Seismic distance estimation device, seismic distance estimation program, and seismic distance estimation method
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- NAGOYA ELECTRICAL EDUCATIONAL FOUNDATION
- Filing Date
- 2022-10-12
- Publication Date
- 2026-08-05
Smart Images
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Abstract
Description
[Technical Field]
[0001] This disclosure relates to a hypocenter distance estimation device, a hypocenter distance estimation program, and a hypocenter distance estimation method for estimating the hypocenter distance. [Background technology]
[0002] To issue an effective warning immediately when an earthquake occurs, methods have been developed to detect P-waves and estimate the hypocenter distance from the time history of the initial P-wave motion. However, methods proposed so far require the accumulation of observational data for a certain period of time, which means that a certain amount of time is needed from P-wave detection to hypocenter distance estimation, and there are issues that need to be improved for issuing early warnings.
[0003] Patent Document 1 discloses an invention titled "Method for determining epicenter distance and magnitude and apparatus therefor." This invention employs a method for detecting seismic waves, calculating the envelope of the time history data of the initial phase of the seismic waves, and obtaining coefficients A and B by fitting the function y = Bt × exp(-At) to the envelope, and then estimating the epicenter distance from coefficient B.
[0004] The method described in Patent Document 1 has several problems, including the fact that it takes several seconds to estimate the epicenter distance because it requires accumulating data for several seconds, and the theoretical validity of the function fitted to the envelope of the observation records.
[0005] Patent Document 2 discloses an invention titled "Epicenter Distance Estimation Device, Epicenter Distance Estimation System, and Epicenter Distance Estimation Method." Similar to Patent Document 1, this invention calculates the envelope of the time history data of the initial phase of the seismic wave, obtains the coefficient B by applying the function y = Bt × exp(-At) to the envelope, and further estimates the incidence direction and incidence angle of the P wave by fitting an ellipse to the seismic motion trajectory calculated from the 3-component time history data after applying a low-pass filter to the initial phase of the P wave in the observation record, and then estimates the epicenter distance from the coefficient B and the P wave incidence angle.
[0006] The method described in Patent Document 2 has the same problem as in Patent Document 1, that it requires the accumulation of observational time history data whether fitting a function to the envelope or fitting an ellipse to the seismic motion trajectory.
[0007] Patent Document 3 discloses an invention titled "Real-time seismometer and method for predicting seismic intensity, etc., using the same." Based on the analysis of many earthquake observation records, Patent Document 3 points out that the rate of increase in the immediate seismic intensity time history at the time of the arrival of the first P-wave is systematically related on average with respect to the distance from the epicenter. The rate of increase in the immediate seismic intensity time history at the time of the arrival of the first P-wave is larger at locations closer to the epicenter and decreases as the distance from the epicenter increases. Patent Document 3 suggests that the distance from the epicenter can be estimated from the rate of increase by utilizing the above relationship. However, Patent Document 3 does not present a quantitative regression equation or anything similar regarding the relationship between the rate of increase and the distance from the epicenter, and does not show a specific method for estimating the distance from the epicenter. [Prior art documents] [Patent Documents]
[0008] [Patent Document 1] Patent No. 3695579 [Patent Document 2] Patent No. 4465509 [Patent Document 3] Patent No. 4472769 [Overview of the project] [Problems that the invention aims to solve]
[0009] In Japan, a country prone to earthquakes, the continuous improvement of earthquake disaster prevention measures is a crucial issue for everyone. As long as it is difficult to predict earthquakes in advance, predicting the maximum intensity and arrival time of shaking immediately after an earthquake occurs, and issuing warnings as quickly as possible, are means of mitigating disaster.
[0010] The closer you are to the epicenter, the faster the shaking arrives and the greater the amplitude. In other words, the damage caused by earthquake shaking is more severe the closer you are to the epicenter. When an earthquake occurs inland, the time from the arrival of the P-wave to the onset of maximum shaking in the area directly above the epicenter can be as short as 2 seconds. Therefore, detecting P-waves and estimating the distance from the epicenter early on in the event of a large earthquake, especially a so-called inland earthquake, is extremely important for earthquake disaster prevention, and developing effective methods for estimating the distance to the epicenter is a crucial task.
[0011] The methods proposed so far rely on extracting parameters useful for estimating the epicenter distance from the analysis of data accumulated over the first few seconds of the P-wave's initial phase. Therefore, a certain amount of time is required between P-wave detection and epicenter distance estimation. Given the urgency of issuing warnings, the specific challenge to be addressed is the development of a new method that accurately detects P-waves and overcomes the several-second delay between P-wave detection and epicenter distance estimation.
[0012] The purpose of this disclosure is to provide a method that can accurately detect P-waves and simultaneously estimate the earthquake source distance with high accuracy. [Means for solving the problem]
[0013] One aspect of this disclosure is a seismic source distance estimation device comprising an acceleration observation record creation unit, a filter calculation unit, a vector composite wave calculation unit, a logarithmic function calculation unit, an immediate seismic intensity time history calculation unit, an increase rate calculation unit, and a seismic source distance calculation unit.
[0014] The acceleration observation record creation unit is configured to create an acceleration observation record showing the time evolution of the first, second, and third acceleration components, respectively, based on acceleration detection signals obtained from seismometers that detect the first, second, and third acceleration components along the directions of the first, second, and third axes, respectively, which constitute the three-dimensional orthogonal coordinate system, for acceleration generated by seismic motion.
[0015] The filter operation unit is configured to perform operations using an IIR filter having filter characteristics preset for seismic intensity calculation on each of the first acceleration component, the second acceleration component, and the third acceleration component in the acceleration observation record.
[0016] The vector composite wave calculation unit is configured to calculate a vector composite wave by vector-composing the first acceleration component, the second acceleration component, and the third acceleration component on which operations using an IIR filter have been performed.
[0017] The logarithmic function calculation unit is configured to calculate a logarithmic function including the logarithm of the vector composite wave. The instantaneous seismic intensity time history calculation unit is configured to calculate an instantaneous seismic intensity time history by executing an operation with an integration duration of 0 for a preset interval length on the logarithmic function.
[0018] The increase rate calculation unit is configured to calculate the increase rate of the instantaneous seismic intensity time history. The hypocenter distance calculation unit is configured to calculate the hypocenter distance by substituting the increase rate calculated by the increase rate calculation unit into at least one of the first distance calculation formula and the second distance calculation formula. Let the increase rate be S, the hypocenter distance of the earthquake that generated the ground motion be R, the preset first, second, and third coefficients be a, b, and c respectively, and S(R) = {a / (R + b)} + c be the first distance calculation formula. Let the preset fourth, fifth, and sixth coefficients be A, B, and C respectively, and R(S) = {A / (S + B)} + C be the second distance calculation formula.
[0019] The hypocenter distance estimation device of the present disclosure configured as described above calculates the hypocenter distance based on the increase rate of the instantaneous seismic intensity time history. Therefore, it can accurately detect the P wave and perform high-precision estimation of the hypocenter distance simultaneously with the arrival of the P wave. For this reason, the hypocenter distance estimation device of the present disclosure can eliminate the time delay from P wave detection to hypocenter distance estimation, which was inevitable with conventional methods. As a result, the hypocenter distance estimation device of the present disclosure can issue an effective warning for the area directly above the hypocenter where urgency is required.
[0020] Another aspect of the present disclosure is a hypocenter distance estimation program for causing a computer to function as a filter operation unit, a vector composite wave calculation unit, a logarithmic function calculation unit, an instantaneous seismic intensity time history calculation unit, an increase rate calculation unit, and a hypocenter distance calculation unit in order to estimate the hypocenter distance.
[0021] The computer controlled by the hypocenter distance estimation program of the present disclosure can constitute a part of the hypocenter distance estimation device of the present disclosure, and the same effects as those of the hypocenter distance estimation device of the present disclosure can be obtained.
[0022] Yet another aspect of the present disclosure is a hypocenter distance estimation method executed by a hypocenter distance estimation device for estimating the hypocenter distance. In the management method of the present disclosure, the hypocenter distance estimation device creates an acceleration observation record based on the acceleration detection signal acquired from the seismometer.
[0023] In the management method of the present disclosure, the hypocenter distance estimation device performs calculations using an IIR filter having filter characteristics preset for seismic intensity calculation on each of the first acceleration component, the second acceleration component, and the third acceleration component in the acceleration observation record.
[0024] In the management method of the present disclosure, the hypocenter distance estimation device vectorially synthesizes the first acceleration component, the second acceleration component, and the third acceleration component on which the calculations using the IIR filter have been performed to calculate a vector composite wave.
[0025] In the management method of the present disclosure, a logarithmic function including the logarithm of the vector composite wave is calculated. In the management method of the present disclosure, the hypocenter distance estimation device calculates an instantaneous seismic intensity time history by executing a calculation with an integration duration of 0 for a preset section length on the logarithmic function.
[0026] In the management method of the present disclosure, the hypocenter distance estimation device calculates the increase rate of the instantaneous seismic intensity time history. In the management method of the present disclosure, the hypocenter distance estimation device calculates the hypocenter distance by substituting the increase rate into at least one of the first distance calculation formula and the second distance calculation formula.
[0027] The earthquake source distance estimation method described herein is a method performed in the earthquake source distance estimation device described herein, and by performing this method, the same effects as the earthquake source distance estimation device described herein can be obtained. [Brief explanation of the drawing]
[0028] [Figure 1] This is a block diagram showing the configuration of the earthquake source distance estimation device. [Figure 2] This graph shows the observation record, filtered time history, vector synthesis time history, common logarithmic time history, immediate seismic intensity time history, and growth rate time history. [Figure 3] This graph shows the relationship between the rate of increase in the initial P-wave motion and the distance from the epicenter. [Figure 4] This graph shows the relationship between the distance from the epicenter and the rate of increase in the initial P-wave motion. [Figure 5] This graph shows the relationship between the rate of increase in the initial P-wave motion and the distance from the epicenter, along with the regression equation. [Figure 6] This figure shows the location of the earthquake's epicenter and the observation point used in the analysis of the immediate seismic intensity time history. [Figure 7] This figure shows the frequency distribution of earthquakes used in the analysis of the immediate seismic intensity time history. [Figure 8] This figure shows the frequency distribution of the data used in the analysis of the immediate seismic intensity time history. [Figure 9] This figure shows the difference in the relationship between the rate of increase in the immediate seismic intensity time history and the distance from the epicenter, depending on the trigger level. [Figure 10] This figure shows the difference in the relationship between the rate of increase in immediate seismic intensity over time and the distance from the epicenter, depending on the length of the measurement interval. [Figure 11] This figure shows the difference in the relationship between the rate of increase in immediate seismic intensity over time and the distance from the epicenter, depending on the depth of the epicenter. [Figure 12] This figure shows the characteristics of the inelastic damping model. [Figure 13] This figure shows the relationship between the maximum value of the increase rate in the immediate seismic intensity time history and the hypocenter distance in the inelastic damping model. [Figure 14]This figure shows the difference in the relationship between the immediate seismic intensity time history increase rate and the distance from the epicenter, depending on the trigger level. [Figure 15] This figure shows the difference in the relationship between the rate of increase in immediate seismic intensity over time and the distance from the epicenter, depending on the segment length. [Figure 16] This figure shows the relationship between the actual distance from the epicenter and the distance calculated using the arithmetic mean. [Figure 17] This figure shows the relationship between the actual distance from the earthquake's epicenter and the distance calculated using geometric mean. [Figure 18] Flowchart for estimating the distance to the earthquake's epicenter. [Modes for carrying out the invention]
[0029] Embodiments of the present disclosure will be described below with reference to the drawings. [1] Configuration of the earthquake source distance estimation device As shown in Figure 1, the earthquake source distance estimation device 1 of this embodiment comprises a processing unit 2 and an input / output unit 3.
[0030] The processing unit 2 is an electronic control unit centered around a microcomputer equipped with a CPU 2a, ROM 2b, RAM 2c, etc. The various functions of the microcomputer are realized by the CPU 2a executing a program stored in a non-transitional physical recording medium. In this example, ROM 2b corresponds to the non-transitional physical recording medium storing the program. Furthermore, the execution of this program executes the method corresponding to the program. Note that some or all of the functions performed by the CPU 2a may be configured hardware-wise using one or more ICs. Also, the number of microcomputers constituting the processing unit 2 may be one or more.
[0031] The input / output unit 3 is a circuit for inputting and outputting analog or digital signals between the outside of the earthquake source distance estimation device 1 and the processing unit 2. The seismometer 4 is connected to the input / output unit 3.
[0032] The seismometer 4 is installed, for example, on the ground surface or underground, and detects the acceleration generated by seismic motion at the observation point where the seismometer 4 is installed, in three components: north-south, east-west, and vertical, and outputs a three-component acceleration detection signal that shows the time change of the detected acceleration.
[0033] [2] Relationship between the rate of immediate increase in seismic intensity and the distance from the epicenter Figure 2 shows examples of immediate seismic intensity time histories for an earthquake with a magnitude of 6.5 and a focal depth of 1.4 km that occurred in Osaka Prefecture in 2019, at observation points close to and far from the epicenter. When calculating the immediate seismic intensity time histories from the observation record time histories, a time-domain filter is used, with a seismic intensity conversion interval length of 0.5 s and an cumulative duration of 0.0 s. The figure on the left is from observation point OSK002 with an epicenter distance of 2.8 km, and the figure on the right is from observation point HYG009 with an epicenter distance of 59.5 km. From top to bottom in Figure 2 are the north-south component observation record, east-west component observation record, vertical component observation record, north-south component filtered time histories, east-west component filtered time histories, vertical component filtered time histories, vector composite time histories, common logarithmic time histories, immediate seismic intensity time histories, and growth rate time histories, with the rise time of the immediate seismic intensity time histories detected as the P-wave initial motion displayed as time 0.
[0034] The amplitude change in the immediate seismic intensity time history is largest when the P-wave arrives, and immediately after the arrival of the initial P-wave, the slope of the immediate seismic intensity time history decreases gradually. Subsequently, the immediate seismic intensity time history increases further with the arrival of S-waves and surface waves, and then declines. It can be observed that the rate of increase in the immediate seismic intensity time history at the arrival of the P-wave is large at observation points close to the epicenter (left figure) and small at observation points farther away (right figure).
[0035] When a P-wave is detected, the rate of increase over several intervals is calculated using the time history data for that time and the data from several subsequent samples. Analysis of numerous seismic motion observation records has revealed that this rate of increase has a systematic relationship with the hypocenter distance. Figures 3 and 4 summarize the relationship between the rate of increase in the immediate seismic intensity time history at the arrival of the first P-wave and the hypocenter distance for many observation records. Small circles represent individual data. In Figure 3, the large circles and line segments represent the average value and standard deviation for every 10 km of hypocenter distance. In Figure 4, the large triangles and line segments represent the increase rate of 10s. -1 The mean and standard deviation for each period are shown. It can be observed that the rate of increase is larger the closer you are to the epicenter and decreases as you move away. The curves in the figures represent the regression equation that expresses the relationship between the distance from the epicenter and the rate of increase; in Figure 3, it is equation S(R), and in Figure 4, it is equation R(S). As will be discussed later, the regression equation is a model function supported by theoretical principles.
[0036] While equations S(R) and R(S) are equivalent as theoretical formulas, they differ as regression equations for data with variability. In the regression of equation S(R), the hypocenter distance R is treated as an independent variable, and for each data point of the increase rate S of the immediate seismic intensity time history, coefficients a, b, and c are determined such that the sum of the squared residuals from equation S(R) is minimized when R is given. The vertical line segment shown in Figure 3 represents the degree of variability of each increase rate S from equation S(R) as the standard deviation over a 10km hypocenter distance interval. On the other hand, in the regression of equation R(S), the increase rate S of the immediate seismic intensity time history is treated as an independent variable, and for each data point of the hypocenter distance R, coefficients A, B, and C are determined such that the sum of the squared residuals from equation R(S) is minimized when S is given. The degree of variability of each hypocenter distance R from equation R(S) is expressed as the standard deviation over a 10km hypocenter distance interval. -1 The horizontal line segments in Figure 3 represent the standard deviation over intervals. Figure 5 shows the difference between regression equation S(R) and regression equation R(S). The small circles represent individual data points, the vertical line segments and large circles represent the mean and standard deviation of the rate of increase S for every 10km of epicenter distance, and the horizontal line segments and large triangles represent the rate of increase 10s -1This shows the average and standard deviation of the epicenter distance R for each earthquake. These are the same as in Figures 3 and 4.
[0037] Figure 6 shows the epicenters and observation point locations of the earthquakes used in the analysis. There were 934 earthquakes, 1675 observation points, and 58,617 earthquake observation records. Figure 7 shows the frequency distribution of the earthquakes used in the analysis by magnitude and by focal depth. Figure 8 shows the frequency distribution of the observation record data used in the analysis by epicenter distance, by measured seismic intensity, by trigger level in P-wave detection, and by time, from the time of P-wave arrival to the time of maximum shaking in the region within 50 km of the epicenter. From the "time, frequency distribution from P-wave arrival to the time of maximum shaking" shown in Figure 8, it can be seen that in regions close to the epicenter, there are quite a few cases where the maximum shaking occurs in a short time from the time of P-wave arrival.
[0038] The relationship between the rate of increase in the immediate seismic intensity time history upon P-wave arrival and the hypocenter distance depends on the trigger level for P-wave detection, which is determined by the steady-state noise level, and this is shown in Figure 9. In the graph in Figure 9, the horizontal axis represents the distance from the epicenter (km), and the vertical axis represents the rate of increase in seismic intensity over a 0.01-second interval ( / s). Small circles represent individual data points, and large circles represent the average value for every 10km of epicenter distance. The vertical line segments associated with the large circles represent the standard deviation of the rate of increase. The curve is the regression curve of equation (12), which will be described later. The epicenter depth ranges from 0 to 60km.
[0039] Furthermore, the relationship between the rate of increase and the distance from the epicenter depends on the length of the section used to calculate the rate of increase, as shown in Figure 10. In the graph in Figure 10, the horizontal axis represents the distance from the epicenter (km), and the vertical axis represents the rate of increase in seismic intensity ( / s) in the interval of 0.01 to 0.06 seconds. Small circles represent individual data points, and large circles represent the average value for every 10km of epicenter distance. The vertical line segments associated with the large circles represent the standard deviation of the rate of increase. The curve is the regression curve of equation (12), which will be described later. The epicenter depth ranges from 0 to 60km. The trigger level is seismic intensity -5.0.
[0040] The properties shown in Figures 9 and 10 are consistent with the theoretical predictions described later. Figure 11 shows the difference in the relationship between the growth rate and focal distance depending on the focal depth. In the graph in Figure 11, the horizontal axis represents the distance from the epicenter (km), and the vertical axis represents the seismic intensity increase rate ( / s). Small circles represent individual data points, and large circles represent the average value for every 10km of epicenter distance. The vertical line segments associated with the large circles represent the standard deviation of the increase rate. The interval length for measuring the increase rate is 0.01 seconds. The trigger level is seismic intensity -5.0.
[0041] There is no significant difference in the relationship between the rate of increase and the distance from the epicenter when the focal depth is between 0 and 60 km, but the difference becomes larger when the focal depth is greater than 60 km. This difference is consistent with the fact that inelastic damping within the crust is greater than inelastic damping within the uppermost mantle.
[0042] [3] Propagation of seismic motion from the epicenter to the surface The main factors influencing the ground motion from the time an earthquake occurs at its epicenter until it reaches a single point on the Earth's surface are (A) the characteristics of the epicenter, (B) the transmission characteristics along the propagation path, and (C) the response characteristics of the surface soil.
[0043] Of the three items above, (A) source characteristics and (C) surface ground response characteristics are factors that influence the frequency characteristics of observed seismic motion, but their influence does not depend on the distance from the epicenter. The factor that causes changes in observed seismic motion depending on the distance from the epicenter is (B) transmission characteristics in the propagation path. Of the transmission characteristics in the propagation path, geometric damping and inelastic damping are included in all observed seismic motion, but inelastic damping is the factor that particularly greatly influences the frequency static characteristics of seismic motion in the high-frequency band. The frequency characteristics of observed seismic motion are the result of the effect of inelastic damping, which has an effect depending on the distance from the epicenter, plus the effects of source characteristics and surface ground response characteristics, which do not depend on the distance from the epicenter.
[0044] The immediate seismic intensity time history I(R,t), obtained as a function of time t at a hypocenter distance R, is obtained by sequentially performing the following processes (P1) to (P4) on the acceleration observation record a(R,t).
[0045] (P1) For each component \(a(R,t)\) of the acceleration observation record \(a(R,t)\), perform an operation using an IIR filter having a characteristic \(J(\omega)\) that approximates the filter characteristics for calculating the measured seismic intensity according to the Meteorological Agency Notice No. 4. IIR is the abbreviation of Infinite Impulse Response. c (R,t)に対して、気象庁告示第4号による計測震度計算用のフィルター特性を近似する特性J(ω)をもつIIRフィルターによる演算を行う。IIRは、Infinite Impulse Responseの略である。
[0046] The effect of this operation is equivalent to multiplying the Fourier transform \(A(R,\omega)\) of \(a(R,t)\) by \(J(\omega)\) to obtain \(F(R,\omega)\) and then performing an inverse Fourier transform on \(F(R,\omega)\) to obtain \(f(R,t)\), and can be expressed as in equations (1), (2), and (3). c (R,t)のフーリエ変換A c (R,ω)に対してJ(ω)を乗じてF c (R,ω)を得てF c (R,ω)を逆フーリエ変換してf c (R,t)を得ることと同値であり、式(1),(2),(3)のように表すことができる。
[0047]
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[0048] (P2) As shown in equation (4), calculate the 3-component vector composite wave \(v(R,t)\) of \(f(R,t)\). c (R,t)の3成分ベクトル合成波v(R,t)を計算する。
[0049]
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[0050] (P3) As shown in equation (5), calculate the function \(w(R,t)\) by doubling the common logarithm of \(v(R,t)\) and adding a constant term \(C\).
[0051]
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[0052] As shown in equation (6) (P4), the immediate seismic intensity time history I(R,t) is obtained by performing an operation S on w(t) with the cumulative duration set to 0 over the interval length L (corresponding to taking the maximum value within the interval). For example, "the value for which the cumulative duration is 0.3 seconds when the interval length is 1 second and the number of samples per second is 100" is the 30th value when the values of the function w(R,t) within the interval length are arranged in descending order. Therefore, for example, "the value for which the cumulative duration is 0 seconds when the interval length is 1 second and the number of samples per second is 100" is the 1st value when the values of the function w(R,t) within the interval length are arranged in descending order, i.e., the maximum value.
[0053]
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[0054] Of the processes (P1) to (P4), the filtering process for measuring seismic intensity calculation in process (P1) clearly changes the frequency characteristics of the immediate seismic intensity time history. However, this change is independent of the hypocenter distance. The three-component vector synthesis process in process (P2) changes the negative part of the immediate seismic intensity time function to a positive value, but since the initial part of the wave has a constant sign, it does not fundamentally change the properties of the initial part. The logarithmic calculation process in process (P3) changes the properties of the immediate seismic intensity time history as a time series, but does not change the frequency characteristics. Furthermore, the calculation process in process (P4) generally affects the frequency characteristics of the immediate seismic intensity time history, but since the immediate seismic intensity time history increases monotonically when the P wave arrives, it does not change the rate of increase of the initial part (i.e., the time derivative of the immediate seismic intensity time history).
[0055] From the above considerations, the frequency characteristics of the immediate seismic intensity time history differ depending on the hypocenter distance due to inelastic attenuation in the propagation path, changes independent of the hypocenter distance occur due to the hypocenter characteristics and surface ground response characteristics, and effects independent of the hypocenter distance are added due to the processing (P1) in the immediate seismic intensity time history calculation.
[0056] [4] Inelastic damping in the propagation path and the rate of increase in the time history of immediate seismic intensity The rate of increase S(R,t) of the immediate seismic intensity time history is obtained by calculating the average slope of I(R,t) using the least squares method for the interval length of the rate of increase measurement. The rate of increase is close to the time derivative of I(R,t), as shown in equation (7).
[0057]
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[0058] Therefore, the rate of increase in the immediate seismic intensity time history upon arrival of the P-wave is determined by the effect of inelastic attenuation along the propagation path, which corresponds to the distance from the epicenter, plus the effects of the epicenter characteristics, surface ground response characteristics, and calculation processing.
[0059] Several models have been proposed for inelastic damping in the seismic motion propagation path. Among these, the model that ignores the phase spectrum and is expressed only by the amplitude spectrum, and does not satisfy the causal law, is unrealistic, but it can analytically represent the effect in the time domain and is meaningful for considering the effect of inelastic damping on the immediate seismic intensity time history. If the complex transfer function is K(ω), the Q value for inelastic damping is Q0, and the phase velocity of seismic motion propagation is c0, then K(ω) is expressed by equation (8).
[0060]
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[0061] In an inelastic damping model that does not satisfy the principle of causality, apart from the phase velocity, the only free parameter is the Q value. To make the effect of inelastic damping on the immediate seismic intensity time history apparent, if the source time function is a delta function, surface ground response characteristics are ignored, and no filtering for instrumental seismic intensity is performed, the immediate seismic intensity time history is obtained as shown in equation (9).
[0062]
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[0063] Because this model does not satisfy the principle of causality, the immediate seismic intensity time history is symmetric with respect to the arrival time of the P wave t = R / c0. The rate of increase of the immediate seismic intensity time history is obtained by differentiating the above equation with respect to time as shown in equation (10), and its maximum value is given by equation (11).
[0064]
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[0065] Figure 12 shows the characteristics of an inelastic damping model that does not satisfy causality when the phase velocity is 6 km / s and the Q value is 100, in the upper left, and Figure 13 shows the relationship between the maximum value of the increase rate of the immediate seismic intensity time history and the source distance when an inelastic damping model that does not satisfy causality is adopted, in the upper left. From equation (11) and Figure 12, the effect of inelastic damping on the immediate seismic intensity time history is that the maximum value of the increase rate is inversely proportional to the source distance, and the proportionality constant is proportional to the product of the phase velocity and the Q value. From this, in the actual case where frequency characteristics that do not depend on the source distance, i.e., frequency characteristics associated with a general source time function, surface ground response characteristics, and frequency characteristics associated with the calculation processing of the immediate seismic intensity time history are added, it is thought that the increase rate of the immediate seismic intensity time history at the arrival of the P wave can be expressed as equation (12) by referring to equation (11) and generalizing this function.
[0066]
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[0067] By rewriting the relationship in equation (12) by swapping the independent and dependent variables, we obtain equation (13).
[0068]
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[0069] Among the inelastic damping models that satisfy the causal principle, in the case of the Futterman model, the complex transfer function is expressed as shown in equation (14).
[0070]
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[0071] The upper right of Figure 12 shows the characteristics of the Futterman model that satisfy the causal principle when the phase velocity c0 = 6 km / s and Q0 = 100. The Futterman model exhibits a nearly constant Q value over a wide frequency range. The upper right of Figure 13 shows the relationship between the rate of increase in the immediate seismic intensity time history during the initial P-wave motion and the hypocenter distance when the Futterman model is adopted. The trigger level for P-wave detection is seismic intensity -5.0, and the interval length for measuring the rate of increase is 0.01 seconds. The curve in the figure is obtained by fitting regression equation (12) to the calculation results, and it can be confirmed that equation (12) is in good agreement with the calculation results.
[0072] Among the inelastic damping models that satisfy the causal principle, in the case of the Strick model, the complex transfer function is expressed as shown in equation (15).
[0073]
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[0074] In the Strick model, apart from the phase velocity, the free parameters are k0 and σ. The lower left of Figure 12 shows the characteristics of the Strick model when the phase velocity is 6 km / s, the Q value at 1 Hz is 100, and σ = 0.8. It is shown that the Q value and phase velocity depend on frequency, which satisfies the causality ratio. The Q value increases with frequency, which is consistent with many observational results. The lower left of Figure 13 shows the relationship between the rate of increase in the immediate seismic intensity time history at the initial P-wave and the hypocenter distance when the Strick model is adopted. The trigger level for P-wave detection is seismic intensity -5.0, and the interval length for measuring the rate of increase is 0.01 seconds. The curve in the figure is obtained by fitting regression equation (12) to the calculation results, and it can be confirmed that equation (12) is in good agreement with the calculation results.
[0075] Among the inelastic damping models that satisfy the causal principle, in the case of the Azimi model, the complex transfer function is expressed as shown in equation (16).
[0076]
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[0077] In the Azimi model, apart from the phase velocity, the free parameters are α0 and α1. The lower right of Figure 12 shows the characteristics of the Azimi model that satisfy the causal principle when the phase velocity is 6 km / s, the Q value at 1 Hz is 100, and α1 = 0.002. It is shown that the phase velocity depends on the frequency, which is why the characteristics satisfy the causal principle. The Q value increases with frequency, which is consistent with many observational results. The lower right of Figure 13 shows the relationship between the rate of increase in the immediate seismic intensity time history at the initial P-wave and the hypocenter distance when the Azimi model is adopted. The trigger level for P-wave detection is seismic intensity -5.0, and the interval length for measuring the rate of increase is 0.01 seconds. The curve in the figure is obtained by fitting regression equation (12) to the calculation results, and it can be confirmed that equation (12) is in good agreement with the calculation results.
[0078] Figure 14 shows the effect of the trigger level during P-wave detection on the relationship between the rate of increase in the initial P-wave motion of the immediate seismic intensity time history and the hypocenter distance. The inelastic damping model used was the Azimi model, which satisfies causality. The interval length for measuring the rate of increase was 0.01 seconds.
[0079] Figure 15 shows the effect of the interval length of the measurement of the increase rate on the relationship between the increase rate in the initial P-wave motion of the immediate seismic intensity time history and the hypocenter distance. The inelastic damping model used was the Azimi model, which satisfies causality. The trigger level for P-wave detection was seismic intensity -5.0.
[0080] The results shown in Figures 14 and 15 indicate that the immediate seismic intensity time history rises sharply simultaneously with the arrival of the P-wave initial motion, and then gradually becomes less steep immediately afterward. The results shown in Figures 9 and 10, obtained from many observational records, are in good agreement with the theoretical results presented here, supporting the idea that the dependence of the rate of increase in the immediate seismic intensity time history at the arrival of the P-wave initial motion on the hypocenter distance is due to inelastic attenuation in the propagation path.
[0081] [5] Detection of the initial P wave For P-wave detection, the immediate seismic intensity time history is used. Immediately after the arrival of the initial P-wave, the slope of the immediate seismic intensity time history decreases gradually. Subsequently, the immediate seismic intensity time history increases further with the arrival of S-waves and surface waves, and then declines. The amplitude change of the immediate seismic intensity time history is largest when the P-wave arrives, and compared to cases where a linear observation time history is used as in the usual case, the algorithm for P-wave detection is simpler regardless of the magnitude of the steady-state noise amplitude.
[0082] P-wave detection utilizes the aforementioned characteristics of the amplitude and increase rate of the immediate seismic intensity time history. The specific procedure is as follows: By monitoring the steady-state noise level at the location, a threshold value a certain value greater than that noise level is set. When the value of the immediate seismic intensity time history exceeds that threshold, it is considered that a P-wave has been detected, the time is recorded, and the increase rate of the immediate seismic intensity time history is measured at the same time. If, after detecting a P-wave at a certain time, an increase rate greater than the increase rate measured at the time of the initial P-wave detection is measured within a certain period of time, that time is set as the new P-wave detection time.
[0083] The difference in amplitude transitions between seismic motion and sudden noise becomes clearer when using the immediate seismic intensity time history than when using the linear time history. This allows us to recognize an earthquake if the amplitude of the immediate seismic intensity time history persists for a certain period of time or longer, and to cancel P-wave detection if it does not, classifying it as sudden noise. Furthermore, when a larger earthquake's P-wave arrives immediately after a smaller earthquake, the amplitude change in the immediate seismic intensity time history is clearer than in the linear time history, and the rate of increase in the immediate seismic intensity time history is larger, allowing for accurate detection of the arrival of a large earthquake's P-wave.
[0084] When P-waves are detected and the rate of increase in the immediate seismic intensity time history is measured, the distance to the epicenter is instantly estimated and used for subsequent predictions of the maximum shaking to be performed. [6] Immediate estimation of the distance from the epicenter The coefficients a, b, and c in equation (12), and the coefficients A, B, and C in equation (13), which represent the relationship between the rate of increase in the immediate seismic intensity time history and the hypocenter distance, are all values that depend on the trigger level in P-wave detection, the interval length for measuring the rate of increase, and the hypocenter depth. The trigger level is a known quantity determined according to the steady-state noise at the location, and the interval length is a known quantity associated with the measurement of the rate of increase. The hypocenter depth is unknown at the time of P-wave detection. In actual hypocenter distance estimation, we decided to use coefficients corresponding to the trigger level at the time of P-wave detection, an interval length of 0.01 seconds, and a hypocenter depth of 0 to 60 km. In this case, the coefficients a, b, and c in equation (12) and the coefficients A, B, and C in equation (13) become values that depend on the trigger level. To explicitly show this, the coefficients a, b, and c in equation (12) and the coefficients A, B, and C in equation (13) are rewritten and expressed as equations (17) and (18).
[0085]
number
[0086] When a P-wave is detected and the rate of increase in the immediate seismic intensity time history at the time of P-wave arrival is measured, the hypocenter distance can be estimated simultaneously with P-wave detection from the relationship between the rate of increase shown in equations (17) and (18) and the hypocenter distance. The method disclosed herein eliminates the time delay between P-wave detection and hypocenter distance estimation that was unavoidable in conventional methods.
[0087] Although equations (17) and (18) are equivalent as theoretical formulas, they are different as regression equations for data with variability, and the estimated focal distance will be different when using equation (17) compared to when using equation (18). Therefore, in this embodiment, the estimated focal distance is adopted as the value obtained by taking the arithmetic mean or geometric mean of the value estimated using equation (17) and the value estimated from equation (18) and adjusting for the deviation of the estimated values.
[0088] Figure 16 shows the estimated hypocenter distance when the arithmetic mean is taken, and Figure 17 shows the estimated hypocenter distance when the geometric mean is taken. In the graph in Figure 16, the horizontal axis represents the actual hypocenter distance, and the vertical axis represents the estimated hypocenter distance calculated using the arithmetic mean. Small circles represent individual data points, and large circles represent the average value for every 10 km of hypocenter distance. The horizontal bars attached to the large circles represent the standard deviation of the hypocenter distance, and the vertical bars represent the standard deviation of the estimated value. The trigger level is seismic intensity -4.5 or lower.
[0089] In the graph in Figure 17, the horizontal axis represents the actual hypocenter distance, and the vertical axis represents the estimated hypocenter distance calculated using geometric mean. Small circles represent individual data points, and large circles represent the average value for every 10 km of hypocenter distance. The horizontal bars attached to the large circles represent the standard deviation of the hypocenter distance, and the vertical bars represent the standard deviation of the estimated value. The trigger level is seismic intensity -4.5 or lower.
[0090] In both cases, the hypocenter distance can be estimated from the rate of increase in the immediate seismic intensity time history at the time of P-wave arrival. It is important to note that the estimated values are slightly underestimated in the range of large hypocenter distances, but the average error in the range of small hypocenter distances is almost zero.
[0091] [7] Processing executed in the processing unit The procedure for the earthquake source distance estimation process performed by the processing unit 2 of the earthquake source distance estimation device 1 is described below. The earthquake source distance estimation process is a process that is repeatedly performed while the processing unit 2 is operating.
[0092] When the earthquake source distance estimation process is executed, the CPU2a of the processing unit 2 first creates an acceleration observation record a(R,t) in S10 based on the three-component acceleration detection signal acquired from the seismometer 4, as shown in Figure 18.
[0093] Next, in S20, CPU2a processes each component a of the acceleration observation record a(R,t). c For (R,t), perform the above IIR filter operation and f c Calculate (R,t). Next, CPU2a, in S30, uses equation (4) above to f c The three-component vector composite wave v(R,t) of (R,t) is calculated.
[0094] Next, in S40, CPU2a calculates the function w(R,t) using equation (5) above. Next, in S50, CPU2a calculates the immediate seismic intensity time history I(R,t) using the above equation (6).
[0095] Next, in S60, CPU2a determines whether or not it has detected a P-wave. Specifically, CPU2a determines whether the value of the immediate seismic intensity time history I(R,t) exceeds a predetermined threshold, and if the value of the immediate seismic intensity time history I(R,t) exceeds the predetermined threshold, it determines that a P-wave has been detected.
[0096] If no P-waves are detected, CPU2a terminates the earthquake source distance estimation process. On the other hand, if P-waves are detected, CPU2a calculates the increase rate S(R,t) of the immediate seismic intensity time history I(R,t) in S70 by determining the average slope of the immediate seismic intensity time history I(R,t) using the least squares method for the interval length of the increase rate measurement, as described above.
[0097] Next, in S80, CPU2a calculates the epicenter distance R by substituting the increase rate S(R,t) calculated in S70 into equation (17). Hereafter, the epicenter distance R calculated in S80 will be referred to as the first epicenter distance.
[0098] Next, in S90, CPU2a calculates the epicenter distance R by substituting the increase rate S(R,t) calculated in S70 into equation (18). Hereafter, the epicenter distance R calculated in S90 will be referred to as the second epicenter distance.
[0099] Next, in S100, CPU2a calculates the average of the first and second epicenter distances using the arithmetic or geometric mean, uses the calculated average as the estimated epicenter distance, and terminates the epicenter distance estimation process.
[0100] [8] Effects The earthquake source distance estimation device 1 configured in this way creates an acceleration observation record a(R,t) showing the time evolution of each of the north-south acceleration component, east-west acceleration component, and vertical acceleration component, based on the three-component acceleration detection signals obtained from the seismometer 4, which detects the north-south acceleration component, east-west acceleration component, and vertical acceleration component along the north-south axis, east-west axis, and vertical axis that constitute the three-dimensional orthogonal coordinate system, respectively, for the acceleration generated by the earthquake motion.
[0101] The earthquake source distance estimation device 1 performs calculations on the north-south acceleration component, east-west acceleration component, and vertical acceleration component of the acceleration observation record a(R,t) using an IIR filter with characteristic J(ω) that approximates the filter characteristics for measuring seismic intensity calculation according to Japan Meteorological Agency Notification No. 4.
[0102] The earthquake source distance estimation device 1 calculates a three-component vector composite wave v(R,t) by vector synthesis of the north-south acceleration component, east-west acceleration component, and vertical acceleration component calculated by the IIR filter.
[0103] The earthquake source distance estimation device 1 calculates a function w(R,t) that includes the common logarithm of the three-component vector composite wave v(R,t). The earthquake source distance estimation device 1 calculates the immediate seismic intensity time history I(R,t) by performing a calculation S on the function w(R,t) with the cumulative duration set to 0 for a predetermined interval length L.
[0104] The epicenter distance estimation device 1 calculates the rate of increase S(R,t) of the immediate seismic intensity time history I(R,t). The earthquake source distance estimation device 1 calculates the earthquake source distance by substituting the increase rate S(R,t) into equations (17) and (18).
[0105] This earthquake source distance estimation device 1 calculates the earthquake source distance based on the rate of increase S(R,t) of the immediate seismic intensity time history I(R,t). Therefore, it can accurately detect P-waves and estimate the earthquake source distance with high accuracy simultaneously with the arrival of the P-waves. As a result, the earthquake source distance estimation device 1 can eliminate the time delay between P-wave detection and earthquake source distance estimation that was unavoidable with conventional methods. This enables the earthquake source distance estimation device 1 to issue effective warnings to areas directly above the earthquake epicenter where urgency is required.
[0106] Furthermore, the earthquake source distance estimation device 1 can accurately distinguish between sudden noise and preceding small earthquakes and the target earthquake using a simple algorithm, and can accurately detect P-waves. Furthermore, since the relationship between the rate of increase S(R,t) of the immediate seismic intensity time history I(R,t) at the time of P-wave arrival and the hypocenter distance is formulated according to the difference in trigger levels based on the calculation results from seismic motion simulation using an inelastic damping model, the hypocenter distance estimation device 1 can estimate the hypocenter distance in a theoretically supported manner.
[0107] Based on the above, the earthquake source distance estimation device 1 is useful for facilities and organizations that need to take earthquake disaster prevention measures and issue emergency warnings, and is particularly effective for issuing warnings in areas near the epicenter where urgency is required.
[0108] In the embodiments described above, S10 corresponds to processing as an acceleration observation record creation unit, S20 corresponds to processing as a filter calculation unit, S30 corresponds to processing as a vector composite wave calculation unit, and S40 corresponds to processing as a logarithmic function calculation unit.
[0109] Furthermore, S50 corresponds to processing as the immediate seismic intensity time history calculation unit, S70 corresponds to processing as the increase rate calculation unit, and S80 to S100 corresponds to processing as the epicenter distance calculation unit. Furthermore, the north-south axis corresponds to the first axis, the east-west axis corresponds to the second axis, the vertical axis corresponds to the third axis, the north-south acceleration component corresponds to the first acceleration component, the east-west acceleration component corresponds to the second acceleration component, the vertical acceleration component corresponds to the third acceleration component, and the three-component acceleration detection signal corresponds to the acceleration detection signal.
[0110] Furthermore, the three-component vector composite wave v(R,t) corresponds to a vector composite wave, the function w(R,t) corresponds to a logarithmic function, equation (17) corresponds to the first distance calculation formula, and equation (18) corresponds to the second distance calculation formula.
[0111] Although one embodiment of the present disclosure has been described above, the present disclosure is not limited to the above embodiment and can be implemented in various modified forms. [Example 1] For example, the above embodiment shows a method for estimating the hypocenter distance based on acceleration detection signals obtained from a seismometer 4 installed at one observation point. However, the hypocenter distance may also be estimated based on acceleration detection signals obtained from multiple seismometers 4 installed at each of multiple observation points.
[0112] [Differentiation 2] In the above embodiment, the hypocentral distance is estimated by the arithmetic or geometric mean of the first hypocentral distance calculated by substituting the growth rate S(R,t) into equation (17) and the second hypocentral distance calculated by substituting the growth rate S(R,t) into equation (18). However, the hypocentral distance may also be estimated based on either the first hypocentral distance calculated by substituting the growth rate S(R,t) into equation (17) or the second hypocentral distance calculated by substituting the growth rate S(R,t) into equation (18).
[0113] Multiple functions of one component in the above embodiment may be realized by multiple components, or one function of one component may be realized by multiple components. Furthermore, multiple functions of multiple components may be realized by one component, or one function realized by multiple components may be realized by one component. Also, some parts of the configuration of the above embodiment may be omitted. Furthermore, at least some parts of the configuration of the above embodiment may be added to or replaced with the configuration of other above embodiments.
[0114] In addition to the earthquake source distance estimation device 1 described above, this disclosure can also be realized in various forms, such as a system that uses the earthquake source distance estimation device 1 as a component, a program for causing a computer to function as the earthquake source distance estimation device 1, a non-transitional physical recording medium such as a semiconductor memory on which this program is recorded, and an earthquake source distance estimation method. [Explanation of symbols]
[0115] 1...Epicenter distance estimation device, 4...Seismograph
Claims
1. An acceleration observation record creation unit is configured to create an acceleration observation record showing the time evolution of the first, second, and third acceleration components, respectively, based on acceleration detection signals obtained from a seismometer that detects the first, second, and third acceleration components along the directions of the first, second, and third axes, respectively, that constitute a three-dimensional orthogonal coordinate system, regarding the acceleration generated by seismic motion. A filter calculation unit is configured to perform calculations on each of the first acceleration component, the second acceleration component, and the third acceleration component in the acceleration observation record using an IIR filter having pre-set filter characteristics for seismic intensity calculation, A vector composite wave calculation unit is configured to calculate a vector composite wave by vector combining the first acceleration component, the second acceleration component, and the third acceleration component calculated by the IIR filter, A logarithmic function calculation unit configured to calculate a logarithmic function including the logarithm of the vector composite wave, An immediate seismic intensity time history calculation unit is configured to calculate the immediate seismic intensity time history by performing a calculation on the aforementioned logarithmic function with the cumulative duration set to 0 for a predetermined interval length, An increase rate calculation unit configured to calculate the increase rate of the immediate seismic intensity time history, A seismic source distance calculation unit is configured to calculate the seismic source distance by substituting the increase rate calculated by the increase rate calculation unit into at least one of the first distance calculation formula and the second distance calculation formula, with S being the increase rate, R being the distance from the epicenter of the earthquake that generated the seismic motion, a, b, and c being the first, second, and third coefficients set in advance, S(R) = {a / (R+b)} + c, and A, B, and C being the fourth, fifth, and sixth coefficients set in advance, R(S) = {A / (S+B)} + C. A device for estimating the distance to the earthquake's epicenter, equipped with the necessary components.
2. A device for estimating the distance to the epicenter according to claim 1, The earthquake source distance calculation unit is an earthquake source distance estimation device that calculates the earthquake source distance as the geometric mean of a first earthquake source distance calculated by substituting the increase rate into the first distance calculation formula and a second earthquake source distance calculated by substituting the increase rate into the second distance calculation formula.
3. A device for estimating the distance to the epicenter according to claim 1, The earthquake source distance calculation unit is an earthquake source distance estimation device that calculates the earthquake source distance as the arithmetic mean of a first earthquake source distance calculated by substituting the increase rate into the first distance calculation formula and a second earthquake source distance calculated by substituting the increase rate into the second distance calculation formula.
4. To estimate the distance from the epicenter, a computer was used. An acceleration observation record creation unit is configured to create an acceleration observation record showing the time evolution of the first, second, and third acceleration components, respectively, based on acceleration detection signals obtained from a seismometer that detects the first, second, and third acceleration components along the directions of the first, second, and third axes, respectively, which constitute a three-dimensional orthogonal coordinate system, regarding the acceleration generated by seismic motion. A filter calculation unit is configured to perform calculations on each of the first acceleration component, the second acceleration component, and the third acceleration component in the acceleration observation record using an IIR filter having pre-set filter characteristics for seismic intensity calculation. A vector composite wave calculation unit is configured to calculate a vector composite wave by vector combining the first acceleration component, the second acceleration component, and the third acceleration component calculated by the IIR filter, A logarithmic function calculation unit configured to calculate a logarithmic function including the logarithm of the vector composite wave, An immediate seismic intensity time history calculation unit is configured to calculate the immediate seismic intensity time history by performing a calculation on the aforementioned logarithmic function with the cumulative duration set to 0 for a predetermined interval length. An increase rate calculation unit configured to calculate the increase rate of the immediate seismic intensity time history, and A seismic source distance calculation unit is configured to calculate the seismic source distance by substituting the increase rate calculated by the increase rate calculation unit into at least one of the first distance calculation formula and the second distance calculation formula, with the increase rate calculated by the increase rate calculation unit, S being the increase rate, R being the distance from the epicenter of the earthquake that generated the seismic motion, a, b, and c being the first, second, and third coefficients which are set in advance, respectively, and S(R) = {a / (R+b)} + c as the first distance calculation formula, and A, B, and C being the fourth, fifth, and sixth coefficients which are set in advance, respectively, and R(S) = {A / (S+B)} + C as the second distance calculation formula. A program for estimating the distance to the earthquake's epicenter, designed to function as such.
5. A method for estimating the distance from the epicenter, performed by an epicenter distance estimating device, The earthquake source distance estimation device creates an acceleration observation record showing the time evolution of the first, second, and third acceleration components, respectively, based on acceleration detection signals obtained from a seismometer that detects the first, second, and third acceleration components along the directions of the first, second, and third axes, respectively, which constitute a three-dimensional orthogonal coordinate system, for the acceleration generated by the seismic motion. The earthquake source distance estimation device performs calculations on each of the first acceleration component, the second acceleration component, and the third acceleration component in the acceleration observation record using an IIR filter having pre-set filter characteristics for seismic intensity calculation. The earthquake source distance estimation device calculates a vector composite wave by vector combining the first acceleration component, the second acceleration component, and the third acceleration component calculated by the IIR filter, The earthquake source distance estimation device calculates a logarithmic function that includes the logarithm of the vector composite wave, The earthquake source distance estimation device calculates the immediate seismic intensity time history by performing a calculation on the logarithmic function with the cumulative duration set to zero for a predetermined interval length, The aforementioned earthquake source distance estimation device calculates the rate of increase in the immediate seismic intensity time history, A method for estimating the source distance, wherein the source distance estimation device calculates the source distance by substituting the increase rate into at least one of the first distance calculation formula and the second distance calculation formula, wherein the increase rate is S, the source distance of the earthquake that caused the ground motion is R, the preset first, second, and third coefficients are a, b, and c, respectively, S(R) = {a / (R+b)} + c, the preset fourth, fifth, and sixth coefficients are A, B, and C, respectively, and the preset second distance calculation formula is R(S) = {A / (S+B)} + C.