Earthquake motion observation system and earthquake motion observation method

Abstract

To provide an earthquake motion observation system which can be realized at a low cost and can accurately observe an earthquake motion within a wide range.SOLUTION: An earthquake motion estimation device 20 estimates a first principal motion waveform S1 being a waveform portion equivalent to a principal motion from a first earthquake waveform W1, adjusts a second earthquake waveform W2, estimates a second principal motion waveform S2 being a waveform portion equivalent to the principal motion from the adjusted second earthquake waveform, and when there is a time range where an amplitude becomes constant in the second principal motion waveform S2, sets a time range prior to the time range as a first range R1 and sets the time range as a second range R2, defines a function expressing a relevance of the waveform characteristics in the second range R2 to the waveform characteristics in the first range R1 of the first principal motion waveform S1, derives a correction waveform based on the waveform characteristics, and corrects the second earthquake waveform W2 by replacing the waveform of the second range R2 of the second principal motion waveform S2 with the correction waveform.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to an earthquake motion observation system and an earthquake motion observation method that use a smart device with a built-in acceleration sensor and a seismometer fixed to a building or the ground. [Background technology]

[0002] When an earthquake occurs, seismic motion is observed at multiple locations located over a wide area. For example, Patent Document 1 discloses a structural health monitoring system comprising: a plurality of sensor devices installed at least once for each of a plurality of structures to detect physical quantities of the target structure; a plurality of collection devices provided in association with each group of structures, each containing at least one of the plurality of structures, to wirelessly collect data of the physical quantities detected by each sensor device; and a data processing device connected to the plurality of collection devices to receive the collected physical quantity data from the plurality of collection devices. In a configuration like that described in Patent Document 1, a large number of sensor devices are required because a sensor device is fixed and installed in conjunction with each of the multiple structures. Consequently, the cost is high.

[0003] In contrast, Patent Document 2 discloses an evaluation system for evaluating earthquake shaking at an evaluation target. This evaluation system includes an acquisition means for acquiring first information indicating earthquake shaking at the evaluation target, which is identified by a terminal device installed at the evaluation target, and second information indicating earthquake shaking around the evaluation target, which is identified by terminal devices installed around the evaluation target; and an evaluation means for performing an evaluation of the earthquake shaking at the evaluation target based on the first and second information acquired by the acquisition means. The terminal device is, for example, a smartphone or a tablet device. Furthermore, Patent Document 3 discloses a configuration comprising: a number of altitude alarms arranged in the vertical direction within a multi-story structure to notify nearby mobile terminals of their respective altitude positions; a number of smartphones equipped with sensors to detect their own vibrations and a location information acquisition unit to acquire their current location and altitude; an observation control unit that detects the orientation of the smartphones and initiates vibration detection by the sensors based on the duration of that orientation; an information collection unit that acquires the number of smartphones that have started detecting vibrations and their respective current locations, and collects the detection results from the sensors of each mobile terminal; and a determination unit that determines, based on the detection results collected by the information collection unit, that the vibrations are caused by an earthquake when the number of smartphones that have detected vibrations exceeds a predetermined number. As described in Patent Documents 2 and 3, if an earthquake detection system is implemented using smart devices such as smartphones and tablet terminals, which are owned by many people, it may be possible to reduce the number of sensors that need to be installed when observing seismic motion at multiple locations located over a wide area, thereby reducing costs.

[0004] However, smart devices are not always able to accurately observe seismic motion when an earthquake occurs. For example, if an earthquake occurs while a smart device is placed on a desk, and the earthquake is small, the smart device will move along the desk due to friction and will not move relative to the desk, allowing for accurate observation of the earthquake's motion. However, if the earthquake is large enough that a force exceeding the friction between the smart device and the desk acts on it, the smart device may move relative to the desk or even fall off. In such cases, the smart device will not be able to accurately observe the earthquake's motion. There is a need to develop a low-cost system that can accurately observe seismic activity over a wide area. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2017-167883 [Patent Document 2] Japanese Patent Publication No. 2020-193935 [Patent Document 3] International Publication No. 2018 / 174296 [Overview of the Initiative] [Problems that the invention aims to solve]

[0006] The problem that this invention aims to solve is to provide an earthquake motion observation system and an earthquake motion observation method that can be implemented at low cost and accurately observe earthquake motion over a wide area. [Means for solving the problem]

[0007] To solve the above problems, the present invention employs the following means. That is, the present invention is an earthquake motion observation system using a smart device with a built-in acceleration sensor and a seismometer fixed to a building or the ground, comprising an earthquake motion estimation device that estimates the earthquake motion at the location of the smart device by correcting a second earthquake waveform observed by the acceleration sensor based on a first earthquake waveform observed by the seismometer, the earthquake motion estimation device comprising a first main motion waveform estimation unit that estimates a first main motion waveform which is the waveform portion corresponding to the main motion from the first earthquake waveform, and a second main motion waveform which is the waveform portion corresponding to the main motion from the adjusted second earthquake waveform The present invention provides an earthquake motion observation system comprising: a second main motion waveform estimation unit that estimates a second main motion waveform; a waveform correction unit that, if there is a time range within the second main motion waveform in which the amplitude is constant, sets the time range prior to that time range as the first range and the said time range as the second range, defines a function that represents the relationship between the waveform characteristics in the second range and the waveform characteristics in the first range of the first main motion waveform; derives the waveform characteristics in the second range of the second main motion waveform based on the waveform characteristics in the first range of the second main motion waveform and the function; derives a corrected waveform based on the said waveform characteristics; and corrects the second earthquake waveform by replacing the waveform in the second range of the second main motion waveform with the corrected waveform. According to the above configuration, the system comprises a smart device with a built-in acceleration sensor and a seismometer fixed to a building or the ground. When an earthquake occurs, the seismometer observes the earthquake as a first seismic waveform, and the acceleration sensor built into the smart device observes the earthquake as a second seismic waveform. In other words, since the seismic motion at each location where the smart device is located is observed by the acceleration sensor built into the smart device, it is possible to observe seismic motion over a wide area. Furthermore, since seismic motion at each location is observed using smart devices, there is no need to install many seismometers. Therefore, a seismic motion observation system can be realized at low cost. However, when observing seismic motion using smart devices, it may not be possible to observe the seismic motion accurately. For example, if the earthquake is strong enough that a force exceeding the frictional force between the smart device and the desk acts on the smart device, the smart device may move relative to the desk or fall off the desk. In such cases, the second seismic waveform observed by the acceleration sensor built into the smart device while the smart device is moving relative to the desk or falling will not be a normal observation of the earthquake. In such cases, the portion of the second seismic waveform that does not accurately observe the earthquake often tends to show a constant amplitude. Here, the seismic motion estimation device estimates the seismic motion at the location of the smart device by correcting the second seismic waveform observed by the acceleration sensor based on the first seismic waveform observed by the seismometer. More specifically, the first main seismic waveform, which corresponds to the main motion, is estimated from the first seismic waveform. Furthermore, the second seismic waveform is adjusted so that its time and direction match the first seismic waveform, and from the adjusted second seismic waveform, the second main seismic waveform, which corresponds to the main motion, is estimated. If there is a time range within this second main seismic waveform where the amplitude is constant, it is considered to be the portion where strong vibrations occurred and the earthquake was not observed normally, as described above. This time range where strong vibrations are thought to have occurred is set as the second range, and the time range prior to the second range, where the earthquake was observed normally, is set as the first range. If we assume that the vibrations in the first range are those of an earthquake that occurred in the first rupture zone of the epicenter, and the vibrations in the second range are those of an earthquake that occurred in a second rupture zone of the epicenter, which is different from the first rupture zone, then if the distance between the location where the seismometer is installed and the location where the smart device is installed is sufficiently smaller than the distance between the first and second rupture zones, then the propagation characteristics of the earthquake vibrations that occurred in the first rupture zone are considered to be approximately the same at both locations, and the propagation characteristics of the earthquake vibrations that occurred in the second rupture zone are also considered to be approximately the same at both locations. Therefore, if we define a function that represents the relationship between the waveform characteristics in the second range and the waveform characteristics in the first range of the first main waveform, then the relationship between the waveform characteristics in the second range and the waveform characteristics in the first range of the second main waveform is considered to be the same as for the first main waveform. Thus, based on the waveform characteristics in the first range of the second main waveform and the function, we can derive the waveform characteristics in the second range of the second main waveform. Based on the waveform characteristics in the second range of the second main motion waveform derived in this way, a corrected waveform can be derived, and the second seismic waveform can be corrected by replacing the waveform in the second range of the second main motion waveform with the corrected waveform. In this way, even if there are parts in the second seismic waveform that do not accurately reflect the earthquake, these can be corrected, allowing for accurate observation of seismic motion at the location where the smart device is installed. Therefore, it is possible to provide a seismic motion observation system that can be implemented at low cost and accurately observe seismic motion over a wide area.

[0008] In one embodiment of the present invention, the waveform characteristic is an acceleration Fourier spectrum, and the waveform correction unit defines the function by the ratio of the acceleration Fourier spectrum in the second range to the acceleration Fourier spectrum in the first range of the first main dynamic waveform, smooths only the amplitude spectrum of the function, applies the smoothed smoothing function to the acceleration Fourier spectrum in the first range of the second main dynamic waveform to derive the acceleration Fourier spectrum in the second range of the second main dynamic waveform, and performs an inverse Fourier transform on this to derive the corrected waveform. With the configuration described above, an earthquake motion observation system can be properly implemented.

[0009] In another embodiment of the present invention, the waveform correction unit, when the amplitude of the second range of the second main motion waveform is less than or equal to the amplitude threshold, applies the waveform characteristics in the first range of the second main motion waveform to the function to derive the waveform characteristics in the second range of the second main motion waveform as the normal assumed waveform characteristics, which are the waveform characteristics expected when the second range of the second main motion waveform is acquired normally. It then calculates a comparison function between the acquired waveform characteristics, which are the waveform characteristics of the waveform actually acquired by the acceleration sensor in the second range of the second main motion waveform, and the normal assumed waveform characteristics. Based on the acquired waveform characteristics and the comparison function, it derives the corrected waveform and corrects the second seismic waveform by replacing the waveform in the second range of the second main motion waveform with the corrected waveform. The second seismic waveform observed by the accelerometer built into the smart device during an earthquake does not accurately reflect the earthquake's occurrence. In cases where the amplitude remains constant for a certain period, the value of this constant amplitude varies depending on the smart device's state during the earthquake. For example, when an earthquake occurs with the smart device placed on a desk, both cases—one where the seismic force exceeds the maximum static friction between the smart device and the desk, causing the device to slide relative to the desk, and another where the seismic force is excessive and the smart device falls off the edge of the desk—both exhibit a constant amplitude. However, the amplitude tends to be larger during the fall than during the sliding motion. In the latter case, the waveform actually acquired by the acceleration sensor in the second range of the second main dynamic waveform is expected to differ significantly from the waveform acquired under normal conditions, making it difficult to use as a reference when deriving the corrected waveform. However, in the former case, the waveform actually acquired by the acceleration sensor in the second range of the second main dynamic waveform is likely to have characteristics similar to the waveform acquired under normal conditions, and using it as a reference when deriving the corrected waveform may allow for the deriving of a more accurate corrected waveform. For this reason, in the former case, that is, when the amplitude of the second range of the second main dynamic waveform is below a predetermined amplitude threshold, the corrected waveform is derived using the waveform actually acquired by the acceleration sensor in the second range of the second main dynamic waveform. As already explained, the relationship between the waveform characteristics in the second range and the waveform characteristics in the first range of the second main dynamic waveform is the same as the relationship between the waveform characteristics in the second range and the waveform characteristics in the first range of the first main dynamic waveform. Therefore, by applying the waveform characteristics in the first range of the second main dynamic waveform to the function representing this relationship, the waveform characteristics in the second range of the second main dynamic waveform can be derived. The waveform characteristics derived in this way can also be called the normal assumed waveform characteristics, which are the waveform characteristics that would be expected if the second range of the second main dynamic waveform were acquired normally. Here, as described above, if the amplitude of the second range of the second main dynamic waveform is below the amplitude threshold, the waveform actually acquired by the acceleration sensor in the second range of the second main dynamic waveform is highly likely to have characteristics similar to the waveform expected when acquired normally. For this reason, a comparison function is calculated between the acquired waveform characteristics, which are the characteristics of the actually acquired waveform, and the normal expected waveform characteristics. Based on this comparison function and the acquired waveform characteristics, a corrected waveform that reflects the acquired waveform characteristics can be derived so that the acquired waveform characteristics are adjusted to a form similar to the normal expected waveform characteristics. In this way, in the configuration described above, when the waveform actually acquired by the acceleration sensor in the second range of the second main dynamic waveform is likely to have characteristics similar to the waveform expected when acquired normally, these characteristics can be appropriately reflected in the corrected waveform to further improve accuracy.

[0010] In another embodiment of the present invention, the waveform characteristic is an acceleration Fourier spectrum, and the waveform correction unit defines the function by the ratio of the acceleration Fourier spectrum in the second range to the acceleration Fourier spectrum in the first range of the first main dynamic waveform, multiplies the acceleration Fourier spectrum in the first range of the second main dynamic waveform by the function and takes the result as the normal assumed waveform characteristic, divides this by the acquired waveform characteristic which is the acceleration Fourier spectrum to calculate the comparison function, approximates the comparison function with an exponential function or a multidimensional polynomial to calculate an approximation function, multiplies the approximation function by the acquired waveform characteristic and performs an inverse Fourier transform on the result to derive the corrected waveform. With the above configuration, the comparison function is made into an approximate function with a more appropriate shape, and the corrected waveform is derived from the approximate function and the acquired waveform characteristics, thereby improving the accuracy of the corrected waveform.

[0011] Furthermore, the present invention relates to a seismic motion observation method that uses a smart device with a built-in acceleration sensor and a seismometer fixed to a building or the ground to observe seismic motion, wherein the first main seismic waveform, which is the waveform portion corresponding to the main motion, is estimated from the first seismic waveform observed by the seismometer, the second seismic waveform observed by the acceleration sensor is adjusted so that the time and direction match the first seismic waveform, the second main seismic waveform, which is the waveform portion corresponding to the main motion, is estimated from the adjusted second seismic waveform, and if there is a time range in the second main seismic waveform where the amplitude is constant, from that time range The present invention provides an earthquake motion observation method characterized by setting a time range prior to the present time range as the first range and the said time range as the second range, defining a function that represents the relationship between the waveform characteristics of the first main motion waveform in the second range and the waveform characteristics in the first range of the first main motion waveform, deriving the waveform characteristics of the second main motion waveform in the second range based on the waveform characteristics of the second main motion waveform in the first range and the function, deriving a corrected waveform based on said waveform characteristics, and correcting the second earthquake waveform by replacing the waveform of the second range of the second main motion waveform with the corrected waveform, thereby estimating the earthquake motion at the location where the smart device is located. With the configuration described above, it is possible to provide a seismic motion observation method that can be implemented at low cost and accurately observe seismic motion over a wide area, similar to the seismic motion observation system described above. [Effects of the Invention]

[0012] According to the present invention, it is possible to provide an earthquake motion observation system and an earthquake motion observation method that can be implemented at low cost and accurately observe earthquake motion over a wide area. [Brief explanation of the drawing]

[0013] [Figure 1] This is an explanatory diagram of an earthquake motion observation system in an embodiment of the present invention. [Figure 2] This is a block diagram of the smart devices in the above-mentioned seismic motion observation system. [Figure 3] The above is a diagram illustrating the smart device. [Figure 4] This is a block diagram of the seismic motion estimation device in the above-mentioned seismic motion observation system. [Figure 5] This figure shows the second seismic waveform when an earthquake is observed correctly on a smart device. [Figure 6] This figure shows the second seismic waveform when an earthquake is not properly observed on a smart device. [Figure 7] This diagram illustrates the relationship between the progression of the main seismic activity and the waveforms observed by seismometers and smart devices. [Figure 8] This figure shows a function that represents the relationship between the waveform characteristics in the second range of the main motion and the waveform characteristics in the first range of the main motion of the first seismic waveform. [Figure 9] This figure shows the smoothed function obtained by smoothing the above function. [Figure 10] This is a flowchart of the seismic motion observation method in an embodiment of the present invention. [Figure 11] This figure shows the first verification results of the seismic motion observation system in the above embodiment, and represents the first seismic waveform observed by the seismometer, the second seismic waveform observed by the smart device, and the corrected second seismic waveform. [Figure 12] This figure shows the response spectra of the first seismic waveform, the second seismic waveform, and the corrected second seismic waveform in the first verification result described above. [Figure 13] This figure shows the second verification result of the above-mentioned seismic motion observation system, specifically the first seismic waveform observed by the seismometer, the second seismic waveform observed by the smart device, and the corrected second seismic waveform. [Figure 14] This figure shows the response spectra of the first seismic waveform, the second seismic waveform, and the corrected second seismic waveform in the second verification result described above. [Figure 15] This figure shows the third verification result of the above-mentioned seismic motion observation system, and represents the first seismic waveform observed by the seismometer, the second seismic waveform observed by the smart device, and the corrected second seismic waveform. [Figure 16]This figure shows the response spectra of the first seismic waveform, the second seismic waveform, and the corrected second seismic waveform in the third verification result described above. [Figure 17] This figure shows examples of the first seismic waveform observed by a seismometer, the second seismic waveform which is the normal waveform when an earthquake is normally observed by a smart device, and the second seismic waveform which is the abnormal waveform when an earthquake is not normally observed, but the time range in which the amplitude remains constant is not large. [Figure 18] Figure 17 is a graph showing the ratio of the acceleration Fourier spectra of the normal waveform and the abnormal waveform, respectively, and the comparison function in the first modified example of the above embodiment. [Figure 19] This graph shows the approximate function obtained by approximating the comparison function in Figure 18 using an exponential function. [Figure 20] This graph shows the approximate function obtained by approximating the comparison function in Figure 18 using a multidimensional polynomial. [Figure 21] This is a flowchart of the seismic motion observation method in the first modified example described above. [Figure 22] This figure shows the first verification results of the seismic motion observation system in the first modified example described above, and represents the first seismic waveform observed by the seismometer, the second seismic waveform observed by the smart device, and the corrected second seismic waveform when an approximation function obtained by approximating the comparison function with an exponential function. [Figure 23] This figure shows the response spectra of the first seismic waveform, the second seismic waveform, and the corrected second seismic waveform in the first verification result described above. [Figure 24] This figure shows the second verification result of the seismic motion observation system in the first modified example described above, and represents the first seismic waveform observed by the seismometer, the second seismic waveform observed by the smart device, and the corrected second seismic waveform when an approximation function is used in which the comparison function is approximated by a multidimensional polynomial. [Figure 25] This figure shows the response spectra of the first seismic waveform, the second seismic waveform, and the corrected second seismic waveform in the second verification result described above. [Modes for carrying out the invention]

[0014] The present invention relates to an earthquake motion observation system and method, which use a seismometer fixed to a building or the ground and a smart device with a built-in acceleration sensor installed on the top surface of a desk or the like to estimate missing portions (non-confidence intervals) of acceleration data not obtained by the smart device from acceleration data observed by the seismometer. Embodiments of the present invention will be described in detail below with reference to the drawings. Figure 1 is an explanatory diagram of the seismic motion observation system in this embodiment. The seismic motion observation system 1 of this embodiment observes seismic motion using a seismometer 2 and a smart device 10. The seismometer 2 is fixed to a building or the ground. In this embodiment, the seismometer 2 observes during an earthquake and acquires acceleration data in the north-south and east-west directions, for example, as the first seismic waveform W1. In this embodiment, the seismometer 2 is a fixed seismometer installed by a public institution, and the acceleration data observed and made public by this fixed seismometer is acquired as the first seismic waveform W1. As a seismometer installed by a public institution, for example, a seismometer installed as part of the strong motion observation network (K-NET, KiK-net) of the National Research Institute for Earth Science and Disaster Resilience may be used. For example, in K-NET, strong-motion observation facilities are installed to uniformly cover the entire country at approximately 20km intervals. Therefore, when attempting to observe seismic motion at a specific location using K-NET, the seismic motion observed at the nearest strong-motion observation facility will be referenced. However, in this case, the distance between the location where seismic motion is to be observed and the nearest strong-motion observation facility may be 10km or more. Even if two locations are only a short distance apart, say about 10m, the seismic shaking can be observed in significantly different ways. For this reason, seismic waveforms observed at locations more than 10km away cannot be said to have sufficiently high accuracy as seismic waveforms representing the seismic motion at that location. In other words, even when using K-NET, for example, the spatial density is insufficient to obtain highly accurate seismic waveforms for any given location. Alternatively, seismometer 2 could be a seismometer installed in a building or on the ground by the operator of seismic motion observation system 1. However, even in such a case, installing multiple seismometers 2 at high density is not easy from a cost perspective. Considering the cost, it is difficult to increase the spatial density of seismometers 2 to the extent that high-precision seismic waveforms can be obtained at each location separated from seismometer 2.

[0015] The seismic motion observation system 1 uses smart devices 10 in addition to seismometers 2 to observe seismic motion in order to increase spatial density. Smart devices 10 are widely available, owned by many people, and are typically distributed at high density over a wide area. Therefore, if sufficiently accurate seismic motion is observed at each of these devices, it becomes possible to accurately observe seismic motion at any given location. Figure 2 is a block diagram of the smart devices in this seismic motion observation system. Figure 3 is an explanatory diagram of the smart devices. The smart device 10 includes an acceleration sensor 11, a storage unit 12, and a transmission unit 13. The acceleration sensor 11 acquires acceleration data for the smart device 10 in the X direction, which is the horizontal direction of the display surface 10a; the Y direction, which is the vertical direction of the display surface 10a; and the Z direction, which is perpendicular to the display surface 10a. The acceleration data acquired by the acceleration sensor 11 is stored in the storage unit 12 at predetermined short time intervals or continuously. If the smart device 10 does not have the function to store acceleration data in the storage unit 12 at predetermined time intervals or continuously, an application that implements this function may be created and added to the smart device 10. The transmitting unit 13 transmits the acceleration data stored in the storage unit 12 at predetermined intervals as a second seismic waveform W2 to the seismic motion estimation device 20, which will be described below, via the network 100. The network 100 is, for example, a public communication network that enables wireless or wired communication between the smart device 10 and the receiving unit 21 of the seismic motion estimation device 20.

[0016] (Overview of the seismic motion observation system) The seismic motion observation system 1 is equipped with a seismic motion estimation device 20. Figure 4 is a block diagram of the seismic motion estimation device in this seismic motion observation system. The seismic motion estimation device 20 includes a receiving unit 21, a storage unit 22, a second seismic waveform determination unit 23, a first main motion waveform estimation unit 24, a second main motion waveform estimation unit 25, and a waveform correction unit 26. The receiving unit 21 identifies a seismometer 2 located closest to the location where seismic motion is to be observed, and acquires the first seismic waveform W1 from the seismometer 2 via the network 100. Furthermore, the receiving unit 21 identifies the smart device 10 located closest to the location where seismic motion is to be observed, and acquires the second seismic waveform W2 from the smart device 10 via the network 100. The receiving unit 21 stores the received first seismic waveform W1 and second seismic waveform W2 in the storage unit 22.

[0017] The second seismic waveform determination unit 23 determines whether the received second seismic waveform W2 is usable or not. When an earthquake occurs, the smart device 10 may be being carried by the user or it may be placed on a desk. When the smart device 10 is being carried by the user, the acquired second seismic waveform W2 contains acceleration caused by transportation other than seismic motion, making it unsuitable for use in observing seismic motion. On the other hand, when the smart device 10 is placed on a desk, it is assumed that basically only seismic motion is reflected in the second seismic waveform W2. Therefore, the second seismic waveform determination unit 23 determines whether the smart device 10 is placed on a horizontal surface such as a desk. Specifically, the second seismic waveform determination unit 23 determines whether the acceleration in the Z direction of the smart device 10 matches the acceleration due to gravity. If the acceleration in the Z direction matches the acceleration due to gravity, it is determined that the smart device 10 is placed on a horizontal surface and that only seismic motion is reflected in the second seismic waveform W2. If the acceleration in the Z direction does not match the acceleration due to gravity, it is determined that the smart device 10 is not placed on a horizontal surface and that there is a possibility that some acceleration other than seismic motion is reflected in the second seismic waveform W2, and the subsequent processing is not performed.

[0018] If the second seismic waveform determination unit 23 is considered to be placed on a horizontal surface such as a desk, it then determines whether the second seismic waveform W2 is normal or not. When an earthquake occurs, the second seismic waveform W2 acquired by the acceleration sensor 11 of the smart device 10 may not necessarily accurately reflect the seismic motion. For example, if an earthquake occurs while smart device 10 is placed on a desk, and the earthquake is small, the smart device 10 will move along with the desk due to the frictional force between it and the desk, and will not move relative to the desk, thus allowing for accurate observation of the earthquake's motion. However, if the earthquake is large enough that a force exceeding the frictional force between smart device 10 and the desk acts on smart device 10, smart device 10 may move relative to the desk or even fall off the desk. In such cases, smart device 10 cannot accurately observe the earthquake's motion.

[0019] Figure 5 shows the second seismic waveform when the earthquake is observed normally by the smart device. Figure 6 shows the second seismic waveform when the earthquake is not observed normally by the smart device. In addition, Figure 1 shows that smart devices 10A and 10B acquired normal second seismic waveforms W2A and W2B, but smart device 10C acquired an abnormal second seismic waveform W2C. For example, during a strong earthquake, a force exceeding the frictional force between the smart device 10 and the desk may instantaneously act, preventing the built-in acceleration sensor 11 from accurately measuring acceleration. As a result, the amplitude of the second seismic waveform W2 may plateau, as shown as section R2 in Figure 6. Alternatively, even if the smart device 10 falls from, for example, a desk, the amplitude of the second seismic waveform W2 may plateau. Thus, when the smart device 10 fails to properly observe the earthquake, there is a tendency for a time range R2 to occur in which the amplitude of the second seismic waveform W2 remains constant. This time range R2 can be said to be a time range in which acceleration data for the earthquake shaking is missing. The second seismic waveform determination unit 23 determines whether or not there is a time range R2 in which the amplitude of the second seismic waveform W2 is constant. If there is no time range R2 in which the amplitude of the second seismic waveform W2 is constant, the second seismic waveform W2 is considered to be acceleration data for which time was observed normally, and is applied to the process and operation of analyzing the second seismic waveform W2 to grasp the seismic motion. If there is a time range R2 in which the amplitude of the second seismic waveform W2 is constant, the seismic motion estimation device 20 performs subsequent processing using the first main motion waveform estimation unit 24, the second main motion waveform estimation unit 25, and the waveform correction unit 26 to correct the second seismic waveform W2 based on the first seismic waveform W1 and estimate the seismic motion at the location where the smart device 10 is located.

[0020] In the second seismic waveform determination unit 23, if there is a time range R2 in which the amplitude of the second seismic waveform W2 is constant, and it is considered that the second seismic waveform W2 is partially missing, the first main motion waveform estimation unit 24 of the seismic motion estimation device 20 estimates the time when the main motion arrived. The simplest and most preferable method for this is to estimate the start time of the main seismic wave from the positional relationship between the epicenter and the measurement point using the Japan Meteorological Agency's travel time data. Other methods may also be used, such as detecting parts where the shape of the data changes abruptly by using the ratio of the STA (Short Time Average) and LTA (Long Time Average) of the seismic wave. In this way, the first main motion waveform estimation unit 24 estimates the first main motion waveform S1 (see Figure 1), which is the waveform portion corresponding to the main motion, from the first seismic waveform W1 by estimating the time when the main motion arrived.

[0021] Next, the second main seismic waveform estimation unit 25 adjusts the second seismic waveform W2 to match the first seismic waveform W1. First, the second main seismic waveform estimation unit 25 adjusts the timing of the second seismic waveform W2 to match that of the first seismic waveform W1. Furthermore, the second main seismic waveform estimation unit 25 adjusts the orientation of the second seismic waveform W2 to match that of the first seismic waveform W1. For example, if the smart device 10 is placed horizontally on a desk rotated 45° clockwise from north so that its Y direction faces northwest, the orientation of the second seismic waveform W2 is adjusted by performing a coordinate transformation to rotate the measured value 45° counterclockwise. Furthermore, the second main seismic waveform estimation unit 25 estimates the second main seismic waveform S2, which is the waveform component corresponding to the main seismic motion in the second seismic waveform W2, from among the second seismic waveform W2 that has been adjusted so that the time and direction match those of the first seismic waveform W1, and which was estimated by the first main seismic waveform estimation unit 24 based on the first seismic waveform W1, to be the second main seismic waveform S2.

[0022] The waveform correction unit 26, if there is a time range R2 in the second seismic waveform W2, that is, within the second main motion waveform S2, in which the amplitude is constant, sets the time range prior to the said time range R2 in the second main motion waveform S2 as the first range R1, and the said time range R2 as the second range R2. For example, in the second seismic waveform W2 in Figure 6, the first portion AM1 where the amplitude is constant is detected, and before this, the time T1 at which the acceleration value is last zero is calculated. The time range before time T1 of the second main seismic waveform S2 is set as the first range R1, and the time range after time T1 of the second main seismic waveform S2 is set as the second range R2. The first range R1, as defined in this way, is the time range in which the smart device 10 normally observed earthquakes and acceleration data was not missing. The second range R2, on the other hand, is the time range in which the smart device 10 normally observed earthquakes and acceleration data was missing. In other words, stronger shaking occurred in the second range R2 than in the first range R1. The waveform correction unit 26 applies the same time ranges as the first main dynamic waveform S1 to the first main dynamic waveform S1, based on the first range R1 and second range R2 calculated as described above, and sets the first range R1 and second range R2 of the first main dynamic waveform S1.

[0023] The calculation of the start time of the second range R2 may be performed by methods other than those described above. For example, if the smart device 10 is equipped with a gyroscope sensor, the result of that sensor could be used. When the smart device 10 is placed on a desk, and an earthquake occurs, causing a force greater than the maximum static friction force to act between the smart device 10 and the desk, the smart device 10 moves relative to the desk. At this time, the smart device 10 lifts slightly off the surface of the desk and becomes suspended. In such a case, the gyro sensor will observe a considerable amount of rotation around the Z axis, which is not observed in a stationary state. Therefore, for example, the start time of the second range R2 may be set to the time when the amount of rotation first exceeds a certain threshold after the seismic motion begins to be observed. In this case, for example, the end time of the second range R2 may be set to the last time when the amount of rotation falls below the above-mentioned certain threshold before the observation of the earthquake ends.

[0024] (Relationship between seismic waveforms observed by seismometers and smart devices) Here, we examine the correlation between the first major seismic waveform S1 and the second major seismic waveform S2. Figure 7 illustrates the relationship between the progression of the major seismic waves and the waveforms observed by seismometers and smart devices. Let's consider the case where an earthquake occurs at epicenter E and then sequentially propagates to the first rupture zone Dα and the second rupture zone Dβ. When an earthquake occurs at epicenter E, it first propagates to the first rupture zone Dα, and the shaking generated in the first rupture zone Dα is transmitted to seismometer 2 and smart device 10, generating shaking corresponding to the waveform data in the first range R1, as shown in Figure 1. Subsequently, the earthquake propagates to the second rupture zone Dβ, and the shaking generated in the second rupture zone Dβ is transmitted to seismometer 2 and smart device 10, generating stronger shaking than in the first range R1, corresponding to the waveform data in the second range R2, as shown in Figure 1. The spectral characteristics D1 in the first range R1 corresponding to the first rupture area Dα at location P1 where seismometer 2 is located, as shown in Figure 7. α (ω) can be expressed by the following equation (1).

number

number

[0025] Also, the spectral characteristic D1 in the second range R2 corresponding to the second failure region Dβ of the location P1 where the seismometer 2 is located β (ω) can be expressed by the following equation (3).

Equation

Equation

[0026] When the above equation (3) is transformed, the following equation (5) is obtained.

Equation

Equation

[0027] When these equations (5) and (6) are sequentially applied to the right side of equation (4), equation (4) can be transformed as follows.

Equation

[0028] Specifically, the waveform correction unit 26 shown in Figure 4 performs a Fourier transform on the waveforms of the first range R1 and the second range R2 of the first main dynamic waveform S1, respectively, and obtains the spectral characteristics D1 α (ω), D1 β Derive (ω). Next, the waveform correction unit 26 processes these derived spectral characteristics D1 α (ω), D1 β (ω) to function D1 β (ω) / D1 α Define (ω). This function D1 β (ω) / D1 α (ω) will actually be smoothed out as a smoothing function, as will be explained later, and this will be used as a function from now on. The waveform correction unit 26 further performs a Fourier transform on the waveform of the first range R1 of the second main dynamic waveform S2, and obtains the spectral characteristics D2 α (ω) is derived. Then, the waveform correction unit 26 processes this spectral characteristic D2 α (ω) is the function D1 derived (and further smoothed) as described above. β (ω) / D1 α Applying (ω), we obtain the spectral characteristics D2 in the second range R2. β Estimate (ω). Then, the waveform correction unit 26 adjusts the spectral characteristics D2β We perform an inverse Fourier transform on (ω) to derive the corrected waveform of the second seismic waveform W2 in the second range R2.

[0029] In this way, the waveform correction unit 26 corrects the waveform characteristics D1 of the first main dynamic waveform S1 in the first range R1. α Waveform characteristics D1 in the second range R2 for (ω) β Function D1 representing the relationship of (ω) β (ω) / D1 α Define (ω). Furthermore, the waveform correction unit 26 adjusts the waveform characteristics D2 of the second main dynamic waveform S2 in the first range R1. α (ω) and function D1 β (ω) / D1 α Based on (ω), the waveform characteristics D2 of the second main dynamic waveform S2 in the second range R2 β (ω) is derived, and the corrected waveform is derived based on the waveform characteristics. In this embodiment, the waveform characteristics are, more specifically, the acceleration Fourier spectrum. In other words, the waveform correction unit 26 corrects the acceleration Fourier spectrum D1 of the first main dynamic waveform S1 in the first range R1. α Acceleration Fourier spectrum D1 in the second range R2 for (ω) β The function D1 depends on the proportion of (ω) β (ω) / D1 α Define (ω), and function D1 β (ω) / D1 α As will be explained later, only the amplitude spectrum of (ω) is smoothed, and the acceleration Fourier spectrum D2 in the first range R1 of the second main dynamic waveform S2 is obtained. α Applying a smoothing function to (ω), we obtain the acceleration Fourier spectrum D2 of the second main dynamic waveform S2 in the second range R2. β We derive (ω), and then perform an inverse Fourier transform on it to derive the corrected waveform. The waveform correction unit 26 corrects the second seismic waveform W2 by replacing the entire waveform of the data-missing portion in the second range R2 of the second main motion waveform S2 with the corrected waveform obtained as described above.

[0030] Next, function D1β (ω) / D1 α Let's explain the smoothing of (ω). Figure 9 shows the smoothed function obtained by smoothing the function shown in Figure 8. Function D1 obtained as described above β (ω) / D1 α (ω) is not necessarily stable. For example, function D1 β (ω) / D1 α (ω) is the denominator D1 α There are frequency bands where the value becomes extremely large due to reasons such as the value of (ω) becoming small. In such cases, function D1 β (ω) / D1 α (ω) is the spectral characteristic D2 of the second main dynamic waveform S2 in the first range R1. α When applied to (ω), a corrected waveform is derived in which the component corresponding to that frequency becomes particularly large. To suppress such phenomena, the waveform correction unit 26 uses the function D1 β (ω) / D1 α Smooth out (ω).

[0031] In this embodiment, function D1 β (ω) / D1 α Of the Fourier spectra obtained as (ω), only the Fourier amplitude spectrum is smoothed. As already explained, the function D1 β (ω) / D1 α The spectral characteristic D2 generated by applying (ω) β (ω) is subjected to an inverse Fourier transform and used as a corrected waveform, i.e., a time history waveform. Therefore, in this embodiment, no processing is performed on the Fourier phase spectrum, and it is used as is. In this way, no smoothing is performed on the phase spectrum, so function D1 β (ω) / D1 αIn (ω), even if the amplitude spectrum is smoothed, the information indicating the phase change from the first range R1 to the second range R2 is retained as is for location P1 where the seismometer 2 is installed, and this information indicating the phase change at location P1 is applied directly to the second range R2 at location P2 where the smart device 10 is installed. The phases from the same source region to the same location are similar. Therefore, if location P1 where seismometer 2 is installed and location P2 where smart device 10 is installed are on the same bedrock, then the phases should be the same, at least from the source to the bedrock. Furthermore, even if the surface ground at location P1 where seismometer 2 is installed and location P2 where smart device 10 is installed are different, in equation (7), only the phase change from the first range R1 to the second range R2 at location P1 where seismometer 2 is installed is applied to location P2 where smart device 10 is installed (spectral characteristic D2). α (Multiply by (ω)) to obtain the spectral characteristics D2 of the second range R2. β Since (ω) is calculated, the phase information contained in the spectrum of the second range R2 is maintained from that of the first range R1 at location P2 where the smart device 10 is installed. Smoothing may be performed using smoothing functions such as the Hanning window or the Parzen window. In Figure 9, the function D1 shown in Figure 8 is used. β (ω) / D1 α (ω) is obtained by applying a Parzen window with a bandwidth of 0.1 Hz to the amplitude.

[0032] (Methods for observing seismic motion) Next, the seismic motion observation method using the above-described seismic motion observation system 1 will be explained using Figures 1 to 9 and Figure 10. Figure 10 is a flowchart of the seismic motion observation method in this embodiment. After an earthquake occurs, the receiving unit 21 identifies a seismometer 2 located closest to the location where the seismic motion is to be observed, and acquires the first seismic waveform W1 from that seismometer 2 via the network 100. Furthermore, the receiving unit 21 identifies the smart device 10 located closest to the location where seismic motion is to be observed, and acquires the second seismic waveform W2 from the smart device 10 via the network 100. The receiving unit 21 stores the received first seismic waveform W1 and second seismic waveform W2 in the storage unit 22 (step S1).

[0033] The second seismic waveform determination unit 23 determines whether the received second seismic waveform W2 is usable (step S3). If it is determined that it is not usable (No. in step S3), the process is terminated (step S5). In this case, for example, a smart device 10 located in the next closest location to the place where seismic motion is to be observed may be identified, the second seismic waveform W2 may be acquired from the smart device 10, and the processing from step S1 onwards may be performed again for it. If it is determined that the second seismic waveform W2 is usable (Yes in step S3), the second seismic waveform determination unit 23 determines whether the second seismic waveform W2 is normal or not (step S7). More specifically, the second seismic waveform determination unit 23 determines whether there is a time range R2 in which the amplitude of the second seismic waveform W2 is constant. If there is no time range R2 in which the amplitude of the second seismic waveform W2 is constant and it is determined that the second seismic waveform W2 is normal (Yes in step S7), the second seismic waveform W2 is treated as acceleration data for which time was observed normally, and is applied to processes and operations to analyze the second seismic waveform W2 and grasp the seismic motion (step S23).

[0034] In the second seismic waveform determination unit 23, if there is a time range R2 in which the amplitude of the second seismic waveform W2 is constant, and it is considered that the second seismic waveform W2 is partially missing (No. in step S7), the first main motion waveform estimation unit 24 of the seismic motion estimation device 20 estimates the first main motion waveform S1, which is the waveform portion corresponding to the main motion, from the first seismic waveform W1 by estimating the time when the main motion arrived (step S9). Next, the second main seismic waveform estimation unit 25 adjusts the second seismic waveform W2 so that its time and direction match those of the first seismic waveform W1. Then, the second main seismic waveform estimation unit 25 estimates the second main seismic waveform S2, which is the waveform component corresponding to the main seismic motion in the second seismic waveform W2, from among the second seismic waveform W2 which has been adjusted so that the time and direction match those of the first seismic waveform W1, based on the first seismic waveform W1 estimated by the first main seismic waveform estimation unit 24, for the time range after the time the main seismic motion arrived (step S11).

[0035] The waveform correction unit 26, if there is a time range R2 in the second seismic waveform W2, i.e., the second main motion waveform S2, in which the amplitude is constant, sets the time range in the second main motion waveform S2 prior to the said time range R2 as the first range R1, and the said time range R2 as the second range R2 (step S13). The waveform correction unit 26 then adjusts the spectral characteristics D1 of the first main dynamic waveform S1 in the first range R1. α Spectral characteristics D1 in the second range R2 for (ω) β Function D1 representing the relationship of (ω) β (ω) / D1 α Define (ω) (step S15). The waveform correction unit 26 uses the function D1 β (ω) / D1 α (ω) is smoothed to derive a smoothing function (step S17), and thereafter, processing is performed using this smoothing function. The waveform correction unit 26 analyzes the acceleration Fourier spectrum D2 of the second main dynamic waveform S2 in the first range R1. α Applying a smoothing function to (ω), we obtain the acceleration Fourier spectrum D2 of the second main dynamic waveform S2 in the second range R2. β (ω) is derived, and the corrected waveform is derived by performing an inverse Fourier transform on it (step S19). The waveform correction unit 26 corrects the second seismic waveform W2 by replacing the entire waveform of the data-missing portion in the second range R2 of the second main motion waveform S2 with the corrected waveform obtained as described above (step S21). The waveform corrected in this way is applied as the second seismic waveform W2 to the process and operation of analyzing acceleration data to understand the seismic motion (step S23).

[0036] (Effects and benefits of seismic motion observation systems and methods) Next, we will explain the effects of the above-mentioned seismic motion observation system and seismic motion observation method. The seismic motion observation system 1 of this embodiment is a seismic motion estimation system 1 that uses a smart device 10 with a built-in acceleration sensor 11 and a seismometer 2 fixed to a building or the ground, and includes a seismic motion estimation device 20 that estimates the seismic motion at the location P2 where the smart device 10 is located by correcting the second seismic waveform W2 observed by the acceleration sensor 11 based on the first seismic waveform W1 observed by the seismometer 2, and the seismic motion estimation device 20 selects the first wave portion of the first seismic waveform W1 which corresponds to the main motion A first main seismic waveform estimation unit 24 estimates the main seismic waveform S1, a second main seismic waveform estimation unit 25 adjusts the second seismic waveform W2 so that its time and direction match the first seismic waveform W1, and estimates the second main seismic waveform S2, which is the waveform portion corresponding to the main seismic motion, from the adjusted second seismic waveform W2, and if there is a time range in the second main seismic waveform S2 in which the amplitude is constant, the time range before that time range is set as the first range R1, and that time range is set as the second range R2, and the waveform characteristics D1 of the first main seismic waveform S1 in the first range R1 α Waveform characteristics D1 in the second range R2 for (ω) β Function D1 representing the relationship of (ω) β (ω) / D1 α Define (ω) and the waveform characteristics D2 in the first range R1 of the second main dynamic waveform S2. α (ω) and function D1 β (ω) / D1 α Based on (ω), the waveform characteristics D2 of the second main dynamic waveform S2 in the second range R2 β (ω) is derived, and the waveform characteristic D2 β The system includes a waveform correction unit 26 that derives a corrected waveform based on (ω) and corrects the second seismic waveform W2 by replacing the waveform in the second range R2 of the second main motion waveform S2 with the corrected waveform. According to the above configuration, the system comprises a smart device 10 with a built-in acceleration sensor 11 and a seismometer 2 fixed to a building or the ground. When an earthquake occurs, the seismometer 2 observes the earthquake as a first seismic waveform W1, and the acceleration sensor 11 built into the smart device 10 observes the earthquake as a second seismic waveform W2. In other words, since the seismic motion at each location where the smart device 10 is located is observed by the acceleration sensor 11 built into the smart device 10, it is possible to observe seismic motion over a wide area. Furthermore, since seismic motion at each location is observed using the smart device 10, there is no need to install many seismometers 2. Therefore, the seismic motion observation system 1 can be realized at low cost. However, when observing seismic motion using the smart device 10, it may not be possible to observe the seismic motion accurately. For example, if the earthquake is large enough that a force exceeding the frictional force between the smart device 10 and the desk acts on the smart device 10, the smart device 10 may move relative to the desk or fall from the desk. In such cases, the second seismic waveform W2 observed by the acceleration sensor 11 built into the smart device 10 while the smart device 10 is moving relative to the desk or falling does not represent a normal observation of the earthquake. In such cases, the portion of the second seismic waveform W2 that does not represent a normal observation of the earthquake often tends to have a constant amplitude. Here, the seismic motion estimation device 20 estimates the seismic motion at location P2 where the smart device 10 is located by correcting the second seismic waveform W2 observed by the acceleration sensor 11 based on the first seismic waveform W1 observed by the seismometer 2. More specifically, from the first seismic waveform W1, a first main motion waveform S1, which is a waveform part corresponding to the main motion, is estimated. Further, after adjusting the second seismic waveform W2 so that the time and azimuth match those of the first seismic waveform W1, from the adjusted second seismic waveform W2, a second main motion waveform S2, which is a waveform part corresponding to the main motion, is estimated. If there is a time range within the second main motion waveform S2 where the amplitude is constant, as described above, it is considered to be a part where strong vibrations occurred and the earthquake was not observed normally. This time range where strong vibrations are considered to have occurred is set as the second range R2, and the time range before the second range R2 is set as the first range R1 where the earthquake was normally observed. If the vibration in the first range R1 is the vibration of an earthquake that occurred in the first rupture area Dα of the seismic source, and the vibration in the second range R2 is the vibration of an earthquake that occurred in the second rupture area Dβ of the seismic source, which is different from the first rupture area Dα, then if the distance between the location P1 where the seismometer 2 is installed and the location P2 where the smart device 10 is installed is sufficiently smaller than the distance between the first rupture area Dα and the second rupture area Dβ, the propagation characteristics of the vibration of the earthquake that occurred in the first rupture area Dα are considered to be almost the same at the above two locations, and moreover, the propagation characteristics of the vibration of the earthquake that occurred in the second rupture area Dβ are also considered to be almost the same at the above two locations. Therefore, the waveform characteristic D1 α (ω) in the first range R1 of the first main motion waveform S1 and the waveform characteristic D1 β (ω) in the second range R2 are represented by a function D1 β (ω) / D1 α (ω) is defined, then the waveform characteristic D2 α (ω) in the first range R1 of the second main motion waveform S2 is considered to have the same relationship as that of the first main motion waveform S1. Therefore, the waveform characteristic D2 α (ω) in the first range R1 of the second main motion waveform S2 and the function D1 β (ω) / D1 α (ω) are based on this, and the waveform characteristic D2 β (ω) in the second range R2 of the second main motion waveform S2 can be derived. The waveform characteristic D2 βBased on (ω), a corrected waveform is derived, and by replacing the waveform in the second range R2 of the second main motion waveform S2 with the corrected waveform, the second seismic waveform W2 can be corrected. In this way, even if there are parts in the second seismic waveform W2 that do not properly observe the earthquake, these can be corrected, allowing for accurate observation of the seismic motion at location P2 where the smart device 10 is installed. Therefore, we can provide an earthquake motion observation system 1 that is feasible at low cost and can accurately observe earthquake motion over a wide area.

[0037] In particular, in this embodiment, since the seismometer 2 is a fixed seismometer installed by a public institution or the like, there is no need to specifically install the seismometer 2 when setting up the seismic motion observation system 1. This makes it possible to further reduce the installation cost of the seismic motion observation system 1. Even in this configuration, many smart devices 10 are located between the seismometers 2, and each of these smart devices 10 can observe seismic motion. Therefore, a high-density observation network can be constructed that allows for the observation of seismic motion at many observation points.

[0038] When correcting the waveform of the second range R2 of the second main dynamic waveform S2, for example, as shown by the dashed line V in Figure 6, it is also possible to generate a corrected waveform by adjusting only the portion of the second range R2 in which the amplitude is constant, rather than the entire second range R2, by extending the rising and falling lines of the waveform that connect to both ends of the portion in which the amplitude is constant. However, in cases such as when a smart device 10 falls, the amplitude remains constant over a long period of time. In such cases, if only the portion where the amplitude is constant is adjusted as described above, the adjusted waveform is highly likely to deviate significantly from the original seismic wave waveform. In contrast, in this embodiment, a corrected waveform is derived in the second range R2 of the second main motion waveform S2, and the waveform in the second range R2 of the second main motion waveform S2 is replaced with the corrected waveform. This makes it possible to generate a corrected waveform with properties similar to the original seismic motion waveform.

[0039] Furthermore, the waveform characteristics are the acceleration Fourier spectrum, and the waveform correction unit 26 corrects the acceleration Fourier spectrum D1 of the first main dynamic waveform S1 in the first range R1. α Acceleration Fourier spectrum D1 in the second range R2 for (ω) β The function D1 depends on the proportion of (ω) β (ω) / D1 α Define (ω), and function D1 β (ω) / D1 α For (ω), only the amplitude spectrum is smoothed, and the acceleration Fourier spectrum D2 in the first range R1 of the second main dynamic waveform S2 is obtained. α Applying a smoothing function to (ω), we obtain the acceleration Fourier spectrum D2 of the second main dynamic waveform S2 in the second range R2. β We derive (ω), and then perform an inverse Fourier transform on it to derive the corrected waveform. With the configuration described above, the seismic motion observation system 1 can be properly implemented.

[0040] Furthermore, the seismic motion observation method of this embodiment is a seismic motion observation method that observes seismic motion using a smart device 10 with a built-in acceleration sensor 11 and a seismometer 2 fixed to a building or the ground, and estimates the first main seismic waveform S1, which is the waveform portion corresponding to the main motion, from the first seismic waveform W1 observed by the seismometer 2, adjusts the second seismic waveform W2 observed by the acceleration sensor 11 so that the time and direction match the first seismic waveform W1, estimates the second main seismic waveform S2, which is the waveform portion corresponding to the main motion, from the adjusted second seismic waveform W2, if there is a time range in the second main seismic waveform S2 in which the amplitude is constant, sets the time range before that time range as the first range R1 and the said time range as the second range R2, and determines the waveform characteristics D1 of the first main seismic waveform S1 in the first range R1 αWaveform characteristics D1 in the second range R2 for (ω) β Function D1 representing the relationship of (ω) β (ω) / D1 α Define (ω) and the waveform characteristics D2 in the first range R1 of the second main dynamic waveform S2. α (ω) and function D1 β (ω) / D1 α Based on (ω), the waveform characteristics D2 of the second main dynamic waveform S2 in the second range R2 β (ω) is derived, and the waveform characteristic D2 β Based on (ω), a corrected waveform is derived, and the waveform in the second range R2 of the second main motion waveform S2 is replaced with the corrected waveform to correct the second seismic waveform W2 and estimate the seismic motion at the location of the smart device 10. With the above configuration, similar to the case of the above-described seismic motion observation system 1, it is possible to provide a seismic motion observation method that can be implemented at low cost and accurately observe seismic motion over a wide area.

[0041] (Example of an embodiment) Next, we will describe an example of the seismic motion observation system 1 described as an embodiment above. First, as the first verification result, we will show the results of an experiment using records from two locations obtained by K-NET and KiK-net for the Tohoku-Pacific Ocean Earthquake that occurred at 2:46 PM on March 11, 2011. In this first verification result, as described in the embodiment above, the bandwidth in the smoothing process is set to 0.1 Hz. Figure 11 shows the first verification results of the above-mentioned seismic motion observation system, and is a diagram showing the first seismic waveform observed by the seismometer, the second seismic waveform observed by the smart device, and the corrected second seismic waveform. Figure 12 shows the response spectra of the first seismic waveform, the second seismic waveform, and the corrected second seismic waveform in the above-mentioned first verification results. Assume that seismometer 2 obtained the first seismic waveform W1 shown at the top of Figure 11, and that at a different location, smart device 10 obtained the second seismic waveform W2 shown in the middle of Figure 11. In this second seismic waveform W2, the data for the first range R1 is normal, but the data for the second range R2 is missing and not normal. The waveform W2' shown below in Figure 11 is the corrected waveform of the second seismic waveform W2 obtained by the seismic motion observation system 1 of the above embodiment. In Figure 12, the spectra corresponding to each of these are drawn. Waveform W2' is approximately equal to the envelope characteristics of waveform W2 and is a waveform with sufficient accuracy from an engineering perspective.

[0042] Next, I will explain the results of the second verification. The second verification is basically the same as the first verification described above, but it differs in that the function smoothing process was not performed. Figure 13 shows the results of the second verification, illustrating the first seismic waveform observed by the seismometer, the second seismic waveform observed by the smart device, and the corrected second seismic waveform. Figure 14 shows the response spectra of the first seismic waveform, the second seismic waveform, and the corrected second seismic waveform in the second verification results. As can be seen from waveform W2' shown below Figure 13, the estimated waveform has an unnatural shape. Furthermore, as shown in Figure 14, the response spectrum is an overestimation of the short-period portion.

[0043] Next, I will explain the results of the third verification. The results of the third verification are basically the same as those of the first verification described above, but the difference is that the bandwidth in the function smoothing process is set to 1.0 Hz. Figure 15 shows the results of the third verification, illustrating the first seismic waveform observed by the seismometer, the second seismic waveform observed by the smart device, and the corrected second seismic waveform. Figure 16 shows the response spectra of the first seismic waveform, the second seismic waveform, and the corrected second seismic waveform in the third verification results. In this third verification result, as with the first verification result, it can be seen that waveforms with sufficient accuracy have been obtained.

[0044] (Modified example of Embodiment 1) Next, a first modified example of the above embodiment will be described. In the above embodiment, the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2 deviates significantly from the normal state and is considered unsuitable as a reference when deriving the corrected waveform. Therefore, only the waveform in the first range R1 is used to derive the corrected waveform, and the waveform in the second range R2 is not used. In this modified example, it is assumed that, under certain conditions, the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2 can be used as a reference, and the aim is to further improve the accuracy of the corrected waveform by using this to derive the corrected waveform.

[0045] The second seismic waveform W2 observed by the acceleration sensor 11 built into the smart device 10 during an earthquake does not represent a normal observation of the earthquake. In cases where there is a gap in the data, such as a time range in which the amplitude remains constant, the value of the constant amplitude differs depending on the state of the smart device 10 during the earthquake. For example, when an earthquake occurs with the smart device 10 placed on a desk, the amplitude value remains constant in both cases: when the seismic force exceeds the maximum static friction force between the smart device 10 and the desk, causing the smart device 10 to slide relative to the desk; and when the seismic force is excessive and the smart device 10 falls off the edge of the desk. However, the amplitude value tends to be larger during the fall than during the sliding motion in the former case. In the latter case, the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2 is expected to be significantly different from the waveform acquired under normal conditions, making it difficult to use as a reference when deriving the corrected waveform. However, in the former case, the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2 is likely to have characteristics similar to the waveform acquired under normal conditions, and using it as a reference when deriving the corrected waveform may allow for the deriving of a more accurate corrected waveform. For this reason, in the former case, that is, when the amplitude of the second range R2 of the second main dynamic waveform S2 is below a predetermined amplitude threshold, the corrected waveform is derived using the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2.

[0046] Figure 17 shows examples of the first seismic waveform observed by a seismometer, the second seismic waveform which is the normal waveform when the earthquake is normally observed by a smart device, and the second seismic waveform which is the abnormal waveform when the earthquake is not normally observed, but the time range in which the amplitude remains constant is not large. As shown in Figure 17, when an earthquake measured as the first seismic waveform W1 by seismometer 2 is normally observed by smart device 10, the waveform characteristics of the waveform DD in the second range R2 portion of the normal waveform W2D, which is the second seismic waveform, are defined as Dc2. β Let (ω) be the value. Furthermore, in the case where the same earthquake as described above was not properly observed by the smart device 10, but the time range in which the amplitude remains constant is not large, the waveform characteristics of the waveform DE in the second range R2 of the anomalous waveform W2E, which is the second seismic waveform, i.e., the acceleration Fourier spectral characteristics are Dm2. β Let's call it (ω). In this case, the ratio F of these spectral characteristics can be expressed as follows (8).

number

[0047] In the above embodiment, the spectral characteristics D2 in the second range R2, which is the strong portion of the main motion in the second seismic waveform W2, are considered to be missing data. β (ω) is estimated by equation (7). That is, the spectral characteristic D2 of equation (7) β (ω) represents the spectral characteristics Dc2 when an earthquake is observed normally. β Since it is equal to (ω), the spectral characteristic D2 β (ω) spectral characteristics Dc2 β Substituting (ω), we get equation (9) below.

number

number

[0048] In equation (10) above, D2 α (ω){D1 β (ω) / D1 α The (ω)} part represents the spectral characteristics D2 in the first range R1, which is the weak part of the main motion where no data is missing. α (ω) and the spectral characteristics D1 of the first seismic waveform W1 acquired by seismometer 2 in the first range R1. α (ω) is the spectral characteristic D1 in the second range R2. β Function D1 to convert to (ω) β (ω) / D1 α This is the spectral characteristics of the normal assumed waveform, which is the waveform that is assumed to have been obtained normally in the second range R2, which is the strong part of the main motion, in the second seismic waveform W2, estimated by multiplying by (ω).Therefore, this is the normal assumed waveform characteristic. β The above F' obtained by dividing by (ω) can be considered a comparison function F' between the acquired waveform characteristics and the assumed normal waveform characteristics.

[0049] Figure 18 is a graph showing the ratio of the acceleration Fourier spectra of the normal waveform and the abnormal waveform in Figure 17, and the comparison function in the first modified example of the above embodiment. In Figure 18, the ratio of the acceleration Fourier spectra of the waveform DD in the second range R2 portion of the normal waveform W2D in Figure 17 and the waveform DE in the second range R2 portion of the abnormal waveform W2E, i.e., the ratio F in equation (8) above, is denoted with the sign F. Similarly, the comparison function F' in equation (10) above is denoted with the sign F'.

[0050] The following characteristics can be observed from Figure 18. First, the ratio F is constant at low frequencies, slightly increases around 1-10 Hz, and decreases at even higher frequencies. When acceleration data is missing and the amplitude of the seismic wave becomes constant, the missing portion takes on a shape closer to a square wave rather than a sine wave, as shown in Figure 6. The Fourier spectrum of a square wave is formed by adding a constant proportion of high frequency to a sine wave. In other words, the acquired waveform characteristic Dm2 is affected by the amount of high frequency added to make the acceleration data take on a shape closer to a square wave. β The value of (ω) increases at high frequencies, and the ratio F is obtained from the waveform characteristic Dm2 β It is thought that the value of the ratio F at high frequencies decreases because it is calculated by dividing by (ω). Furthermore, it can be seen that the ratio F and the comparison function F' have the same shape overall. Furthermore, as shown in Figure 17, the normal waveform W2D and the abnormal waveform W2E have similar waveform shapes overall, and even with loss, the waveform shape of the abnormal waveform W2E is maintained to be close to that of the normal waveform W2D. Therefore, the spectral characteristics Dc2 of waveforms DD and DE in the second range R2 portion are... β (ω), Dm2 β (ω) is also thought to have a roughly similar shape. Therefore, the shape of ratio F is also thought to be a relatively smooth shape with few irregularities, as shown in Figure 18. In contrast, the comparison function F' has a more irregular shape compared to the ratio F, partly because, as can be seen from equation (10), it uses the first seismic waveform W1, which is a seismic waveform from a different location than the second seismic waveform W2, when calculating it.

[0051] If the second seismic waveform W2 is acquired by smart device 10 and it is found to be missing, the waveform characteristic Dc2 described above is the waveform characteristic when it is observed normally by smart device 10. β Naturally, (ω) cannot be obtained. In other words, the ratio F calculated using equation (8) above cannot actually be obtained either. However, as mentioned above, the comparison function F' has a more irregular shape compared to the ratio F, so even if the corrected waveform is derived using this comparison function F', the accuracy may be lower. Therefore, in this modified example, using the characteristics of the ratio F and the comparison function F' described above, we calculate an approximate function Ffunc by approximating the comparison function F' from the comparison function F' in such a way that the shape is as close to the ratio F as possible and has small irregularities and is smooth, and then use this approximate function Ffunc. In this modified example, we define the approximate function Ffunc by approximating the comparison function F' with an exponential function or a multidimensional polynomial, as shown in equations (11) and (12) below.

number

number

[0052] Figure 19 is a graph showing the approximate function obtained by approximating the comparison function in Figure 18 using the exponential function equation (11). In Figure 19, the function is shown when a=2.0094, b=-0.0508, c=1.0930, and d=0.7772. Figure 20 is a graph showing the approximate function obtained by approximating the comparison function in Figure 18 with a multidimensional polynomial (12). In Figure 20, the function is shown when the degree n is 20. In all of these cases, the approximation function Ffunc closely approximates the shape of the ratio F, reducing the variability in the values ​​observed in the comparison function F', and thus mitigating the negative effects in calculations using it.

[0053] The approximate function Ffunc obtained in this way is used to acquire the waveform characteristic Dm2 as shown in equation (13). β By multiplying by (ω), the spectral characteristics D2 in the second range R2 of the second seismic waveform W2 are obtained. β (ω) can be estimated.

number

[0054] Based on the above considerations, in this modified example, the waveform correction unit 26 first corrects the acceleration Fourier spectrum D1 of the first main dynamic waveform S1 in the first range R1, similar to the above embodiment. α Acceleration Fourier spectrum D1 in the second range R2 for (ω) β Depending on the ratio of (ω), the function D1 β (ω) / D1 α Define (ω). Furthermore, if the amplitude of the second range R2 of the second main dynamic waveform S2 is less than or equal to the amplitude threshold, the waveform correction unit 26 first calculates the spectral characteristics D2 of the first range R1 of the second main dynamic waveform S2 using the above equation (10). α (ω) and function D1 β (ω) / D1 α Multiply by (ω) to obtain the waveform characteristics of the second main dynamic waveform S2 in the second range R2, which is the waveform characteristics that would be expected if the second main dynamic waveform S2 were acquired normally in the second range R2, D2. α (ω){D1 β (ω) / D1 α This is derived as (ω)}, and this result is the acquired waveform characteristic Dm2, which is the waveform characteristic of the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2. β Divide by (ω) to obtain the waveform characteristic Dm2 β (ω) and the normal assumed waveform characteristic D2 α (ω){D1 β (ω) / D1 α Calculate the comparison function F' with (ω). Then, the waveform correction unit 26 approximates the comparison function F' with an exponential function or a multidimensional polynomial using equations (11) and (12) above, and calculates the approximate function Ffunc. Furthermore, the waveform correction unit 26 calculates the approximate function Ffunc and the acquired waveform characteristic Dm2 according to equation (13) above. β Multiply by (ω) to obtain the spectral characteristics D2 of the second seismic waveform W2 in the second range R2. β We estimate (ω), perform an inverse Fourier transform on it, and derive the corrected waveform. Finally, the waveform correction unit 26 corrects the second seismic waveform W2 by replacing the waveform in the second range R2 of the second main motion waveform S2 with the corrected waveform.

[0055] (Methods for observing seismic motion) Next, the seismic motion observation method using the seismic motion observation system of this modified example will be explained using Figure 21. Figure 21 is a flowchart of the seismic motion observation method in this modified example. In the seismic motion observation method of this modified example, steps S31, S33, S35, and S37 are added to the flowchart shown in Figure 10. More specifically, in this modified example, it is determined whether the amplitude of the second range R2 of the second main motion waveform S2 is below a predetermined amplitude threshold, and if it is below the amplitude threshold, steps S33, S35, and S37 are performed instead of steps S17 and S19 explained in the above embodiment using Figure 10, which is different from the above embodiment. Therefore, only steps S31, S33, S35, and S37 will be explained in detail here.

[0056] In step S15, the waveform correction unit 26 corrects the spectral characteristics D1 of the first main dynamic waveform S1 in the first range R1. α Spectral characteristics D1 in the second range R2 for (ω) β Function D1 representing the relationship of (ω) β (ω) / D1 α Define (ω). Subsequently, the waveform correction unit 26 determines whether the amplitude of the second range R2 of the second main dynamic waveform S2 is less than or equal to the amplitude threshold (step S31). If the amplitude of the second range R2 of the second main dynamic waveform S2 is not below the amplitude threshold (No. in step S31), the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2 is significantly different from the waveform acquired under normal conditions and is not useful as a reference when deriving the corrected waveform. Therefore, the process proceeds to step S17 and the processing of the above embodiment continues. If the amplitude of the second range R2 of the second main dynamic waveform S2 is less than or equal to the amplitude threshold (Yes in step S31), then the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2 is likely to have characteristics similar to the waveform acquired under normal conditions. In this case, referring to it when deriving the corrected waveform may allow for the deriving of a more accurate corrected waveform, so the process proceeds to step S33 related to this modified example.

[0057] If the amplitude of the second range R2 of the second main dynamic waveform S2 is less than or equal to the amplitude threshold, the waveform correction unit 26 first calculates the spectral characteristics D2 of the first range R1 of the second main dynamic waveform S2 using the above equation (10). α (ω) and function D1 β (ω) / D1 α Multiply by (ω) to obtain the waveform characteristics of the second main dynamic waveform S2 in the second range R2, which is the waveform characteristics that would be expected if the second main dynamic waveform S2 were acquired normally in the second range R2, D2. α (ω){D1 β (ω) / D1 α This is derived as (ω)}, and this result is the acquired waveform characteristic Dm2, which is the waveform characteristic of the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2. β Divide by (ω) to obtain the waveform characteristic Dm2 β (ω) and the normal assumed waveform characteristic D2 α (ω){D1 β (ω) / D1 α Calculate the comparison function F' with (ω) (Step S33). Then, the waveform correction unit 26 approximates the comparison function F' with an exponential function or a multidimensional polynomial using equations (11) and (12) above, and calculates the approximate function Ffunc (step S35). Furthermore, the waveform correction unit 26 calculates the approximate function Ffunc and the acquired waveform characteristic Dm2 according to equation (13) above. β Multiply by (ω) to obtain the spectral characteristics D2 of the second seismic waveform W2 in the second range R2. β (ω) is estimated, and the corrected waveform is derived by performing an inverse Fourier transform on it (step S37). Subsequently, the process transitions to step S21, where the waveform correction unit 26 corrects the second seismic waveform W2 by replacing the waveform in the second range R2 of the second main motion waveform S2 with the corrected waveform.

[0058] In the seismic motion observation system 1 as shown in this modified example, the waveform correction unit 26 corrects the waveform characteristics D2 in the first range R1 of the second main motion waveform S2 if the amplitude of the second range R2 of the second main motion waveform S2 is less than or equal to the amplitude threshold. α (ω) is function D1 β (ω) / D1 α Applying this to (ω), the waveform characteristics of the second main dynamic waveform S2 in the second range R2 are given by the normal assumed waveform characteristics D2, which are the waveform characteristics expected when the second main dynamic waveform S2 is acquired normally in the second range R2. α (ω){D1 β (ω) / D1 α Derived as (ω), the acquired waveform characteristic Dm2 is the waveform characteristic of the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2. β (ω) and the normal assumed waveform characteristic D2 α (ω){D1 β (ω) / D1 α Calculate the comparison function F' with (ω) and obtain the waveform characteristic Dm2 β Based on (ω) and the comparison function F', a corrected waveform is derived, and the second seismic waveform W2 is corrected by replacing the waveform in the second range R2 of the second main motion waveform S2 with the corrected waveform. The second seismic waveform W2 observed by the acceleration sensor 11 built into the smart device 10 during an earthquake does not represent a normal observation of the earthquake, and in cases where there is a time range in which the amplitude remains constant, the value of that constant amplitude differs depending on the state of the smart device 10 during the earthquake. For example, when an earthquake occurs with the smart device 10 placed on a desk, the amplitude value remains constant in both cases: when the seismic force exceeds the maximum static friction force between the smart device 10 and the desk, causing the smart device 10 to slide on the desk and move relative to the desk; and when the seismic force is excessive and the smart device 10 falls off the edge of the desk. However, the amplitude value tends to be larger during the latter case (falling) than during the former case (sliding). In the latter case, the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2 is expected to be significantly different from the waveform acquired under normal conditions, making it difficult to use as a reference when deriving the corrected waveform. However, in the former case, the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2 is likely to have characteristics similar to the waveform acquired under normal conditions, and using it as a reference when deriving the corrected waveform may allow for the deriving of a more accurate corrected waveform. For this reason, in the former case, that is, when the amplitude of the second range R2 of the second main dynamic waveform S2 is below a predetermined amplitude threshold, the corrected waveform is derived using the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2. As already explained, the waveform characteristic D2 in the first range R1 for the second main dynamic waveform S2 α Waveform characteristics D2 in the second range R2 for (ω) β The relationship of (ω) is the waveform characteristic D1 in the first range R1 of the first main dynamic waveform S1. α Waveform characteristics D1 in the second range R2 for (ω) β Since this is similar to the association of (ω), the function D1 represents this association. β (ω) / D1 α (ω) represents the waveform characteristics D2 of the second main dynamic waveform S2 in the first range R1. αBy applying (ω), the waveform characteristics of the second main dynamic waveform S2 in the second range R2 are derived. The waveform characteristics derived in this way are the normal assumed waveform characteristics D2, which are the waveform characteristics that would be expected if the second main dynamic waveform S2 were acquired normally in the second range R2. α (ω){D1 β (ω) / D1 α It could also be said as (ω)}. Here, as described above, if the amplitude of the second range R2 of the second main dynamic waveform S2 is less than or equal to the amplitude threshold, the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2 is highly likely to have characteristics similar to the waveform expected when acquired normally. Therefore, the acquired waveform characteristic Dm2 is the characteristic of the actually acquired waveform. β (ω) and the normal assumed waveform characteristic D2 α (ω){D1 β (ω) / D1 α Calculate the comparison function F' with (ω), and compare this comparison function F' with the acquired waveform characteristic Dm2. β Based on (ω), the acquired waveform characteristic Dm2 β (ω) represents the normal assumed waveform characteristic D2 α (ω){D1 β (ω) / D1 α Adjust the acquired waveform characteristic Dm2 to a shape close to (ω)}. β A corrected waveform that reflects (ω) can be derived. In this way, in the configuration described above, when the waveform actually acquired by the acceleration sensor 11 in the second range R2 of the second main dynamic waveform S2 is likely to have characteristics similar to the waveform expected when acquired normally, these characteristics can be appropriately reflected in the corrected waveform to further improve accuracy.

[0059] Furthermore, the waveform characteristics are the acceleration Fourier spectrum, and the waveform correction unit 26 calculates the acceleration Fourier spectrum D1 of the first main dynamic waveform S1 in the first range R1. α Acceleration Fourier spectrum D1 in the second range R2 for (ω) β The function D1 depends on the proportion of (ω) β (ω) / D1 αDefine (ω) and the acceleration Fourier spectrum D2 in the first range R1 of the second main dynamic waveform S2. α (ω) and function D1 β (ω) / D1 α The result of multiplying by (ω) is taken as the normal expected waveform characteristic, and this is the acquired waveform characteristic Dm2, which is the acceleration Fourier spectrum. β Divide by (ω) to calculate the comparison function F', approximate the comparison function F' with an exponential function or a multidimensional polynomial to calculate the approximate function Ffunc, and compare the approximate function Ffunc with the acquired waveform characteristic Dm2 β The corrected waveform is derived by multiplying by (ω) and then performing an inverse Fourier transform on the result. With the above configuration, the comparison function F' is made into an approximate function Ffunc with a more appropriate shape, and the approximate function Ffunc and the acquired waveform characteristic Dm2 β Since the corrected waveform is derived from (ω), the accuracy of the corrected waveform is further improved.

[0060] (Example of the first variation) Next, we will explain an example of the seismic motion observation system 1 described as the first modified example above. Figure 22 shows the first verification results of the seismic motion observation system in the first modified example described above, and is a diagram showing the first seismic waveform W1 observed by the seismometer, the second seismic waveform W2 observed by the smart device, and the corrected second seismic waveform W2' when an approximation function obtained by approximating the comparison function with an exponential function. Figure 23 shows the response spectra of the first seismic waveform W1, the second seismic waveform W2, and the corrected second seismic waveform W2' in the first verification results. Figure 24 shows the second verification results of the seismic motion observation system in the first modified example described above, and is a diagram showing the first seismic waveform W1 observed by the seismometer, the second seismic waveform W2 observed by the smart device, and the corrected second seismic waveform W2' when an approximation function is used in which the comparison function is approximated by a multidimensional polynomial. Figure 24 shows the response spectra of the first seismic waveform W1, the second seismic waveform W2, and the corrected second seismic waveform W2' in the second verification results. In both of these cases, it can be seen that response spectra are obtained with higher accuracy than in the examples described in Figures 14 and 16 with respect to the above embodiments.

[0061] It should be noted that the seismic motion observation system and seismic motion observation method of the present invention are not limited to the embodiments described above with reference to the drawings, and various other modifications are conceivable within their technical scope. For example, in the above embodiment, the calculated function D1 β (ω) / D1 α (ω) was used after smoothing, but the function D1 has sufficient precision. β (ω) / D1 α If (ω) is obtained, the smoothing process may be omitted. Furthermore, when smoothing is performed, the method is not limited to that described in the above embodiment. In addition to the above, it is possible to select or replace the configurations listed in each of the above embodiments and modifications, or to change them to other configurations as appropriate, as long as it does not deviate from the spirit of the present invention. [Explanation of symbols]

[0062] 1. Earthquake motion observation system 24. First main motion waveform estimation unit 2 Seismograph 25 2nd principal motion waveform estimation section 10 Smart device 26 Waveform correction unit 11 Accelerometer W1 First seismic waveform 12 Memory Unit W2 Second seismic waveform 13 Transmitter S1 1st main dynamic waveform 20. Earthquake motion estimation device S2 Second main motion waveform 21 Receiving unit R1 First range 22 Memory Unit R2 Second Range 23 Second seismic waveform determination section

Claims

1. A seismic motion observation system using a smart device with a built-in acceleration sensor and a seismometer fixed to a building or the ground, The device includes a seismic motion estimation device that estimates the seismic motion at the location of the smart device by correcting the second seismic waveform observed by the acceleration sensor based on the first seismic waveform observed by the seismometer, The aforementioned seismic motion estimation device is A first main seismic waveform estimation unit estimates a first main seismic waveform, which is the waveform portion corresponding to the main motion, from among the first seismic waveforms, A second main seismic waveform estimation unit adjusts the second seismic waveform so that its time and direction match those of the first seismic waveform, and estimates the second main seismic waveform, which is the waveform portion corresponding to the main motion, from the adjusted second seismic waveform. A waveform correction unit corrects the second seismic waveform by: if there is a time range within the second main motion waveform in which the amplitude is constant, setting the time range prior to that time range as the first range and the said time range as the second range; defining a function that represents the relationship between the waveform characteristics in the second range and the waveform characteristics in the first range of the first main motion waveform; deriving the waveform characteristics in the second range of the second main motion waveform based on the waveform characteristics in the first range of the second main motion waveform and the function; deriving a corrected waveform based on these waveform characteristics; and replacing the waveform in the second range of the second main motion waveform with the corrected waveform. An earthquake motion observation system characterized by being equipped with the following features.

2. The waveform characteristics are the acceleration Fourier spectrum, The earthquake motion observation system according to claim 1, characterized in that the waveform correction unit defines the function based on the ratio of the acceleration Fourier spectrum in the second range to the acceleration Fourier spectrum in the first range of the first main motion waveform, smooths only the amplitude spectrum of the function, applies the smoothed smoothing function to the acceleration Fourier spectrum in the first range of the second main motion waveform to derive the acceleration Fourier spectrum in the second range of the second main motion waveform, and performs an inverse Fourier transform on this to derive the corrected waveform.

3. The waveform correction unit, when the amplitude of the second range of the second main dynamic waveform is less than or equal to the amplitude threshold, The waveform characteristics in the first range of the second main dynamic waveform are applied to the function to derive the waveform characteristics in the second range of the second main dynamic waveform as the normal assumed waveform characteristics, which are the waveform characteristics expected when the second range of the second main dynamic waveform is acquired normally, and a comparison function is calculated between the acquired waveform characteristics, which are the waveform characteristics of the waveform actually acquired by the acceleration sensor in the second range of the second main dynamic waveform, and the normal assumed waveform characteristics. Based on the acquired waveform characteristics and the comparison function, the corrected waveform is derived. The second seismic waveform is corrected by replacing the waveform in the second range of the second main motion waveform with the corrected waveform. The seismic motion observation system according to feature 1.

4. The waveform characteristics are the acceleration Fourier spectrum, The waveform correction unit, The function is defined by the ratio of the acceleration Fourier spectrum in the second range to the acceleration Fourier spectrum in the first range of the first main dynamic waveform, The result of multiplying the acceleration Fourier spectrum in the first range of the second main dynamic waveform by the function is taken as the normal assumed waveform characteristic, and this is divided by the acquired waveform characteristic, which is the acceleration Fourier spectrum, to calculate the comparison function. The comparison function is approximated by an exponential function or a multidimensional polynomial to calculate the approximate function. The corrected waveform is derived by multiplying the approximation function by the acquired waveform characteristics and performing an inverse Fourier transform on the result. The seismic motion observation system according to claim 3, characterized in that it is as described above.

5. A seismic motion observation method that uses a smart device with a built-in acceleration sensor and a seismometer fixed to a building or the ground to observe seismic motion, From the first seismic waveform observed by the seismometer, the first main motion waveform, which is the waveform portion corresponding to the main motion, is estimated. The second seismic waveform observed by the acceleration sensor is adjusted so that its time and direction match those of the first seismic waveform, and the second main seismic waveform, which is the waveform portion corresponding to the main motion, is estimated from the adjusted second seismic waveform. If there is a time range within the second main seismic waveform in which the amplitude is constant, the time range prior to that time range is set as the first range, and that time range is set as the second range. A function is defined that represents the relationship between the waveform characteristics in the second range and the waveform characteristics in the first range of the first main seismic waveform. Based on the waveform characteristics in the first range of the second main seismic waveform and the function, the waveform characteristics in the second range of the second main seismic waveform are derived. Based on these waveform characteristics, a corrected waveform is derived, and the waveform in the second range of the second main seismic waveform is replaced with the corrected waveform to correct the second seismic waveform and estimate the seismic motion at the location of the smart device. A method for observing seismic motion characterized by the following features.

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