Method of setting observed value applicable range in earthquake motion distribution estimation

Abstract

To enable a highly-reliable earthquake motion distribution to be estimated by setting an applicable range of the observed value of an earthquake motion according to the degree of dispersion of ground properties, and by using the observed value of the earthquake motion obtained by a seismometer in combination with an estimated value of the earthquake motion obtained by a system for estimating the earthquake motion.SOLUTION: An applicable range of the observed value of an earthquake motion is set correspondingly to the degree of dispersion of ground properties around each of multiple observation points for observing the earthquake motion using a seismometer, according to a set radius from the observation point and the classification of standard deviation of ARV within the set radius. Inside the range, the observed value by each seismometer is adopted as the value of the earthquake motion. Outside the range, the estimated value obtained by the system for estimating the earthquake motion is adopted as the value of the earthquake motion.SELECTED DRAWING: Figure 16

Description

Technical Field

[0001] The present disclosure relates to a method for setting the applicable range of observed values for earthquake motion distribution estimation.

Background Art

[0002] In the railway field, it is important to enhance the seismic resistance of railway facilities. However, when there are concerns about the safety of running trains due to strong earthquake motions or when damage to railway facilities is feared, it is also important to quickly stop the running trains and resume operation after confirming that there are no deformations in structures, tracks, etc. during earthquake train operation regulations.

[0003] The applicant of the present application has developed and is operating a railway earthquake damage estimation information distribution system (Damage Information System for Earthquake on Railway : DISER), which is an information distribution system for earthquake motion distribution estimation information, for the purpose of providing information to support the quick resumption of train operation after an earthquake. This system called DISER has been utilized in some railway operators for prioritizing inspections of railway facilities after an earthquake and for determining the movement of stopped trains between stations to the next station at the slowest speed possible.

[0004] The inventors of the present application analyzed the error in the handling of earthquake motions in current earthquake train operation regulations and the estimation error of the areal earthquake motion at an arbitrary point regarding the relationship between observed values and estimated values in order to improve the reliability of earthquake motions estimated by DISER and the like. As a result, it was shown that by applying the observed values as they are up to a predetermined distance (for example, 2 [km].) from the earthquake observation point and applying the estimated values farther away, the reliability of the estimated earthquake motion throughout the target route is enhanced (see, for example, Patent Document 1 and Non-Patent Document 1).

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Non-Patent Literature

[0006]

Non-Patent Literature 1

Summary of the Invention

Problems to be Solved by the Invention

[0007] However, in the conventional method, the range to which the observed value is applied is uniformly set as a predetermined distance from the seismic observation point. However, if the range to which the observed value is applied is changed according to the ground characteristics around the seismic observation point, it is considered that the estimation error can be reduced and the reliability of the estimated ground motion for the entire target route can be further enhanced.

[0008] Here, the problems of the conventional method are solved, the range to which the observed value of ground motion is applied is set according to the degree of variation in ground characteristics, and by using together the observed value of ground motion by a seismometer and the estimated value of ground motion by a system for estimating ground motion, a method for setting the observed value application range for estimating a highly reliable ground motion distribution is provided.

Means for Solving the Problems

[0009] Therefore, in the method for setting the observed value application range for estimating ground motion distribution, around each of a plurality of observation points where ground motion is observed by seismometers, the range to which the observed value of ground motion is applied is set according to the degree of variation in ground characteristics, in accordance with the set radius from the observation point and the classification of the standard deviation of ARV within the set radius. Within the range, the observed value of each seismometer is adopted as the value of ground motion, and outside the range, the estimated value obtained by a system for estimating ground motion is adopted as the value of ground motion.

[0010] In the method for setting the applicable range of observed values for other ground motion distribution estimations, further, pairs of K-NET observation points and KiK-net observation points are selected, the separation distance which is the distance between the K-NET observation point and the KiK-net observation point, and the measured seismic intensity difference between K-NET and KiK-net in the same earthquake are calculated, the K-NET observation point is set as the observation point, the standard deviation of the ARV within a plurality of set radii from the observation point is calculated, for each section of a plurality of sections of the standard deviation of the ARV within each set radius from the observation point, an approximate curve showing the relationship between the separation distance and the measured seismic intensity difference is created, the value of the separation distance corresponding to the point where the RMS of the estimation error, which is the difference between the estimated value and the actual ground motion value, intersects with the approximate curve is calculated, and the range is set as the range where the distance from the observation point is less than or equal to the value of the separation distance.

[0011] In another method for setting the applicable range of observed values for ground motion distribution estimations, further, the value of the RMS of the estimation error is a value statistically calculated by comparing the estimated value and the observed value at the same KiK-net observation point.

[0012] In another method for setting the applicable range of observed values for ground motion distribution estimations, further, when the set radius from the observation point is less than or equal to a first value and the section of the standard deviation of the ARV within the set radius is greater than or equal to a second value, the range is set as the range where the distance from the observation point is less than or equal to the first value.

[0013] In another method for setting the applicable range of observed values for ground motion distribution estimations, further, the first value is 1 [km] or 2 [km], and the second value is 0.4.

[0014] In another method for setting the applicable range of observed values for ground motion distribution estimations, further, when the section of the standard deviation of the ARV within the set radius is less than or equal to a third value, the range is set as the range where the distance from the observation point is less than or equal to a fourth value.

[0015] In another method for setting the applicable range of observed values for ground motion distribution estimations, further, the third value is 0.2, and the fourth value is 6 [km].

Advantages of the Invention

[0016] According to the present disclosure, a highly reliable ground motion distribution can be estimated.

Brief Description of the Drawings

[0017]

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Embodiment for Carrying out the Invention

[0018] Hereinafter, the embodiments will be described in detail with reference to the drawings.

[0019] FIG. 1 is a diagram showing the ARV distribution around Shizuoka Prefecture and the along-line detection points of the virtual route in this embodiment, FIG. 2 is a diagram showing an example of the ARV histogram with a radius of 8 [km] of the along-line detection points of the virtual route in this embodiment, and FIG. 3 is a diagram showing an example of the ARV standard deviation of each radius of the along-line detection points of the virtual route in this embodiment. In FIG. 2, (a) shows an example of the ARV histogram of the along-line detection point SZOH34 of the virtual route, and (b) shows an example of the ARV histogram of the along-line detection point KNGH11 of the virtual route. In FIG. 3, (a) shows an example of the ARV standard deviation of the along-line detection point SZOH34 of the virtual route, and (b) shows an example of the ARV standard deviation of the along-line detection point KNGH11 of the virtual route.

[0020] In this embodiment, a method for setting the applicable range of observation values for earthquake motion distribution estimation is provided, so that a highly reliable earthquake motion distribution can be estimated. In this embodiment, the information on earthquake motion distribution is useful for the maintenance and operation of all kinds of structures and facilities nationwide. For example, it can be used for the maintenance of various buildings, the maintenance of social infrastructure facilities such as electric wires, gas pipes, and water pipes, and the maintenance of road facilities such as tunnels and viaducts. It is not limited to the applicable fields, types, regions, etc. Here, for the sake of explanation, the case of application to train operation regulations and facility inspections in railways will be described. Also, here, the measured seismic intensity is used as the earthquake motion index for explanation, but it can also be applied to any other earthquake motion index such as maximum acceleration, maximum velocity, and SI value. Furthermore, here, the standard deviation and RMS (Root Mean Square) are used as statistical quantities for evaluating errors, but other statistical quantities such as variance can also be used for evaluation. Here, the data of the K-NET and KiK-net earthquake observation networks operated by the National Research and Development Agency for Earthquake Science and Technology (hereinafter referred to as "NIED") are used to evaluate errors, but it is not necessarily required to use these earthquake observation networks.

[0021] In the methods shown in Patent Document 1 and Non-Patent Document 1, the applicable range of observation values is uniformly set as a predetermined distance (for example, 2 [km]) from the earthquake observation point. However, regarding the applicable range of observation values, when the ground characteristics around the observation point are similar, it is considered that the observation values can be applied over a wide range. On the other hand, when the ground characteristics are significantly different, it is presumed that the application of the observation values is limited to a narrow range. That is, it can be said that the distance to which the observation values are applied should be set individually according to the degree of change in the ground characteristics around the observation point. In this embodiment, the seismic amplification characteristics of the surface ground on a regional scale by public institutions are used to evaluate the degree of variation in the ground characteristics within a certain range, and a practical concept for setting the applicable range of observation values according to the degree of variation is presented.

[0022] Next, the evaluation of the degree of variation in the ground characteristics around the observation point will be considered.

[0023] Examples of areal ground characteristic information include AVS30, ARV, Tg, etc. Here, ARV, which directly represents the seismic motion amplification characteristics of the surface ground and is publicly available in J-SHIS of the Disaster Prevention Research Institute, is used. The ARV is defined as the amplification ratio of the maximum velocity of seismic motion from the reference bedrock surface to the ground surface. The publicly available ARV of areal information is on a 250 [m] mesh (1 / 4 regional mesh). Fig. 1 shows the ARV distribution around Shizuoka Prefecture and the detection points along the virtual route. From Fig. 1, it can be confirmed that generally, the ARV value is large in river floodplains and plains, etc., and small in mountainous areas, etc.

[0024] In this embodiment, in order to confirm the degree of variation in ARV between the target point and its surroundings, the standard deviation of ARV (hereinafter referred to as "ARV standard deviation") around the central mesh is obtained. When evaluating the variation, the range from the central evaluation point is important. In this embodiment, the range is simply evaluated as a circle. The standard deviation of ARV for each radius represents the variation in the surface ground amplification characteristics between the central point and its surroundings and is considered to have a relationship with the applicable range of the observed values.

[0025] In this embodiment, the ARV standard deviation within the circle is calculated for each radius from the evaluation point. Note that typical indicators representing variation include variance and standard deviation, etc. Here, the standard deviation is adopted. The standard deviation is adopted as an indicator for quantifying the degree of variation, and the normality of ARV within the target radius is not considered.

[0026] Figure 2 shows a histogram of the ARV at 0.02 intervals with a radius of 8 [km] for the detection points along the virtual route in the KiK-net seismic observation network shown in Figure 1. Looking at Figures 2(a) and (b), it can be seen that the ARV of the detection point SZOH34 along the virtual route located in the mountainous area with a high elevation is concentrated around 0.7, and the ARV of the detection point KNGH11 along the virtual route located in the plain area with a low elevation is widely distributed from 0.8 to 2.9. Note that Figure 2 shows an example with a radius of 8 [km], but it can be seen that the degree of variation in ARV varies greatly depending on the location.

[0027] Also, Figures 3(a) and (b) show the standard deviation of the ARV at 1 [km] intervals up to a radius of 20 [km] for the detection points SZOH34 and KNGH11 along the virtual route. According to Figure 1, the detection point SZOH34 along the virtual route is located in the mountainous area, but the surrounding area is also extensive mountainous terrain. In the example shown in Figure 3(a), the ARV standard deviation is generally less than 0.1 up to a radius of about 10 [km], but when it exceeds 10 [km], flat areas and the like are included, so the value of the ARV standard deviation gradually increases and stabilizes at about 0.3 from about a radius of 16 [km]. On the other hand, the detection point KNGH11 along the virtual route is located in the plain area according to Figure 1, but there are mountainous areas and the like around it. In the example shown in Figure 3(b), the value of the ARV standard deviation increases as the radius increases, and the value converges to about 0.38 from about a radius of 10 [km]. Thus, basically, the larger the radius, the larger the ARV standard deviation (the greater the variation), and a tendency to converge to a certain value is confirmed, but it is confirmed that the ARV standard deviation according to the radius varies greatly depending on the location.

[0028] In the vicinity of Shizuoka Prefecture as shown in Figure 1, the areas with a large ARV standard deviation (large variation in ARV) are the boundary areas between the mountainous and plain areas. And as the radius increases, the areas with a large ARV standard deviation in the mountainous and plain areas become wider, and the values of the ARV standard deviation are overall leveled. In the areas with a large variation in ARV, the ARV standard deviation is about 0.6.

[0029] In this embodiment, regarding earthquakes that may affect railways, attention is paid to earthquakes with a relatively large scale and a focal depth of about 60 [km] or less. The earthquake dataset handled in this embodiment is the same 81 earthquakes as those shown in Non-Patent Document 1. A list of information regarding the hypocenters of the target earthquakes is shown in Non-Patent Document 1.

[0030] Next, the handling error according to the ARV standard deviation will be described.

[0031] FIG. 4 is a diagram for explaining the outline of train operation regulation during an earthquake in this embodiment, FIG. 5 is a diagram showing the outline of the separation distance, the measured seismic intensity difference, and the ARV standard deviation calculation radius in this embodiment, and FIG. 6 is a diagram showing the histogram of the ARV standard deviation with a radius of 2 [km] in this embodiment.

[0032] For train operation regulation during an earthquake, railway operators install seismographs (hereinafter referred to as "line detection points") at generally regular intervals along the line. Generally, the inspection judgment after the train stops is made based on the observed values of the line detection points. As shown in FIG. 4, a responsible section is defined with the approximate midpoint between an adjacent line detection point as the boundary for a certain line detection point. When the observed ground motion at a certain line detection point exceeds the operation regulation reference value, operation regulations such as inspection and slowdown are issued for the responsible section of that line detection point. The characteristic of the conventional (current) train operation regulation during an earthquake is that, like the thick solid line shown in FIG. 4, the observed value of the line detection point is uniformly handled within the responsible section of that line detection point. On the other hand, the actual ground motion varies under the influence of factors such as the distance to the hypocenter and the surface ground, as shown by the thin solid line in FIG. 4. It is obvious that there are differences between the conventionally (currently) handled ground motion (thick solid line) and the actual ground motion (thin solid line). Also, when estimating the ground motion along the line, the estimated ground motion shown by the dashed curve in FIG. 4 may have differences from the actual ground motion (thin solid line), and there is an estimation error.

[0033] In the method described in Non-Patent Document 1, in the earthquake-time train operation regulation of railways, the error caused by the handling of seismic motion is organized as a handling error as shown in Fig. 4. Since such a handling error is considered to be generally equivalent to the error of the conventional (current) earthquake-time train operation regulation of railways, in the range where the estimated error of the estimated seismic motion is smaller than the handling error, even if it is estimated information including an error, the reliability of the seismic motion is considered to be improved compared to the handling of the seismic motion in the conventional (current) earthquake-time train operation regulation.

[0034] In the present embodiment, as shown in Fig. 5, by combining K-NET and KiK-net, which are strong-motion observation networks of the Disaster Prevention Science and Technology Institute, the difference in the observed seismic motion between two points (measurement seismic intensity difference) for the separation distance between two points and the ARV standard deviation within the set radius set from the K-NET observation point are organized. Note that the seismic motion indicators for the earthquake-time train operation regulation of railways include the maximum acceleration for warning, SI value, and measurement seismic intensity, and the seismic motion indicators used by railway operators are different. In the present embodiment, similar to Non-Patent Document 1, the study is conducted based on the measurement seismic intensity, which is a general seismic motion indicator defined by the Japan Meteorological Agency for the calculation method. Also, when evaluating the variation of ARV around the K-NET observation point, if the variation of ARV in a range wider than the separation distance between the K-NET observation point and the KiK-net observation point is targeted, an overly large range will be evaluated. In the present embodiment, only the data with a separation distance smaller than the radius for calculating the ARV standard deviation is targeted. Note that, as also explained in Non-Patent Document 1, the measurement seismic intensity difference shown in Fig. 5 is a value corresponding to the handling error shown in Fig. 4.

[0035] The number of combinations within a separation distance of 40 [km] between K-NET installed at approximately 20 [km] intervals across the country and KiK-net also installed at approximately 20 [km] intervals is extremely large, and in the earthquake dataset targeted in this embodiment, it is 123,475 combinations. In Fig. 6, a histogram of the ARV standard deviation in increments of 0.01 within a radius of 2 [km] from the K-NET observation point position is shown as "all data". In this embodiment, based on the same concept as in Non-Patent Document 1, since distant earthquakes are considered to have little impact on railways, the source distance is set to within 200 [km] for both the K-NET observation point and the KiK-net observation point. In addition, in the earthquake train operation regulation where inspections are ordered when there are concerns about the impact on railway facilities, when the ground motion is small, it is excluded, so seismic waveform data with a measured seismic intensity of 1.5 (seismic intensity 2) or more is used. As a result of selecting data according to this criterion for both selected pairs, it is 37,859 combinations. As an example, a histogram of the ARV standard deviation in increments of 0.01 within a radius of 2 [km] after data selection is shown as "target data" overlaid on "all data" in Fig. 6. In the example shown in Fig. 6, the ARV standard deviation within a radius of 2 [km] is distributed up to about 0.6, and there is a large amount of data from 0.1 to 0.2. K-NET is often installed within the sites of public facilities such as town halls and schools in urban areas, and it is considered that there are many installations on flat ground. The change in ARV within a radius of 2 [km] is relatively small, and it is considered that there are many relatively small values of the ARV standard deviation from 0.1 to 0.2.

[0036] Next, the relationship between the ARV standard deviation and the difference in measured seismic intensity between two points will be described.

[0037] Fig. 7 is a diagram showing an example of the relationship between the ARV standard deviation and the difference in measured seismic intensity in this embodiment, Fig. 8 is a diagram showing an example of the relationship between the separation distance and the difference in measured seismic intensity in this embodiment, Fig. 9 is a diagram showing an example of the evaluation of the applicable distance of observed values due to handling errors in this embodiment, and Fig. 10 is a diagram showing an example of the evaluation of estimation errors in this embodiment. In Figs. 7 and 9, (a) shows an example for a radius of 2 [km], and (b) shows an example for a radius of 8 [km].

[0038] For the purpose of confirming the relationship between the difference in shaking between the central point and a point away from it, while considering the variation in ground characteristics around the central point, the relationships between the ARV standard deviation and the measured seismic intensity difference within a radius of 2 [km] and within a radius of 8 [km] are shown in FIGS. 7(a) and (b). Here, the separation distance between the K-NET observation point and the KiK-net observation point for each plot is limited to within the target radius from the K-NET observation point as described above. For example, when the radius is 8 [km], only the data with a separation distance of 8 [km] or less are plotted. In FIG. 7, the RMS calculated by dividing the ARV standard deviation classification into four categories of 0.0 or more and less than 0.1, 0.1 or more and less than 0.2, 0.2 or more and less than 0.4, and 0.4 or more are superimposed and shown. Looking at the RMS for each classification in FIG. 7, it can be seen that the smaller the ARV standard deviation, the smaller the measured seismic intensity difference tends to be.

[0039] Thus, within the same target range, there is a relationship between the variation in the ground motion amplification characteristics of the surface ground around the K-NET observation point and the difference in ground motion between the two points of the K-NET observation point and the KiK-net observation point within that range, indicating that it is important to consider ground characteristics regarding the distance at which the observed values are applied.

[0040] Next, for each classification of the ARV standard deviation at each radius, the relationship between the separation distance and the measured seismic intensity difference is organized. In the present embodiment, for the ARV standard deviation, classifications are determined and organized. Similar to the classification in FIG. 7, four classifications of 0.0 or more and less than 0.1, 0.1 or more and less than 0.2, 0.2 or more and less than 0.4, and 0.4 or more are determined and organized. In the histogram of the ARV standard deviation within a radius of 2 [km] shown in FIG. 6, since the distribution of the ARV standard deviation reaches up to about 0.6, here, the classification for 0.4 or more will not be further subdivided. To evaluate this, the handling error RMS with a separation distance interval of 1 [km] for each ARV standard deviation classification by radius is approximated by a function.

[0041] In the present embodiment, when the separation distance is 0 [km] (i.e., the same location), since there is naturally no difference in the measured seismic intensity, the following equation (1), which is an exponential function as a functional form, is used.

[0042] y = ax b ···Equation (1)

[0043] FIG. 8 shows an example of the relationship between the separation distance and the difference in measured seismic intensity when the ARV standard deviation (SD) at a radius of 2 [km] is 0.1 or more and less than 0.2. FIG. 8 shows the RMS of the handling error at 1 [km] intervals, and the RMS of the handling error is approximated by the above equation (1). As described above, the difference in measured seismic intensity is a value corresponding to the handling error. At this time, as shown by the circles in FIG. 8, for the center of the 1 [km] interval, for example, in the case of the interval from 9 [km] to 10 [km], 9.5 [km], a function approximation is performed for the measured seismic intensity in that interval (interval). In FIG. 8, the approximate curve is shown by a broken line.

[0044] FIG. 9 shows the approximate curve and the estimated error RMS in each section of the ARV standard deviation (SD). FIG. 9(a) shows an example for a radius of 2 [km], and FIG. 9(b) shows an example for a radius of 8 [km]. In the example for a radius of 2 [km] shown in FIG. 9(a), the approximate curve and the estimated error RMS in each section of the ARV standard deviation section intersect. In the method described in Non-Patent Document 1, the separation distance corresponding to the point where the approximate curve and the estimated error RMS in the ARV standard deviation section intersect is called the observed value application distance. In FIG. 9(a), when the ARV standard deviation is 0.4 or more, the separation distance corresponding to the intersecting point is the smallest. That is, in the evaluation at a radius of 2 [km], when the variation in ARV is large (when the ARV standard deviation is in the maximum section of 0.4 or more), it indicates that the observed value application distance is set small. Also, in the example for a radius of 8 [km] shown in FIG. 9(b), in the range up to a separation distance of 20 [km], the approximate curve shows that the measured seismic intensity difference increases in the order from the section with a small ARV standard deviation to the section with a large ARV standard deviation at the same separation distance. That is, as confirmed in FIG. 7(b), there is a tendency for the measured seismic intensity difference to be smaller when the ARV standard deviation is smaller. Also, the separation distance corresponding to the point where the approximate curve and the estimated error RMS intersect becomes larger as the ARV standard deviation section is smaller. That is, in the evaluation at a radius of 8 [km], it is shown that the smaller the variation in ARV, the larger the observed value application distance is set.

[0045] In addition, when calculating the ARV standard deviation for evaluating the applicable distance of observed values for estimating ground motions along railway lines, it is considered appropriate to determine the maximum radius in consideration of the installation intervals of detection points along the line. For example, in the case of the Shinkansen, the interval between detection points along the line (i.e., the jurisdiction shown in Fig. 4) is from 10 [km] to 20 [km]. Therefore, the one-sided distance of the jurisdiction is from 5 [km] to 10 [km]. It is considered appropriate to set the radius for evaluating the degree of variation of ARV within the jurisdiction to be approximately the same as or shorter than such one-sided distance. Therefore, in the present embodiment, in consideration of the detection point intervals along the Shinkansen line, the calculation radius of the ARV standard deviation is considered up to 8 [km].

[0046] In the method described in Non-Patent Document 1, for area ground motion estimation, a method of fusing observed data and estimated data is proposed, and the observed values are applied within the applicable distance of the observed values where the handling error RMS and the estimation error RMS intersect. That is, the observed values are directly applied to the range smaller than the applicable distance of the observed values, and the estimated values are used for the range larger than the applicable distance of the observed values.

[0047] In the present embodiment, the handling error approximated by a curve is used to obtain the intersection point of the curve and the estimation error RMS. The estimation error of the area ground motion estimation using the inverse distance weighting method is statistically calculated by comparing the estimated values and the observed values at the same location (specifically, the location of the KiK-net observation point), similar to the method described in Non-Patent Document 1. As described above, in the present embodiment, the measured seismic intensity is targeted at 1.5 (seismic intensity 2) or more, and the result of organizing the target data is shown in Fig. 10. As a result, the statistical estimation error RMS was 0.55. This value is regarded as a value representing the accuracy of area ground motion estimation at an arbitrary location.

[0048] Next, the concept of setting the applicable distance of the observed values will be described.

[0049] FIG. 11 is a diagram showing an example of the relationship between the ARV standard deviation classification for each radius and the observed value application distance in the present embodiment, and FIG. 12 is a diagram showing an example of setting the observed value application distance according to the ARV standard deviation classification for each radius in the present embodiment.

[0050] FIG. 11 shows the relationship of the observed value application distance at which the approximation curve of the handling error RMS according to each ARV standard deviation classification for each radius intersects the estimated error RMS. For example, looking at FIG. 9(b), in the case of a radius of 8 [km], in the classification where the ARV standard deviation is 0.2 or more and less than 0.4, the separation distance corresponding to the point where the approximation curve intersects the estimated error RMS, that is, the observed value application distance is 6 [km], and such an observed value application distance is plotted in FIG. 11. In FIG. 11, the ARV standard deviation is plotted assuming it is constant within a predetermined interval. Looking at FIG. 11, it is confirmed that for any radius, the smaller the ARV standard deviation, the greater the tendency for the observed value application distance to be larger. From this, it is considered that the observed values can be applied to a wide area whether in a narrow range (small radius) or a wide range (large radius) when the variation of ARV is small. On the other hand, in a narrow range (small radius), when the variation of ARV is large, it is considered necessary to limit the application of the observed values to a narrow range.

[0051] Next, a method for setting the observed value application distance will be described based on the relationship between the ARV standard deviation classification for each radius and the observed value application distance as shown in FIG. 11. This method may include the concepts described in the following (1) to (4). (1) When the approximation curve of the handling error RMS based on the observed values is smaller than the estimated error RMS based on the estimated values of the ground motion, based on the concept that applying the observed values can reduce the statistical error, the observed value application distance is obtained from the separation distance corresponding to the point where the approximation curve intersects the estimated error RMS. (2) When the ARV standard deviation is large (the variation of ARV is large) within a narrow range, the degree of change in ARV around it is large. Therefore, it is appropriate to set the observed value application distance small. At this time, it is desirable that the observed value application distance is the same as or smaller than the radius for obtaining the ARV standard deviation. This is because it makes no sense to evaluate the variation of ARV in a range wider than the observed value application distance. From FIG. 11, when the ARV standard deviation with a radius of 1 [km] is 0.4 or more, the observed value application distance is set to 1 [km] which is the same as the radius. When the ARV standard deviation with a radius of 2 [km] is 0.4 or more, the observed value application distance is set to 2 [km] which is the same as the radius. (3) When the ARV standard deviation is small (the variation of ARV is small) both within a narrow range and within a wide range, the degree of change in ARV around it is small. Therefore, it is appropriate to set the observed value application distance large. From FIG. 11, when the ARV standard deviations with radii of 1 [km], 2 [km], 4 [km], and 8 [km] are all less than 0.2, the observed value application distance is set to 6 [km]. (4) In the example shown in FIG. 11, except for the ARV standard deviations of 0.4 or more with radii of 1 [km] and 2 [km], the observed value application distance is 3 [km] or more for each radius with an ARV standard deviation of 0.2 or more. Thus, except for the cases described in (1) to (3) above, the observed value application distance is set to 3 [km].

[0052] FIG. 12 summarizes the method of setting the observed value application distance according to each ARV standard deviation category for each radius described in (1) to (4) above.

[0053] Next, an example of applying the method of this embodiment to past earthquakes will be described.

[0054] FIG. 13 is a diagram showing the along-track detection points and the ARV standard deviation along the virtual route in the present embodiment, FIG. 14 is a table showing an example of setting the observation value application distance of the along-track detection points of the virtual route in the present embodiment, FIG. 15 is a diagram showing an example of the estimated surface ground motion around the virtual route in the present embodiment, FIG. 16 is a diagram showing an example of the estimated along-track ground motion of the virtual route in the present embodiment, and FIG. 17 is a diagram showing the application status of the observation values around the along-track detection points of the virtual route in the present embodiment.

[0055] As described above, in the present embodiment, the observation value application distance is set. By calculating in advance the ARV standard deviations at radii of 1 [km], 2 [km], 4 [km], and 8 [km] of the along-track detection points installed along the railway line, the observation value application distance can be determined. In FIG. 13, the ARV standard deviations at each radius on the virtual route shown in FIG. 1 are indicated by solid lines. Also, the positions of the along-track detection points are indicated by filled plots. According to FIG. 13, at the along-track detection point SZOH26 (about 63.909 [km]), the along-track detection point SZOH33 (about 111.938 [km]), and around about 210 [km], the ARV standard deviation is larger than that in other sections for each radius. On the other hand, around the along-track detection point SZOH34 (about 126.352 [km]), the ARV standard deviation is relatively small for each radius.

[0056] FIG. 14 shows the ARV standard deviations at each radius for each along-track detection point and the observation value application distance determined by FIG. 13. In the example shown here, when the ARV standard deviation at a radius of 1 [km] is 0.4 or more, there is no detection point with an observation value application distance of 1 [km], there is 1 along-track detection point with an observation value application distance of 6 [km], 8 along-track detection points with an observation value application distance of 3 [km], and 1 along-track detection point with an observation value application distance of 2 [km].

[0057] Here, when the method of the present embodiment is applied using the virtual route shown in FIG. 1, the along-track detection points of the virtual route, and the observation value application distance shown in FIG. 14 determined for the along-track detection points, for the Suruga Bay Earthquake that occurred in 2009 (M jAn example of estimating ground motion along a railway line in (6.5) will be described. The areal ground motion estimation method is based on the K-NET observation data of the Disaster Prevention Science and Technology Institute. For all K-NET observation points used in the estimation, a setting example of the applicable distance of the observed value corresponding to each ARV standard deviation category of each radius shown in Fig. 12 is applied.

[0058] Fig. 15 shows the estimated areal ground motion around Shizuoka Prefecture in the Suruga Bay earthquake when the method of this embodiment is applied. The estimated areal ground motion is the ground motion estimated according to the applicable distance of the observed value shown in Fig. 12 with respect to the observed values of the K-NET observation points and the detection points along the virtual route.

[0059] Fig. 16 shows an example of the estimated ground motion along the virtual route extracted from the estimated areal ground motion shown in Fig. 15. In Fig. 16, the estimated ground motion along the line when the observed value of the detection point along the line is not applied is shown by a solid line called the estimated value (K-NET), the estimated ground motion along the line when the observed value of the detection point along the line is applied is shown by a solid line called the estimated value (K-NET + detection point along the line), and the observed values of the virtual detection points along the line are shown by circles.

[0060] According to Fig. 16, before and after the detection points along the line SZOH33 (about 111.938 [km] in kilometers) and the detection points along the line SZOH34 (about 126.352 [km] in kilometers), it is recognized that the estimated ground motion along the line when the observed value of the detection point along the line shown by the solid line called the estimated value (K-NET) is not applied is smaller than the observed value shown by the circle and is underestimated. On the other hand, the estimated ground motion along the line when the observed value of the detection point along the line shown by the solid line called the estimated value (K-NET + detection point along the line) is applied is the same as the observed value at all detection points along the line. From this, it can be confirmed that the underestimation is improved by applying the observed value to the applicable distance of the observed value.

[0061] According to this embodiment, since the observed values are applied within the observed value application distance, there is a part that becomes a rectangular shape as the ground motion along the line. However, as described in Non-Patent Document 1, the accuracy of the estimated ground motion is increased by applying the observed values in the closer vicinity. Therefore, by introducing the observed values of the virtual along-line detection points, the reliability of the estimated ground motion is improved.

[0062] In addition, when the observation points are close to each other, there may be a range that is within the observed value application distance from a plurality of observation points. In such a case, in view of treating the estimated ground motion as disaster prevention information, it is desirable to apply the larger observed value. Specifically, for example, in FIG. 17 corresponding to the enlarged view of the range indicated by the black square frame in FIG. 15, the virtual along-line detection point KNGH20 and the surrounding K-NET observation point KNG014 have a common range within the observed value application distance. Therefore, within this range, the observed value of KNG014 with a larger value is applied. This range is the range indicated by a circle in FIG. 17, but within this range, the observed value and the estimated value do not match even at the position of the along-line detection point.

[0063] As described above, according to this embodiment, since the ground motion along the line is estimated by combining the observed values and the estimated values considering the amplification characteristics of the surface ground, it is considered to be more reliable than the ground motion handled by the conventional (current) earthquake time series train operation regulations. The estimated value of the ground motion distribution obtained by this embodiment is useful for judgments such as the optimization of the inspection section and the movement of the stopped train between stations to the next station, and is considered to contribute to the early resumption of operation of the train stopped during an earthquake.

[0064] As described above, in this embodiment, in the estimation of the ground motion by combining the observed values and the estimated values, the application distance of the observed values is set in consideration of the ground motion amplification characteristics of the surface ground. Regarding the ground motion amplification characteristics of the surface ground, attention is paid to the ARV publicly released by the Disaster Prevention Science and Technology Institute as area information, and the standard deviation of ARV within a circle centered on the earthquake observation point is used as an index for evaluating its variation.

[0065] The method for setting the observed value application range of the ground motion distribution estimation in this embodiment may include the following steps (1) to (8). (1) Select pairs of K-NET observation points and KiK-net observation points, and calculate the distance between the K-NET observation point and the KiK-net observation point, that is, the separation distance, and the difference in measured seismic intensities between K-NET and KiK-net in the same earthquake. (2) Taking the K-NET observation point as the center point, calculate the ARV standard deviation at radii of 1 [km], 2 [km], 4 [km], and 8 [km] from the center point. (3) For each of the four categories where the ARV standard deviation at each radius from the center point is 0.0 or more and less than 0.1, 0.1 or more and less than 0.2, 0.2 or more and less than 0.4, and 0.4 or more, organize the relationship between the separation distance and the measured seismic intensity difference. (4) Approximate the handling error RMS at intervals of 1 [km] of the separation distance for each category of the ARV standard deviation at each radius from the center point with a function. (5) Using the value 0.55 of the statistical estimation error RMS for the areal ground motion estimation at an arbitrary location, calculate the separation distance corresponding to the point where the approximate curve of the handling error RMS represented by the function intersects the estimation error RMS. (6) Determine the observed value application distance from the calculated separation distance corresponding to each category of the ARV standard deviation at each radius from the center point. (7) In advance, determine the observed value application distance for each observation point based on each category of the ARV standard deviation at each radius from the center point, and apply the observed values in the areal ground motion estimation. (8) Extract the ground motion along the target route from the areal ground motion combined with the observed values and the estimated values.

[0066] In this embodiment, an example of the estimated ground motion along a virtual route obtained by performing some of the steps (1) to (8) is shown.

[0067] Compared with the conventional (current) method that only uses the observed values of the in-line detection points installed at regular intervals near the line, the method of this embodiment that uses both observed values and estimated values is a practical data fusion method that reduces the average estimation error of the entire line to be estimated. By utilizing the estimated in-line seismic motion information obtained by the method of this embodiment for judgments such as the optimization of the inspection section and the movement of stopped trains between stations to the next station, it is possible to contribute to the early resumption of operation of stopped trains during an earthquake. Furthermore, highly reliable in-line seismic motion information can also prevent overlooking large shakes between seismographs, thus leading to an increase in safety during an earthquake.

[0068] Thus, in the method for setting the applicable range of observed values for seismic motion distribution estimation of this embodiment, around each of the plurality of observation points where seismic motion is observed by seismographs, the range to which the observed value of seismic motion is applied according to the degree of variation in ground characteristics is set according to the set radius from the observation point and the classification of the standard deviation of ARV within the set radius. Within that range, the observed values of each seismograph are adopted as the values of seismic motion, and outside that range, the estimated values obtained by a system that performs seismic motion estimation are adopted as the values of seismic motion. Thereby, a highly reliable seismic motion distribution can be estimated.

[0069] Also, a pair of K-NET observation points and KiK-net observation points is selected, the separation distance which is the distance between the K-NET observation point and the KiK-net observation point, and the measured seismic intensity difference between K-NET and KiK-net in the same earthquake are calculated. Taking the K-NET observation point as the observation point, the standard deviation of ARV within a plurality of set radii from this observation point is calculated. For each classification of the plurality of classifications of the standard deviation of ARV within each set radius from the observation point, an approximate curve showing the relationship between the separation distance and the measured seismic intensity difference is created, and the value of the separation distance corresponding to the point where the RMS of the estimation error, which is the difference between the estimated value and the actual value of seismic motion, intersects the approximate curve is calculated. The range to which the observed value is applied is set as the range where the distance from the observation point is less than or equal to the value of the separation distance. Furthermore, the value of the RMS of the estimation error is a value statistically calculated by comparing the estimated value and the observed value at the same KiK-net observation point.

[0070] Furthermore, when the set radius from the observation point is less than or equal to the first value and the category of the standard deviation of the ARV at the set radius is greater than or equal to the second value, the range to which the observed value is applied is set to be the range where the distance from the observation point is less than or equal to the first value. Note that the first value is 1 [km] or 2 [km], and the second value is 0.4.

[0071] Furthermore, when the category of the standard deviation of the ARV within the set radius from the observation point is less than or equal to the third value, the range to which the observed value is applied is set to be the range where the distance from the observation point is less than or equal to the fourth value. Note that the third value is 0.2, and the fourth value is 6 [km].

[0072] Also, the disclosure herein describes the features of preferred and exemplary embodiments. Various other embodiments, modifications, and variations within the scope and spirit of the appended claims will be naturally contemplated by those skilled in the art upon reviewing the disclosure herein.

Industrial Applicability

[0073] This disclosure can be applied to a method for setting the range of observed values for earthquake motion distribution estimation.

Claims

1. For each of a plurality of observation points where ground motions are observed by seismographs, a range to which an observed value of a ground motion is applied is set according to the degree of variation in ground characteristics, and is set according to a set radius from the observation point and a classification of the standard deviation of ARV within the set radius, within the range, the observed values of the respective seismographs are adopted as the values of the ground motions, A method for setting an observation value application range for ground motion distribution estimation, characterized in that outside the range, an estimated value obtained by a system that performs ground motion estimation is adopted as the value of the ground motion.

2. A pair of a K-NET observation point and a KiK-net observation point is selected, a separation distance that is the distance between the K-NET observation point and the KiK-net observation point, and a measured seismic intensity difference between K-NET and KiK-net in the same earthquake are calculated, taking the K-NET observation point as the observation point, calculating the standard deviation of ARV within a plurality of set radii from the observation point, For each classification of a plurality of classifications of the standard deviation of ARV within each set radius from the observation point, an approximate curve showing the relationship between the separation distance and the measured seismic intensity difference is created, and the value of the separation distance corresponding to the point where the RMS of the estimation error, which is the difference between the estimated value and the actual ground motion value, intersects the approximate curve is calculated, The method for setting an observation value application range for ground motion distribution estimation according to claim 1, wherein the range is a range where the distance from the observation point is equal to or less than the value of the separation distance.

3. The method for setting an observation value application range for ground motion distribution estimation according to claim 2, wherein the value of the RMS of the estimation error is a value statistically calculated by comparing the estimated value and the observed value at the same KiK-net observation point.

4. The method for setting an observation value application range for ground motion distribution estimation according to claim 1, wherein when the set radius from the observation point is equal to or less than a first value and the classification of the standard deviation of ARV within the set radius is equal to or greater than a second value, the range is a range where the distance from the observation point is equal to or less than the first value.

5. The method for setting the applicable range of observed values for earthquake motion distribution estimation according to claim 4, wherein the first value is 1 [km] or 2 [km], and the second value is 0.

4.

6. The method for setting the applicable range of observed values for earthquake motion distribution estimation according to claim 1, wherein when the classification of the standard deviation of ARV within the set radius is equal to or less than a third value, the range is set to a range where the distance from the observation point is equal to or less than a fourth value.

7. The method for setting the applicable range of observed values for earthquake motion distribution estimation according to claim 6, wherein the third value is 0.2 and the fourth value is 6 [km].

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