefficient between the spectral intensity ratios;
The correlation calculated in the correlation coefficient deriving step by repeatedly executing the correlation coefficient deriving step while changing the first frequency range and the second frequency range set in the setting step. A combination of the first frequency range and the second frequency range whose number is closest to 1 is obtained, and the first frequency range and the second frequency range are set as a low frequency range and a high frequency range, respectively. A predetermined frequency range setting step;
A distribution derivation step for deriving a distribution of the spectral density of the amplitude in the frequency domain of the vertical motion component in the waveform data including the initial fracture phase of the initial tremor of the observed earthquake;
A first spectrum for deriving, as a first spectrum intensity, an amplitude spectrum intensity value obtained by integrating the distribution of the amplitude spectral density derived in the distribution deriving step in the low frequency range determined in the frequency range setting step. An intensity derivation step;
A second spectrum for deriving as a second spectrum intensity a value of the spectrum intensity of the amplitude obtained by integrating the distribution of the spectrum density of the amplitude derived in the distribution deriving step in the high frequency range determined in the frequency range setting step. An intensity derivation step;
Assuming that the distance parameter of the observed earthquake can be obtained by a linear expression of a spectral ratio obtained by dividing the first spectral intensity by the second spectral intensity, an estimation step for estimating the distance parameter;
Having a plurality of steps including:
A method for estimating the distance parameters of observed earthquakes. Based on observation data of observation earthquakes observed at the observation point where the vertical motion waveforms of multiple earthquakes with different distance parameter values corresponding to the distance from the epicenter are recorded. A distance parameter estimation program for causing a computer to estimate the distance parameter of the observed earthquake.
In the computer,
For one of the plurality of seismic vertical motion waveforms recorded in the past, waveform data including the initial fracture phase of the initial tremor in the seismic vertical motion waveform is extracted as a discrete function of the spectral density of the amplitude in the frequency domain An extraction step to extract as data;
A setting step of setting a first frequency range that is a relatively low frequency range and a second frequency range that is a relatively high frequency range so that the frequency ranges do not overlap each other;
For the extracted data extracted in the extraction step, a value of an amplitude spectrum intensity obtained by integrating the extracted data in the first frequency range, and an amplitude spectrum obtained by integrating the extracted data in the second frequency range. A spectral intensity ratio deriving step for obtaining a ratio of the intensity value as a spectral intensity ratio;
The extraction step and the spectral intensity ratio derivation step are performed for each of the plurality of earthquake vertical motion waveforms recorded in the past, and the distance parameter of the earthquake corresponding to each earthquake vertical motion waveform and each of the earthquake vertical motion waveforms A correlation coefficient deriving step for deriving a correlation coefficient between the spectral intensity ratios;
The correlation calculated in the correlation coefficient deriving step by repeatedly executing the correlation coefficient deriving step while changing the first frequency range and the second frequency range set in the setting step. A combination of the first frequency range and the second frequency range whose number is closest to 1 is obtained, and the first frequency range and the second frequency range are set as a low frequency range and a high frequency range, respectively. A predetermined frequency range setting step;
A distribution derivation step for deriving a distribution of the spectral density of the amplitude in the frequency domain of the vertical motion component in the waveform data including the initial fracture phase of the initial tremor of the observed earthquake;
A first spectrum for deriving, as a first spectrum intensity, an amplitude spectrum intensity value obtained by integrating the distribution of the amplitude spectral density derived in the distribution deriving step in the low frequency range determined in the frequency range setting step. An intensity derivation step;
A second spectrum for deriving as a second spectrum intensity a value of the spectrum intensity of the amplitude obtained by integrating the distribution of the spectrum density of the amplitude derived in the distribution deriving step in the high frequency range determined in the frequency range setting step. An intensity derivation step;
Assuming that the distance parameter of the observed earthquake can be obtained by a linear expression of a spectral ratio obtained by dividing the first spectral intensity by the second spectral intensity, an estimation step for estimating the distance parameter;
To execute multiple steps including
Distance parameter estimation program. Based on observation data of observation earthquakes observed at the observation point where the vertical motion waveforms of multiple earthquakes with different distance parameter values corresponding to the distance from the epicenter are recorded. A computer-readable recording medium recording a distance parameter estimation program for causing a computer to estimate the distance parameter of the observed earthquake.
In the computer,
For one of the plurality of seismic vertical motion waveforms recorded in the past, waveform data including the initial fracture phase of the initial tremor in the seismic vertical motion waveform is extracted as a discrete function of the spectral density of the amplitude in the frequency domain An extraction step to extract as data;
A setting step of setting a first frequency range that is a relatively low frequency range and a second frequency range that is a relatively high frequency range so that the frequency ranges do not overlap each other;
For the extracted data extracted in the extraction step, a value of an amplitude spectrum intensity obtained by integrating the extracted data in the first frequency range, and an amplitude spectrum obtained by integrating the extracted data in the second frequency range. A spectral intensity ratio deriving step for obtaining a ratio of the intensity value as a spectral intensity ratio;
The extraction step and the spectral intensity ratio derivation step are performed for each of the plurality of earthquake vertical motion waveforms recorded in the past, and the distance parameter of the earthquake corresponding to each earthquake vertical motion waveform and each of the earthquake vertical motion waveforms A correlation coefficient deriving step for deriving a correlation coefficient between the spectral intensity ratios;
The correlation calculated in the correlation coefficient deriving step by repeatedly executing the correlation coefficient deriving step while changing the first frequency range and the second frequency range set in the setting step. A combination of the first frequency range and the second frequency range whose number is closest to 1 is obtained, and the first frequency range and the second frequency range are set as a low frequency range and a high frequency range, respectively. A predetermined frequency range setting step;
A distribution derivation step for deriving a distribution of the spectral density of the amplitude in the frequency domain of the vertical motion component in the waveform data including the initial fracture phase of the initial tremor of the observed earthquake;
A first spectrum for deriving, as a first spectrum intensity, an amplitude spectrum intensity value obtained by integrating the distribution of the amplitude spectral density derived in the distribution deriving step in the low frequency range determined in the frequency range setting step. An intensity derivation step;
A second spectrum for deriving as a second spectrum intensity a value of the spectrum intensity of the amplitude obtained by integrating the distribution of the spectrum density of the amplitude derived in the distribution deriving step in the high frequency range determined in the frequency range setting step. An intensity derivation step;
Assuming that the distance parameter of the observed earthquake can be obtained by a linear expression of a spectral ratio obtained by dividing the first spectral intensity by the second spectral intensity, an estimation step for estimating the distance parameter;
To execute multiple steps including
A computer-readable recording medium on which a distance parameter estimation program is recorded.

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