WO2022018789A1 - Prediction method, learning method, prediction device, learning device, prediction program, and learning program - Google Patents

Prediction method, learning method, prediction device, learning device, prediction program, and learning program Download PDF

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WO2022018789A1
WO2022018789A1 PCT/JP2020/028048 JP2020028048W WO2022018789A1 WO 2022018789 A1 WO2022018789 A1 WO 2022018789A1 JP 2020028048 W JP2020028048 W JP 2020028048W WO 2022018789 A1 WO2022018789 A1 WO 2022018789A1
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learning
data
prediction
information
earthquake
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PCT/JP2020/028048
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French (fr)
Japanese (ja)
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忍 工藤
隆一 谷田
英明 木全
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日本電信電話株式会社
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Priority to JP2022538499A priority Critical patent/JP7469703B2/en
Priority to PCT/JP2020/028048 priority patent/WO2022018789A1/en
Publication of WO2022018789A1 publication Critical patent/WO2022018789A1/en

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting

Definitions

  • the present invention relates to a prediction method, a learning method, a prediction device, a learning device, a prediction program, and a learning program.
  • Non-Patent Document 1 As a method for predicting a seismic wave reaching a prediction target point, for example, as shown in Non-Patent Document 1, the following two methods are known.
  • the first method there is known a method of predicting a seismic wave reaching a prediction target point by applying the magnitude of the epicenter and the distance from the epicenter to the prediction target point in a distance attenuation formula.
  • a second method there is known a method of modeling the information of the stratum between the epicenter and the prediction target point and predicting the seismic wave reaching the prediction target point.
  • the information of the stratum is an element indicating the property of the stratum, and is, for example, information such as the ground characteristic, the propagation characteristic, the dominant frequency characteristic, and the impedance characteristic.
  • the method using the distance attenuation formula which is the first method, has a problem that the prediction accuracy is low because the information of the stratum from the epicenter to the prediction target point is not taken into consideration.
  • the second method in order to model the information of the stratum, a huge amount of information of the stratum is required, and there are many problems such as a great deal of labor and time for collecting the information.
  • an object of the present invention is to provide a technique capable of easily predicting information on a seismic wave at an arbitrary point with high accuracy.
  • One aspect of the present invention is a prediction method for predicting information about a seismic wave at a desired point, which includes an input step for inputting desired point information indicating a desired point, at least the desired point information, and epicenter position information. It has a prediction step of predicting information about seismic waves at the desired point using earthquake magnitude information, and in the prediction step, information on the geological formation between the location of the epicenter and the desired point. This is a prediction method that is not used.
  • One aspect of the present invention is learning target earthquake-related data used for learning prediction of information about seismic waves, including at least position information of a seismic source and magnitude information of an earthquake, between the position of the seismic source and the desired point.
  • the learning target earthquake-related data that does not include the geological formation information, the learning target point data indicating the points where the seismic waves generated by the earthquake of the learning target earthquake-related data were measured, and the points indicated by the learning target point data were measured.
  • the data separation step for separating the seismic wave vector into the amplitude value and the waveform vector, the learning target earthquake-related data, and the learning target earthquake-related data.
  • the learning target point data is obtained from the input data, the estimated value of the amplitude value obtained based on the coefficient updated by learning, the estimated vector of the waveform vector, and the seismic wave vector corresponding to the input data. It is a learning method including a learning step of updating the coefficient based on the said amplitude value and the said waveform vector.
  • One aspect of the present invention is a predictor that predicts information about a seismic wave at a desired point, and includes an input unit for inputting desired point information indicating a desired point, at least the desired point information, and epicenter position information.
  • the prediction unit includes a prediction unit that predicts information about a seismic wave at the desired point using the magnitude information of the earthquake, and the prediction unit determines the position of the epicenter and the desired point when predicting the seismic wave. It is a prediction device that does not use the information of the strata in between.
  • the learning target point data is obtained from the input data, the estimated value of the amplitude value obtained based on the coefficient updated by learning, the estimated vector of the waveform vector, and the seismic wave vector corresponding to the input data. It is a learning device including a learning unit for updating the coefficient based on the generated amplitude value and the waveform vector.
  • One aspect of the present invention is the desired point using an input step of inputting desired point information indicating a desired point into a computer, at least the desired point information, the location information of the epicenter, and the magnitude information of the earthquake. It is a prediction program that executes a prediction step of predicting information about a seismic wave in the above, and does not use the information of the stratum between the position of the epicenter and the desired point in the prediction step.
  • One aspect of the present invention is learning target earthquake-related data used for learning prediction of information about seismic waves in a computer, including at least position information of the earthquake source and magnitude information of the earthquake, and the position of the earthquake source and the desired point.
  • the learning target earthquake-related data that does not include the geological information between the two, the learning target point data indicating the point where the seismic wave generated by the earthquake of the learning target earthquake-related data was measured, and the point indicated by the learning target point data.
  • An input step for inputting a seismic wave vector indicating the measured seismic wave a data separation step for separating the seismic wave vector into an amplitude value and a waveform vector, the learning target earthquake-related data, and the learning target earthquake-related.
  • the learning device 1 shown in FIG. 1 performs the learning process.
  • the prediction device 2 shown in FIG. 3 is executed in a flow of predicting information about a seismic wave at a desired point for prediction using the trained coefficients generated by the learning process.
  • t may be every "1 millisecond” or every “10 milliseconds”.
  • any integer value from 0 to (N-1) is represented by “n”
  • any integer value from 0 to (K-1) is represented by “k”.
  • "input” is used to mean “capture”.
  • Learning target seismic related data I n is data about the earthquake which occurred in the past, for example, and past the epicenter position data indicating the position of the epicenter earthquake seismic scale data indicating the magnitude of earthquake of magnitude or the like of the earthquake And include.
  • the epicenter position data is, for example, three-dimensional coordinate data in which the depth from the position of the epicenter to the position of the epicenter is added to the coordinates of the epicenter, which is one point on the surface of the earth.
  • the learning target point data Lk is coordinate data indicating the coordinates of an arbitrary point on the surface of the earth, and is, for example, two-dimensional coordinate data.
  • the epicenter of the coordinates of the focal position data included in the learning object location data L k is the coordinate and the learning target seismic related data I n shown are the coordinates in the same two-dimensional coordinate system, for example, the epicenter of the coordinates It may be the coordinates in the two-dimensional coordinate system as the origin.
  • Seismic wave vector w n, k (t) is a seismic wave vector indicating the seismic waves of earthquakes that occurred in the past indicated by the learning target earthquake-related data I n, seismic wave vector, which is measured at a point indicated by the learning target point data L k Is. Since t is a parameter indicating the time, the seismic wave vectors w n, k (t) are time-series vectors, and w n, k (0), w n, k (1), ..., W. It is composed of T vectors n, k (T-2), w n, k (T-1).
  • the input unit 11 randomly selects any one "n” from the integer values of 0 to (N-1) and any one "k” from the integer values of 0 to (K-1). select.
  • the input unit 11 outputs the seismic wave vectors w n, k (t) corresponding to the selected “n” and “k” to the data separation unit 12.
  • the input unit 11 outputs the learning object seismic associated data I n and the learning target spot data L k corresponding to the selected "n", "k”, the amplitude prediction unit 21 and the waveform predictor 31 of the learning section 13 ..
  • the data separation unit 12 calculates the amplitude values pn and k from the seismic wave vectors w n and k (t) output by the input unit 11 based on the following equation (1).
  • the data separation unit 12 applies the seismic wave vector w n, k (t) output by the input unit 11 and the amplitude values pn, k calculated based on the equation (1) to the following equation (2).
  • the waveform vector v n, k (t) is calculated.
  • the amplitude values pn and k are the sum of the absolute values of the seismic wave vectors w n and k (t) in the time axis direction and are scalars.
  • the waveform vectors v n and k (t) are vectors obtained by dividing the seismic wave vectors w n and k (t) by the amplitude values pn and k.
  • the waveform vector v n, k (t) is a time-series vector similar to the seismic wave vector w n, k (t), and v n, k (0), v n, k (1), ..., It is composed of T vectors of v n, k (T-2) and v n, k (T-1).
  • the first coefficient storage unit 22 stores the coefficient applied to the function approximator internally provided in the amplitude prediction unit 21.
  • the coefficient stored in the first coefficient storage unit 22 is, for example, a weight value and a bias value when the function approximation device included in the amplitude prediction unit 21 is a neural network such as a multi-layer perceptron.
  • the first coefficient storage unit 22 stores the coefficient initialized with a random value.
  • Amplitude prediction unit 21 takes in the learning object seismic related data I n and the learning target spot data L k input unit 11 outputs as the input data, and a function approximator output one of the output data therein.
  • the output data output by the function approximator of the amplitude prediction unit 21 is an estimated value of the amplitude values pn and k represented by the following equation (3).
  • the second coefficient storage unit 32 stores the coefficient applied to the function approximator internally provided in the waveform prediction unit 31.
  • the coefficient stored in the second coefficient storage unit 32 is, for example, a weight value and a bias value when the function approximation device included in the waveform prediction unit 31 is a neural network such as a multi-layer perceptron.
  • the second coefficient storage unit 32 stores the coefficient initialized with a random value.
  • Waveform predictor 31 includes captures learning object seismic related data I n and the learning target spot data L k input unit 11 outputs as the input data, a function approximator outputs T output data therein.
  • the T output data output by the function approximator of the waveform prediction unit 31 are estimation vectors of the waveform vectors vn, k (t) represented by the following equation (4).
  • the waveform prediction unit 31 reads a coefficient from the second coefficient storage unit 32 and applies the read coefficient to a function approximator provided therein.
  • the waveform predictor 31 gives input data to the function approximator to which the coefficient is applied, and outputs the estimated waveform vector ⁇ v n, k (t) output by the function approximator by giving the input data to the waveform error calculation unit 33. do.
  • the amplitude error calculation unit 23 calculates the amplitude error E p based on the amplitude values pn and k and the estimated amplitude values ⁇ pn and k .
  • the optimization unit 41 has a new coefficient applied to the function approximator of the amplitude prediction unit 21 by solving a minimization problem for the objective function determined based on the amplitude error E p and the waveform error E v. A new coefficient to be applied to the function approximator of the waveform predictor 31 is calculated.
  • the optimization unit 41 overwrites the first coefficient storage unit 22 with a new coefficient applied to the function approximator of the calculated amplitude prediction unit 21 to update the coefficient.
  • the optimization unit 41 overwrites the second coefficient storage unit 32 with a new coefficient applied to the calculated function approximator of the waveform prediction unit 31 to update the coefficient.
  • FIG. 2 is a flowchart showing the flow of learning processing by the learning device 1.
  • the input unit 11 includes N learning target earthquake-related data I 0 to (N-1) , K learning target point data L 0 to (K-1) , and N ⁇ K seismic wave vectors w 0 to. (N-1), 0 to (K-1) (t) are input (step S101).
  • the input unit 11 initializes the learning step number counter r that counts the number of learning steps provided internally to “1” (step S102).
  • M is a predetermined batch size, and for example, a value of about "64" is applied.
  • the input unit 11 randomly selects any one "n” from the integer values of 0 to (N-1) and any one "k” from the integer values of 0 to (K-1). select.
  • the input unit 11 outputs the seismic wave vectors w n, k (t) corresponding to the selected “n” and “k” to the data separation unit 12.
  • the input unit 11 outputs the learning object seismic related data I n and the learning target spot data L k corresponding to the selected "n", "k”, the amplitude prediction part 21 and the waveform predictor 31 of the learning section 13 (Step S103).
  • the data separation unit 12 separates the seismic wave vectors w n, k (t) into amplitude values pn, k and waveform vectors v n, k (t) based on the equations (1) and (2). ..
  • the data separation unit 12 outputs the separated amplitude values pn and k to the amplitude error calculation unit 23, and outputs the separated waveform vectors v n and k (t) to the waveform error calculation unit 33 (step S104).
  • Amplitude prediction unit 21 takes in the learning object seismic related data I n and the learning target spot data L k is the input unit 11 and output.
  • the amplitude prediction unit 21 reads a coefficient from the first coefficient storage unit 22 and applies the read coefficient to a function approximator internally provided (step S105-1).
  • the amplitude error calculation unit 23 takes in the amplitude values pn and k output by the data separation unit 12 and the estimated amplitude values ⁇ pn and k output by the amplitude prediction unit 21.
  • the amplitude error calculation unit 23 calculates the amplitude error E p from the amplitude values pn and k and the estimated amplitude values ⁇ pn and k according to the equation (5).
  • Amplitude error calculating unit 23 outputs the calculated amplitude error E p in the optimization unit 41 (Step S107-1).
  • Waveform predictor 31 takes in the learning object seismic related data I n and the learning target spot data L k is the input unit 11 and output.
  • the waveform prediction unit 31 reads a coefficient from the second coefficient storage unit 32 and applies the read coefficient to a function approximator internally provided (step S105-2).
  • Waveform predictor 31 the function approximator according to the read-out coefficients to provide a learning object seismic related data I n and learning object location data L k as input data.
  • the function approximation unit of the waveform prediction unit 31 calculates the estimated waveform vector ⁇ v n, k (t) based on the given input data and the coefficient.
  • the function approximator of the waveform predictor 31 outputs the calculated estimated waveform vector ⁇ v n, k (t) as output data.
  • the waveform prediction unit 31 outputs the estimated waveform vector ⁇ v n, k (t) output by the function approximator to the waveform error calculation unit 33 (step S106-2).
  • the waveform error calculation unit 33 takes in the waveform vector v n, k (t) output by the data separation unit 12 and the estimated waveform vector ⁇ v n, k (t) output by the waveform prediction unit 31.
  • the waveform error calculation unit 33 calculates the waveform error E v from the waveform vector v n, k (t) and the estimated waveform vector ⁇ v n, k (t) according to the equation (6).
  • Waveform error calculating unit 33 outputs the calculated waveform error E v optimization unit 41 (Step S107-2).
  • Optimization unit 41 takes in the amplitude error E p for the amplitude error calculating unit 23 outputs, and a waveform error E v waveform error calculating unit 33 is outputted.
  • m is an integer value between 1 and M
  • the m-th amplitude error E p is shown as E p, m
  • the m-th waveform error E v is shown as E v, m.
  • the optimization unit 41 writes and stores the amplitude error E p, m , the waveform error E v, m, and the internal storage area (step S108).
  • the optimization unit 41 When m is less than M, that is, when the repetition of M times has not been completed, the optimization unit 41 outputs a processing continuation instruction signal indicating the continuation of processing to the input unit 11. When the input unit 11 receives the processing continuation instruction signal from the optimization unit 41, the processing of step S103 is performed again, and the processing of steps S104 to S108 is performed accordingly. On the other hand, when m matches M, that is, when the repetition of M times is completed, the processing of loops La1s to La1e ends (loop La1e).
  • the optimization unit 41 reads out the amplitude errors E p, 1 to M and the waveform errors E v, 1 to M for M times stored in the internal storage area.
  • the optimization unit 41 solves the minimization problem using the following equation (7) as the objective function based on the read amplitude errors E p, 1 to M and the waveform errors E v, 1 to M, and thereby the amplitude prediction unit.
  • a new coefficient applied to the function approximation device of 21 and a new coefficient applied to the function approximation device of the waveform prediction unit 31 are calculated.
  • a gradient method such as the steepest descent method is applied.
  • the optimization unit 41 overwrites the first coefficient storage unit 22 with a new coefficient applied to the function approximator of the calculated amplitude prediction unit 21 to update the coefficient.
  • the optimization unit 41 overwrites the second coefficient storage unit 32 with a new coefficient applied to the calculated function approximator of the waveform prediction unit 31 to update the coefficient (step S109).
  • the optimization unit 41 outputs a coefficient update notification signal for notifying that the coefficient has been updated to the input unit 11.
  • the input unit 11 determines whether or not the learning step number counter r matches the predetermined learning step upper limit number (step S110).
  • a value of the number of learning times to which the error E represented by the objective function of the equation (7) sufficiently converges is applied to the predetermined upper limit number of learning steps, and for example, a value of about "10000" is applied. Will be done.
  • step S110-No When the input unit 11 determines that the learning step number counter r does not match the learning step upper limit number (step S110-No), 1 is added to the learning step number counter r (step S111). After that, the loops La1s to La1e are processed again.
  • the input unit 11 determines that the learning step number counter r matches the upper limit number of learning steps (step S110-Yes).
  • the input unit 11 ends the process.
  • the first coefficient storage unit 22 and the second coefficient storage unit 32 store the learned coefficients in which the error E represented by the objective function of the equation (7) is sufficiently converged. become.
  • step S104 the series of processes of steps S105-1, S106-1, and S107-1, and the series of processes of steps S105-2, S106-2, and S107-2? It is performed in parallel, and the processing of step S103 is performed so as to be completed by at least the processing of steps S107-1 and S107-2 is started.
  • step S104 the series of processes of steps S105-1, S106-1, and S107-1 and the series of processes of steps S105-2, S106-2, and S107-2 do not necessarily have to be performed in parallel.
  • the process of step S104, the series of processes of steps S105-1, S106-1, and S107-1 may be performed, and the series of processes of steps S105-2, S106-2, and S107-2 may be performed in this order.
  • the order of the series of processes of -1, S106-1, S107-1 and the series of processes of steps S105-2, S106-2, and S107-2 may be exchanged.
  • the process of applying the coefficients of steps S105-1 and S105-2 to the function approximator the coefficients are not updated during the M times of loop processing La1s to La1e. Therefore, the process of applying the coefficient to the function approximation device may be performed only once at the first time, instead of being performed each time of the loop processes La1s to La1e.
  • FIG. 3 is a block diagram showing the configuration of the prediction device 2.
  • the prediction device 2 includes an input unit 51 and a prediction unit 52.
  • the input unit 51 inputs the predicted earthquake-related data represented by the symbol of the formula (8) and the desired point data represented by the symbol of the formula (9).
  • the symbol of the formula (8) is shown as “ ⁇ I”
  • the symbol of the formula (9) is shown as “ ⁇ L”.
  • the desired point data "-L” is coordinate data indicating the coordinates of the desired point for predicting the seismic wave generated by the earthquake of the prediction target earthquake-related data "-I", and is, for example, two-dimensional coordinate data.
  • the prediction unit 52 includes an amplitude prediction unit 21, a learned first coefficient storage unit 62, a waveform prediction unit 31, a learned second coefficient storage unit 72, and a data synthesis unit 81.
  • the learned first coefficient storage unit 62 stores the learned coefficient finally written in the first coefficient storage unit 22 in the learning process by the learning device 1 shown in FIG.
  • the learned coefficient finally written in the first coefficient storage unit 22 is a coefficient at the time when the input unit 11 determines “Yes” in step S110 and finishes the process.
  • the learned second coefficient storage unit 72 stores the learned coefficient finally written in the second coefficient storage unit 32 in the learning process by the learning device 1 shown in FIG.
  • the learned coefficient finally written in the second coefficient storage unit 32 is a coefficient at the time when the input unit 11 determines “Yes” in step S110 and finishes the process.
  • the data synthesis unit 81 is a seismic wave generated by the earthquake of the earthquake-related data “ ⁇ I” to be predicted, and the desired point data “ ⁇ . Calculate the seismic wave that reaches the point indicated by "L”.
  • the amplitude prediction unit 21 takes in the prediction target earthquake-related data “ ⁇ I” and the desired point data “ ⁇ L” output by the input unit 51.
  • the amplitude prediction unit 21 reads the learned coefficient from the learned first coefficient storage unit 62, and applies the read learned coefficient to the function approximation device provided therein (step S202-1).
  • the amplitude prediction unit 21 gives the prediction target earthquake-related data " ⁇ I" and the desired point data " ⁇ L” as input data to the function approximation device to which the learned coefficients are applied.
  • the function approximation unit of the amplitude prediction unit 21 calculates the predicted amplitude value represented by the symbol of the following equation (10) based on the given input data and the coefficient.
  • the function approximator of the amplitude prediction unit 21 outputs the calculated predicted amplitude value “ ⁇ p” as output data.
  • the amplitude prediction unit 21 outputs the predicted amplitude value “ ⁇ p” output by the function approximator to the data synthesis unit 81 (step S203-1).
  • the waveform prediction unit 31 takes in the prediction target earthquake-related data “ ⁇ I” and the desired point data “ ⁇ L” output by the input unit 51.
  • the waveform prediction unit 31 reads the learned coefficient from the learned second coefficient storage unit 72, and applies the read learned coefficient to the function approximator internally provided (step S202-2).
  • the waveform prediction unit 31 gives the prediction target earthquake-related data " ⁇ I" and the desired point data " ⁇ L” as input data to the function approximation device to which the learned coefficients are applied.
  • the function approximation unit of the waveform prediction unit 31 calculates the prediction waveform vector represented by the symbol of the following equation (11) based on the given input data and the coefficient.
  • the function approximator of the waveform prediction unit 31 outputs the calculated predicted waveform vector “ ⁇ v” (t) as output data. Since t is a parameter indicating the time, the predicted waveform vector " ⁇ v” (t) is a time series vector, and " ⁇ v” (0), " ⁇ v” (1), ..., It is composed of T vectors " ⁇ v” (T-2) and " ⁇ v” (T-1).
  • the waveform prediction unit 31 outputs the prediction waveform vector “ ⁇ v” (t) output by the function approximator to the data synthesis unit 81 (step S203-2).
  • the predicted seismic wave vector " ⁇ w” (t) is a vector obtained by multiplying the predicted waveform vector " ⁇ v” (t) by the predicted amplitude value " ⁇ p". Therefore, the predicted seismic wave vector " ⁇ w” (t) is a time-series vector like the predicted waveform vector " ⁇ v” (t), and is “ ⁇ w” (0), “ ⁇ w” (1), ..., It is composed of T vectors of " ⁇ w" (T-2) and " ⁇ w" (T-1).
  • steps S202-1 and S203-1 and the series of processes in steps S202-2 and S203-2 are shown to be performed in parallel, they do not necessarily have to be performed in parallel.
  • the processes may be performed in the order of the series of processes of steps S202-1 and S203-1, and the series of processes of steps S202-2 and S203-2, or may be performed in the reverse order.
  • (simulation result) 5 to 12 are graphs showing the waveforms of seismic waves generated by eight different earthquakes at points where eight different predictions are desired.
  • the seismic wave vectors w n, k (t) having the configuration as shown below are set to the amplitude values pn, k and the waveform vector vn .
  • a simulation is performed using a learning device that does not separate into k (t) and a prediction device corresponding to the learning device.
  • the learning device is referred to as a "learning device without separation”
  • the prediction device is referred to as a "prediction device without separation”.
  • No separation learning apparatus includes a learning object seismic related data I n, a learning object location data L k and input data, seismic vector w n, k function approximator to output data to estimate a vector of (t) There is.
  • No separation learning device function so as to reduce the estimated vector of seismic vector w n, k (t), seismic vector w n corresponding to the input data, calculates an error between the k (t), the calculated error Performs learning processing to update the coefficients applied to the approximator.
  • the non-separation prediction device is equipped with the same function approximation device as the non-separation learning device, and the function approximation is performed by giving the prediction target earthquake-related data " ⁇ I" and the desired point data " ⁇ L” as input data.
  • the instrument calculates the predicted seismic wave vector “ ⁇ w” (t) by using the trained coefficient generated by the learning device without separation by the learning process.
  • the graph of (a) in FIGS. 5 to 12 shows the correct answer data, that is, the graph of the actually measured seismic wave.
  • the graphs (b) in FIGS. 5 to 12 are the results of a simulation using the non-separation prediction device to which the learned coefficient generated by the above-mentioned non-separation learning device is applied, and the prediction calculated by the non-separation prediction device. It is a graph of the seismic wave vector " ⁇ w" (t).
  • the graphs (c) in FIGS. 5 to 12 are the results of simulations using the learning device 1 and the prediction device 2 of the present embodiment, and are the predicted seismic wave vectors “ ⁇ w” (t) calculated by the prediction device 2. It is a graph. Note that FIGS. 5 to 12 (b) and (c) are graphs when the batch size M is "64" and the upper limit of the number of learning steps is "10000".
  • the horizontal axis is time, and the unit of t is "10 milliseconds".
  • the vertical axis is the amplitude of the seismic wave.
  • the learning process is performed without separating the seismic wave vectors w n, k (t) into the amplitude values pn, k and the waveform vectors vn , k (t).
  • the predicted seismic wave vectors " ⁇ w" (t) all have almost the same waveform.
  • the waveform of the predicted seismic wave vector “ ⁇ w” (t) calculated by the prediction device 2 of the present embodiment The characteristics are similar to the characteristics of the waveform of the correct answer data, and it can be seen that the learning process is properly performed and the prediction accuracy is improved.
  • the input unit 11 a learning object seismic related data I n, a learning object location data L k indicating the points of measurement of seismic waves generated by earthquakes learning object seismic related data I n ,
  • the seismic wave vector w n, k (t) indicating the seismic wave measured at the point indicated by the learning target point data L k is input.
  • the data separation unit 12 separates the seismic wave vector w n, k (t) into an amplitude value pn, k and a waveform vector v n, k (t).
  • a learning object seismic related data I n is obtained by providing the function approximator amplitude prediction unit 21 is provided as input data and a learning target spot data estimated amplitude value ⁇ p n, and k, the amplitude value
  • the error E p with pn and k is calculated.
  • the learning unit 13 has an error E v between the estimated waveform vector ⁇ v n, k (t) obtained by giving the input data to the function approximator included in the waveform prediction unit 31 and the waveform vector v n, k (t). Is calculated.
  • the learning unit 13 updates the coefficient of the function approximation unit included in the amplitude prediction unit 21 and the coefficient of the function approximation unit included in the waveform prediction unit 31 based on the error E p and the error E v.
  • the input unit 51 is the seismic wave generated by the earthquake of the prediction target earthquake-related data "-I” which is the data related to the prediction target earthquake and the prediction target earthquake-related data "-I". Enter the desired point data " ⁇ L” indicating the desired point for prediction.
  • the prediction unit 52 uses the prediction target earthquake-related data "-I” and the desired point data "-L” as input data, and uses the learned coefficient obtained by the learning process by the learning device 1 to predict the predicted amplitude value.
  • the predicted seismic wave vector is calculated based on the predicted amplitude value " ⁇ p" and the predicted waveform vector " ⁇ v" (t) calculated by calculating " ⁇ p" and the predicted waveform vector " ⁇ v” (t). " ⁇ W” (t) is calculated.
  • the predicted seismic wave vector "-w” (t) has characteristics similar to those of the waveform of the seismic wave generated by the earthquake of the predicted earthquake-related data "-I” and reaching a desired point.
  • a learning object location data L k indicating the points of measurement of seismic waves generated by earthquakes learning object seismic related data I n
  • the relation between k (t) can be modeled in the function approximator comprising the amplitude prediction part 21 and the waveform predictor 31 in k.
  • This model would learn from the position of source included in the target seismic related data I n, which indirectly indicates the formation model between at the point until the indicated learning object location data L k. Therefore, the prediction device 2 can easily construct a stratum model and predict information on seismic waves with high prediction accuracy by using the learned coefficients obtained by the learning process of the learning device 1. Therefore, it is possible to easily predict information on seismic waves at any point with high accuracy.
  • the learning device 1 separates the seismic wave vectors w n and k (t) into an amplitude component that is difficult to predict and a waveform component that is easy to predict, and performs learning processing. Therefore, the learning efficiency is improved, and as shown in the above simulation result, it becomes possible to make a prediction with higher accuracy than directly predicting the seismic wave vector.
  • the impact of each region when an earthquake occurs is determined based on the seismic motion measured by seismographs installed in each region. Since seismic motion is generated by the seismic wave that reaches the seismograph, it is natural that only the seismic wave at the point where the seismograph is installed can be acquired. Here, the seismograph can be installed only in the place where the conditions set in detail are satisfied. Therefore, there is a problem that seismic waves cannot be measured at points that do not meet the criteria for installing seismographs. Even at a point where equipment such as a seismograph can be installed, it is difficult in terms of time to install equipment such as a seismograph immediately after an earthquake occurs.
  • the learning device 1 and the prediction device 2 can predict information about seismic waves at any point without installing equipment such as a seismograph. This is because, in the learning apparatus 1, the learning target seismic related data I n, learning object location data L k, and seismic wave vector w n, because the observation data of k (t) models the transfer function of the earthquake continuous space Is. As a result, the prediction device 2 makes it possible to predict seismic waves at any point of any earthquake by using this modeled transfer function. Therefore, by using the learning device 1 and the prediction device 2, seismic waves are expected to reach points that do not meet the criteria for installing seismographs or where equipment such as seismographs cannot be installed in advance. Can be predicted.
  • the learning target seismic related data I n is the focal position data indicating the hypocenter location, although a and a seismic scale data indicating the magnitude of earthquake of magnitude or the like of the earthquake, Other information may be included.
  • the learning target seismic related data I n are as other information, great collection of depth or the like of the shape of the types and sea terrain between the point indicated by the learning target location data L k hypocenter locations may contain not require information costs, but shall not include the information that requires a lot of cost to collect as information of the formation between the point indicated by the learning target location data L k hypocenter locations ..
  • the stratum information is an element indicating the properties of the stratum, and is, for example, information uncorrelated with individual earthquakes such as ground characteristics, propagation characteristics, predominant frequency characteristics, and impedance characteristics.
  • information correlated with the individual seismic for information associated with each seismic such as for example humidity or ground temperature, be included in the learning target seismic related data I n good.
  • learning object seismic related data I n is if it contains a type of data other than seismic position data and seismic scale data, the prediction target seismic related data " ⁇ I" also will contain a similarly the type of data.
  • the magnitude is shown as the magnitude of the earthquake, but an index showing the magnitude of the earthquake other than the magnitude, for example, the seismic moment may be applied.
  • the learning device 1 performs so-called mini-batch learning in which the batch size M is set to a value of about "64" and the upper limit of the number of learning steps is set to a value of about "10000". It may be changed arbitrarily.
  • the learning process shown in FIG. 2 may be terminated when the error E shown in the equation (7) is sufficiently converged.
  • the batch size M is set to "64”
  • batch learning may be performed in which the processes of loops La1s to La1e are repeated until all combinations of "n” and "k” are completed. .. Optimization unit 41, in place of the step S209, the amplitude error E p obtained at the timing of step S208, on the basis of the waveform error E v, in the processing in step S208, the online learning to update the coefficients You may do it.
  • the neural network is a multi-layer perceptron or the like, but it is used in machine learning other than the neural network such as the multi-layer perceptron.
  • the means may be applied, or the function represented by the mathematical formula including the coefficient may be applied.
  • the function approximator for which the learning process is completed becomes a trained model.
  • the amplitude and the waveform may be expressed by non-linear functions, respectively.
  • the point is to predict the separated amplitude and waveform individually.
  • the desired point is an arbitrary point including the point indicated by the learning target point data L k.
  • each of the amplitude prediction unit 21 and the waveform prediction unit 31 of the learning device 1 is provided with a function approximation device, but even if one function approximation device is used instead of two function approximation devices. good. That takes a learning object seismic associated data I n and learning object location data L k as the input data, as output data, the output estimated amplitude value ⁇ p n, and k, the estimated waveform vector ⁇ v n, and k (t) You may also use a function approximator. In this case, the coefficient obtained by the learning process by the learning device 1 is a coefficient applied to one function approximation device.
  • the prediction device 2 also has one function approximation device that is the same as the learning device 1, applies the trained coefficient to the function approximation device, and inputs the prediction target earthquake-related data “ ⁇ I” and the desired point data.
  • the prediction target earthquake-related data “ ⁇ I” and the desired point data By giving “ ⁇ L” to the function approximation device, the predicted amplitude value " ⁇ p" and the predicted waveform vector " ⁇ v" (t) can be obtained as output data.
  • a "computer-readable recording medium” is a communication line for transmitting a program via a network such as the Internet or a communication line such as a telephone line, and dynamically holds the program for a short period of time. It may also include a program that holds a program for a certain period of time, such as a volatile memory inside a computer system that is a server or a client in that case. Further, the above program may be for realizing a part of the above-mentioned functions, and may be further realized for realizing the above-mentioned functions in combination with a program already recorded in the computer system. It may be realized by using a programmable logic device such as FPGA (Field Programmable Gate Array).
  • FPGA Field Programmable Gate Array

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Abstract

A prediction method, according to the present invention, for predicting information pertaining to seismic waves at a desired location, said method comprising: an input step for inputting desired location information indicating a desired location; and a prediction step for predicting information pertaining to seismic waves at the desired location by using at least the desired location information, epicenter position information, and earthquake magnitude information, wherein, in the prediction step, geological information between the epicenter position and desired location is not used.

Description

予測方法、学習方法、予測装置、学習装置、予測プログラム及び学習プログラムPrediction method, learning method, prediction device, learning device, prediction program and learning program
　本発明は、予測方法、学習方法、予測装置、学習装置、予測プログラム及び学習プログラムに関する。 The present invention relates to a prediction method, a learning method, a prediction device, a learning device, a prediction program, and a learning program.
　地震シミュレーションにおいて、任意の地震に関する情報、例えば震源の位置や地震の規模等の情報から任意の地点における地震波を予測すること及びその予測の精度を向上させることは重要な課題である。予測対象地点に到達する地震波を予測する手法として、例えば非特許文献１に示されるように、以下の２つの手法が知られている。 In earthquake simulation, it is an important issue to predict seismic waves at any point from information on any earthquake, such as the position of the epicenter and the scale of the earthquake, and to improve the accuracy of the prediction. As a method for predicting a seismic wave reaching a prediction target point, for example, as shown in Non-Patent Document 1, the following two methods are known.
　第１の手法として、震源のマグニチュードと、震源から予測対象地点までの距離とを距離減衰式に適用することにより、予測対象地点に到達する地震波を予測するという手法が知られている。第２の手法として、震源と予測対象地点との間の地層の情報をモデル化して、予測対象地点に到達する地震波を予測するという手法が知られている。ここで、地層の情報とは、地層の性質を示す要素であり、例えば、地盤特性、伝搬特性、卓越周波数特性、インピーダンス特性などの情報である。 As the first method, there is known a method of predicting a seismic wave reaching a prediction target point by applying the magnitude of the epicenter and the distance from the epicenter to the prediction target point in a distance attenuation formula. As a second method, there is known a method of modeling the information of the stratum between the epicenter and the prediction target point and predicting the seismic wave reaching the prediction target point. Here, the information of the stratum is an element indicating the property of the stratum, and is, for example, information such as the ground characteristic, the propagation characteristic, the dominant frequency characteristic, and the impedance characteristic.
　しかしながら、第１の手法である距離減衰式を用いる手法では、震源から予測対象地点までの地層の情報が考慮されていないため予測精度が低くなるという問題がある。第２の手法では、地層の情報をモデル化するためには、膨大な地層の情報が必要であり、情報の収集に多大な労力と時間を要してしまうなど多くの問題がある。 However, the method using the distance attenuation formula, which is the first method, has a problem that the prediction accuracy is low because the information of the stratum from the epicenter to the prediction target point is not taken into consideration. In the second method, in order to model the information of the stratum, a huge amount of information of the stratum is required, and there are many problems such as a great deal of labor and time for collecting the information.
　上記事情に鑑み、本発明は、簡易に任意の地点における地震波に関する情報を高い精度で予測することができる技術の提供を目的としている。 In view of the above circumstances, an object of the present invention is to provide a technique capable of easily predicting information on a seismic wave at an arbitrary point with high accuracy.
　本発明の一態様は、所望の地点の地震波に関する情報を予測する予測方法であって、所望の地点を示す所望地点情報を入力する入力ステップと、少なくとも前記所望地点情報と、震源の位置情報と、地震の規模情報とを用いて前記所望の地点における地震波に関する情報を予測する予測ステップと、を有し、前記予測ステップにおいて、前記震源の位置と前記所望の地点との間の地層の情報を用いない予測方法である。 One aspect of the present invention is a prediction method for predicting information about a seismic wave at a desired point, which includes an input step for inputting desired point information indicating a desired point, at least the desired point information, and epicenter position information. It has a prediction step of predicting information about seismic waves at the desired point using earthquake magnitude information, and in the prediction step, information on the geological formation between the location of the epicenter and the desired point. This is a prediction method that is not used.
　本発明の一態様は、地震波に関する情報の予測の学習に用いられる学習対象地震関連データであって、少なくとも震源の位置情報及び地震の規模情報を含み前記震源の位置と前記所望の地点との間の地層の情報を含まない学習対象地震関連データと、前記学習対象地震関連データの地震によって発生した地震波を測定した地点を示す学習対象地点データと、前記学習対象地点データが示す地点において測定された前記地震波を示す地震波ベクトルとを入力する入力ステップと、前記地震波ベクトルを、振幅値と、波形ベクトルとに分離するデータ分離ステップと、前記学習対象地震関連データと、前記学習対象地震関連データに対応する前記学習対象地点データとを入力データと、学習により更新される係数とに基づいて得られる前記振幅値の推定値及び前記波形ベクトルの推定ベクトルと、前記入力データに対応する前記地震波ベクトルから得られた前記振幅値及び前記波形ベクトルとに基づいて、前記係数を更新する学習ステップと、を含む学習方法である。 One aspect of the present invention is learning target earthquake-related data used for learning prediction of information about seismic waves, including at least position information of a seismic source and magnitude information of an earthquake, between the position of the seismic source and the desired point. The learning target earthquake-related data that does not include the geological formation information, the learning target point data indicating the points where the seismic waves generated by the earthquake of the learning target earthquake-related data were measured, and the points indicated by the learning target point data were measured. Corresponds to the input step for inputting the seismic wave vector indicating the seismic wave, the data separation step for separating the seismic wave vector into the amplitude value and the waveform vector, the learning target earthquake-related data, and the learning target earthquake-related data. The learning target point data is obtained from the input data, the estimated value of the amplitude value obtained based on the coefficient updated by learning, the estimated vector of the waveform vector, and the seismic wave vector corresponding to the input data. It is a learning method including a learning step of updating the coefficient based on the said amplitude value and the said waveform vector.
　本発明の一態様は、所望の地点の地震波に関する情報を予測する予測装置であって、所望の地点を示す所望地点情報を入力する入力部と、少なくとも前記所望地点情報と、震源の位置情報と、地震の規模情報とを用いて前記所望の地点における地震波に関する情報を予測する予測部と、を備え、前記予測部は、前記地震波を予測する際、前記震源の位置と前記所望の地点との間の地層の情報を用いない予測装置である。 One aspect of the present invention is a predictor that predicts information about a seismic wave at a desired point, and includes an input unit for inputting desired point information indicating a desired point, at least the desired point information, and epicenter position information. The prediction unit includes a prediction unit that predicts information about a seismic wave at the desired point using the magnitude information of the earthquake, and the prediction unit determines the position of the epicenter and the desired point when predicting the seismic wave. It is a prediction device that does not use the information of the strata in between.
　本発明の一態様は、地震波に関する情報の予測の学習に用いられる学習対象地震関連データであって、少なくとも震源の位置情報及び地震の規模情報を含み前記震源の位置と前記所望の地点との間の地層の情報を含まない学習対象地震関連データと、前記学習対象地震関連データの地震によって発生した地震波を測定した地点を示す学習対象地点データと、前記学習対象地点データが示す地点において測定された前記地震波を示す地震波ベクトルとを入力する入力部と、前記地震波ベクトルを、振幅値と、波形ベクトルとに分離するデータ分離部と、前記学習対象地震関連データと、前記学習対象地震関連データに対応する前記学習対象地点データとを入力データと、学習により更新される係数とに基づいて得られる前記振幅値の推定値及び前記波形ベクトルの推定ベクトルと、前記入力データに対応する前記地震波ベクトルから得られた前記振幅値及び前記波形ベクトルとに基づいて、前記係数を更新する学習部と、を備える学習装置である。 One aspect of the present invention is learning target earthquake-related data used for learning prediction of information about seismic waves, including at least position information of a seismic source and magnitude information of an earthquake, between the position of the seismic source and the desired point. The learning target earthquake-related data that does not include the geological formation information, the learning target point data indicating the points where the seismic waves generated by the earthquake of the learning target earthquake-related data were measured, and the points indicated by the learning target point data were measured. Corresponds to the input unit for inputting the seismic wave vector indicating the seismic wave, the data separation unit for separating the seismic wave vector into the amplitude value and the waveform vector, the learning target earthquake-related data, and the learning target earthquake-related data. The learning target point data is obtained from the input data, the estimated value of the amplitude value obtained based on the coefficient updated by learning, the estimated vector of the waveform vector, and the seismic wave vector corresponding to the input data. It is a learning device including a learning unit for updating the coefficient based on the generated amplitude value and the waveform vector.
　本発明の一態様は、コンピュータに、所望の地点を示す所望地点情報を入力する入力ステップと、少なくとも前記所望地点情報と、震源の位置情報と、地震の規模情報とを用いて前記所望の地点における地震波に関する情報を予測する予測ステップと、を実行させ、前記予測ステップにおいて、前記震源の位置と前記所望の地点との間の地層の情報を用いない予測プログラムである。 One aspect of the present invention is the desired point using an input step of inputting desired point information indicating a desired point into a computer, at least the desired point information, the location information of the epicenter, and the magnitude information of the earthquake. It is a prediction program that executes a prediction step of predicting information about a seismic wave in the above, and does not use the information of the stratum between the position of the epicenter and the desired point in the prediction step.
　本発明の一態様は、コンピュータに、地震波に関する情報の予測の学習に用いられる学習対象地震関連データであって、少なくとも震源の位置情報及び地震の規模情報を含み前記震源の位置と前記所望の地点との間の地層の情報を含まない学習対象地震関連データと、前記学習対象地震関連データの地震によって発生した地震波を測定した地点を示す学習対象地点データと、前記学習対象地点データが示す地点において測定された前記地震波を示す地震波ベクトルとを入力する入力ステップと、前記地震波ベクトルを、振幅値と、波形ベクトルとに分離するデータ分離ステップと、前記学習対象地震関連データと、前記学習対象地震関連データに対応する前記学習対象地点データとを入力データと、学習により更新される係数とに基づいて得られる前記振幅値の推定値及び前記波形ベクトルの推定ベクトルと、前記入力データに対応する前記地震波ベクトルから得られた前記振幅値及び前記波形ベクトルとに基づいて、前記係数を更新する学習ステップと、を実行させるための学習プログラムである。 One aspect of the present invention is learning target earthquake-related data used for learning prediction of information about seismic waves in a computer, including at least position information of the earthquake source and magnitude information of the earthquake, and the position of the earthquake source and the desired point. At the learning target earthquake-related data that does not include the geological information between the two, the learning target point data indicating the point where the seismic wave generated by the earthquake of the learning target earthquake-related data was measured, and the point indicated by the learning target point data. An input step for inputting a seismic wave vector indicating the measured seismic wave, a data separation step for separating the seismic wave vector into an amplitude value and a waveform vector, the learning target earthquake-related data, and the learning target earthquake-related. The seismic wave corresponding to the input data, the estimated value of the amplitude value and the estimated vector of the waveform vector obtained based on the input data of the learning target point data corresponding to the data, and the coefficient updated by the learning, and the seismic wave corresponding to the input data. It is a learning program for executing a learning step of updating the coefficient based on the amplitude value obtained from the vector and the waveform vector.
　この発明によれば、簡易に任意の地点における地震波に関する情報を高い精度で予測することが可能となる。 According to the present invention, it is possible to easily predict information on seismic waves at any point with high accuracy.
実施形態における学習装置の構成を示すブロック図である。It is a block diagram which shows the structure of the learning apparatus in embodiment. 実施形態における学習装置が行う学習処理の流れを示すフローチャートである。It is a flowchart which shows the flow of the learning process performed by the learning apparatus in embodiment. 実施形態における予測装置の構成を示すブロック図である。It is a block diagram which shows the structure of the prediction apparatus in an embodiment. 実施形態における予測装置が行う予測処理の流れを示すフローチャートである。It is a flowchart which shows the flow of the prediction processing performed by the prediction apparatus in embodiment. 実施形態におけるシミュレーション結果（その１）を示した図である。It is a figure which showed the simulation result (the 1) in an embodiment. 実施形態におけるシミュレーション結果（その２）を示した図である。It is a figure which showed the simulation result (the 2) in an embodiment. 実施形態におけるシミュレーション結果（その３）を示した図である。It is a figure which showed the simulation result (the 3) in an embodiment. 実施形態におけるシミュレーション結果（その４）を示した図である。It is a figure which showed the simulation result (the 4) in an embodiment. 実施形態におけるシミュレーション結果（その５）を示した図である。It is a figure which showed the simulation result (the 5) in an embodiment. 実施形態におけるシミュレーション結果（その６）を示した図である。It is a figure which showed the simulation result (the 6) in an embodiment. 実施形態におけるシミュレーション結果（その７）を示した図である。It is a figure which showed the simulation result (the 7) in an embodiment. 実施形態におけるシミュレーション結果（その８）を示した図である。It is a figure which showed the simulation result (the 8) in an embodiment.
　以下、本発明の実施形態について図面を参照して説明する。本発明の実施形態では、簡易に任意の地点における地震波に関する情報を高い精度で予測する。より具体的には、本発明の実施形態では、所望する地点に到達することが想定される地震波に関するベクトルを算出することにより、結果として所望する地点に到達することが想定される地震波を予測する。そのために、図１に示す学習装置１が学習処理を行う。次に、図３に示す予測装置２が、学習処理によって生成された学習済みの係数を用いて予測を所望する地点における地震波に関する情報を予測する予測処理を行う流れで実施される。 Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the embodiment of the present invention, information on seismic waves at an arbitrary point is easily predicted with high accuracy. More specifically, in the embodiment of the present invention, by calculating a vector relating to a seismic wave that is expected to reach a desired point, a seismic wave that is expected to reach a desired point as a result is predicted. .. Therefore, the learning device 1 shown in FIG. 1 performs the learning process. Next, the prediction device 2 shown in FIG. 3 is executed in a flow of predicting information about a seismic wave at a desired point for prediction using the trained coefficients generated by the learning process.
（学習装置の構成）
　図１は、実施形態における学習装置１の構成を示すブロック図である。
　学習装置１は、入力部１１、データ分離部１２及び学習部１３を備える。入力部１１は、Ｎ個の学習対象地震関連データＩ０～（Ｎ－１）、Ｋ個の学習対象地点データＬ０～（Ｋ－１）及びＮ×Ｋ個の地震波ベクトルｗ０～（Ｎ－１），０～（Ｋ－１）（ｔ）を入力する。ここで、Ｎ，Ｋは、いずれも１以上の整数である。ｔは、時刻を示すパラメータである。ｔは、０～Ｔ－１の何れかの整数値であり、Ｔは１以上の整数である。ｔの単位は、例えば、「ミリ秒」程度の単位である。ｔは、「１ミリ秒」毎であってもよいし、「１０ミリ秒」毎であってもよい。以下、０～（Ｎ－１）の中の任意の整数値を「ｎ」で表し、０～（Ｋ－１）の中の任意の整数値を「ｋ」で表す。本明細書において、「入力する」は、「取り込む」の意味で用いるものとする。 (Configuration of learning device)
FIG. 1 is a block diagram showing the configuration of the learning device 1 in the embodiment.
The learning device 1 includes an input unit 11, a data separation unit 12, and a learning unit 13. The input unit 11 includes N learning target earthquake-related data I 0 to (N-1) , K learning target point data L 0 to (K-1), and N × K seismic wave vectors w 0 to (N). -1), 0 to (K-1) (t) are input. Here, N and K are all integers of 1 or more. t is a parameter indicating the time. t is an integer value from 0 to T-1, and T is an integer of 1 or more. The unit of t is, for example, a unit of about "milliseconds". t may be every "1 millisecond" or every "10 milliseconds". Hereinafter, any integer value from 0 to (N-1) is represented by "n", and any integer value from 0 to (K-1) is represented by "k". In the present specification, "input" is used to mean "capture".
　学習対象地震関連データＩｎは、過去に発生した地震に関するデータであり、例えば過去に発生した地震の震源の位置を示す震源位置データと、当該地震のマグニチュード等の地震の規模を示す地震規模データとを含んでいる。なお、震源位置データとは、例えば、地球の表面における１点である震央の座標に、震央の位置から震源の位置までの深さが加えられた三次元の座標データである。 Learning target seismic related data I n is data about the earthquake which occurred in the past, for example, and past the epicenter position data indicating the position of the epicenter earthquake seismic scale data indicating the magnitude of earthquake of magnitude or the like of the earthquake And include. The epicenter position data is, for example, three-dimensional coordinate data in which the depth from the position of the epicenter to the position of the epicenter is added to the coordinates of the epicenter, which is one point on the surface of the earth.
　学習対象地点データＬｋは、地球の表面における任意の地点の座標を示す座標データであり、例えば二次元の座標データである。なお、学習対象地点データＬｋが示す座標及び上記の学習対象地震関連データＩｎに含まれる震源位置データの震央の座標は、同一の二次元座標系における座標であり、例えば、震央の座標を原点とする二次元座標系における座標であってもよい。 The learning target point data Lk is coordinate data indicating the coordinates of an arbitrary point on the surface of the earth, and is, for example, two-dimensional coordinate data. Incidentally, the epicenter of the coordinates of the focal position data included in the learning object location data L k is the coordinate and the learning target seismic related data I n shown are the coordinates in the same two-dimensional coordinate system, for example, the epicenter of the coordinates It may be the coordinates in the two-dimensional coordinate system as the origin.
　地震波ベクトルｗｎ，ｋ（ｔ）は、学習対象地震関連データＩｎが示す過去に発生した地震の地震波を示す地震波ベクトルであって、学習対象地点データＬｋが示す地点で測定された地震波ベクトルである。なお、ｔが時刻を示すパラメータであることから、地震波ベクトルｗｎ，ｋ（ｔ）は、時系列のベクトルであり、ｗｎ，ｋ（０），ｗｎ，ｋ（１），…，ｗｎ，ｋ（Ｔ－２），ｗｎ，ｋ（Ｔ－１）というＴ個のベクトルから構成される。 Seismic wave vector w n, k (t) is a seismic wave vector indicating the seismic waves of earthquakes that occurred in the past indicated by the learning target earthquake-related data I n, seismic wave vector, which is measured at a point indicated by the learning target point data L k Is. Since t is a parameter indicating the time, the seismic wave vectors w n, k (t) are time-series vectors, and w n, k (0), w n, k (1), ..., W. It is composed of T vectors n, k (T-2), w n, k (T-1).
　学習対象地震関連データＩｎと、学習対象地点データＬｋと、地震波ベクトルｗｎ，ｋ（ｔ）とは、以下のような関連性がある。例えば、入力部１１に与える１つの学習対象地震関連データＩｎを任意に選択した場合、選択した学習対象地震関連データＩｎには、複数の地点で測定された複数の地震波ベクトルが存在する。選択した学習対象地震関連データＩｎに対応する複数の地震波ベクトルの中から入力部１１に与える地震波ベクトルｗｎ，ｋ（ｔ）を選択する。そうすると、選択された地震波ベクトルｗｎ，ｋ（ｔ）が測定された地点が自ずと入力部１１に与える学習対象地点データＬｋとして選択されるという関連性がある。 And the learning target earthquake-related data I n, and the learning target point data L k, seismic wave vector w n, and is k (t), there is a relevance such as the following. For example, if you select any one of the learning target seismic related data I n given to the input unit 11, the learning object seismic related data I n the selected, there are a plurality of seismic wave vectors measured at multiple points. Seismic vector w n to be given to the input unit 11 from among a plurality of seismic waves vector corresponding to the selected learning object seismic related data I n, selects a k (t). Then, there is a relation that the point where the selected seismic wave vector w n, k (t) is measured is naturally selected as the learning target point data L k to be given to the input unit 11.
　入力部１１は、０～（Ｎ－１）の整数値の中から何れか１つの「ｎ」と、０～（Ｋ－１）の整数値の中から何れか１つの「ｋ」をランダムに選択する。入力部１１は、選択した「ｎ」と「ｋ」に対応する地震波ベクトルｗｎ，ｋ（ｔ）をデータ分離部１２に出力する。入力部１１は、選択した「ｎ」と「ｋ」に対応する学習対象地震関連データＩｎ及び学習対象地点データＬｋを、学習部１３の振幅予測部２１と波形予測部３１とに出力する。 The input unit 11 randomly selects any one "n" from the integer values of 0 to (N-1) and any one "k" from the integer values of 0 to (K-1). select. The input unit 11 outputs the seismic wave vectors w n, k (t) corresponding to the selected “n” and “k” to the data separation unit 12. The input unit 11 outputs the learning object seismic associated data I n and the learning target spot data L k corresponding to the selected "n", "k", the amplitude prediction unit 21 and the waveform predictor 31 of the learning section 13 ..
　データ分離部１２は、入力部１１が出力する地震波ベクトルｗｎ，ｋ（ｔ）から次式（１）に基づいて振幅値ｐｎ，ｋを算出する。 The data separation unit 12 calculates the amplitude values pn and k from the seismic wave vectors w n and k (t) output by the input unit 11 based on the following equation (1).
Figure JPOXMLDOC01-appb-M000001
Figure JPOXMLDOC01-appb-M000001
　データ分離部１２は、次式（２）に、入力部１１が出力する地震波ベクトルｗｎ，ｋ（ｔ）と、式（１）に基づいて算出した振幅値ｐｎ，ｋとを適用して波形ベクトルｖｎ，ｋ（ｔ）を算出する。 The data separation unit 12 applies the seismic wave vector w n, k (t) output by the input unit 11 and the amplitude values pn, k calculated based on the equation (1) to the following equation (2). The waveform vector v n, k (t) is calculated.
Figure JPOXMLDOC01-appb-M000002
Figure JPOXMLDOC01-appb-M000002
　式（１）から分かるように、振幅値ｐｎ，ｋは、地震波ベクトルｗｎ，ｋ（ｔ）の絶対値の時間軸方向の総和であり、スカラーである。式（２）から分かるように、波形ベクトルｖｎ，ｋ（ｔ）は、地震波ベクトルｗｎ，ｋ（ｔ）を振幅値ｐｎ，ｋで除算することにより求められるベクトルである。そのため、波形ベクトルｖｎ，ｋ（ｔ）は、地震波ベクトルｗｎ，ｋ（ｔ）と同様に時系列のベクトルであり、ｖｎ，ｋ（０），ｖｎ，ｋ（１），…，ｖｎ，ｋ（Ｔ－２），ｖｎ，ｋ（Ｔ－１）というＴ個のベクトルから構成される。 As can be seen from the equation (1), the amplitude values pn and k are the sum of the absolute values of the seismic wave vectors w n and k (t) in the time axis direction and are scalars. As can be seen from the equation (2), the waveform vectors v n and k (t) are vectors obtained by dividing the seismic wave vectors w n and k (t) by the amplitude values pn and k. Therefore, the waveform vector v n, k (t) is a time-series vector similar to the seismic wave vector w n, k (t), and v n, k (0), v n, k (1), ..., It is composed of T vectors of v n, k (T-2) and v n, k (T-1).
　学習部１３は、振幅予測部２１、第１係数記憶部２２、振幅誤差算出部２３、波形予測部３１、第２係数記憶部３２、波形誤差算出部３３及び最適化部４１を備える。 The learning unit 13 includes an amplitude prediction unit 21, a first coefficient storage unit 22, an amplitude error calculation unit 23, a waveform prediction unit 31, a second coefficient storage unit 32, a waveform error calculation unit 33, and an optimization unit 41.
　第１係数記憶部２２は、振幅予測部２１が内部に備える関数近似器に適用される係数を記憶する。ここで、第１係数記憶部２２が記憶する係数とは、例えば、振幅予測部２１が内部に備える関数近似器が多層パーセプトロン等のニューラルネットワークである場合、重みの値及びバイアスの値である。初期状態では、第１係数記憶部２２は、ランダム値で初期化された係数を記憶する。 The first coefficient storage unit 22 stores the coefficient applied to the function approximator internally provided in the amplitude prediction unit 21. Here, the coefficient stored in the first coefficient storage unit 22 is, for example, a weight value and a bias value when the function approximation device included in the amplitude prediction unit 21 is a neural network such as a multi-layer perceptron. In the initial state, the first coefficient storage unit 22 stores the coefficient initialized with a random value.
　振幅予測部２１は、入力部１１が出力する学習対象地震関連データＩｎ及び学習対象地点データＬｋを入力データとして取り込み、１つの出力データを出力する関数近似器を内部に備える。ここで、振幅予測部２１の関数近似器が出力する出力データは、次式（３）で示される振幅値ｐｎ，ｋの推定値である。 Amplitude prediction unit 21 takes in the learning object seismic related data I n and the learning target spot data L k input unit 11 outputs as the input data, and a function approximator output one of the output data therein. Here, the output data output by the function approximator of the amplitude prediction unit 21 is an estimated value of the amplitude values pn and k represented by the following equation (3).
Figure JPOXMLDOC01-appb-M000003
Figure JPOXMLDOC01-appb-M000003
　以下、式（３）で示される振幅値ｐｎ，ｋの推定値を推定振幅値＾ｐｎ，ｋとして示す。振幅予測部２１は、第１係数記憶部２２から係数を読み出し、読み出した係数を内部に備える関数近似器に適用する。振幅予測部２１は、係数を適用した関数近似器に入力データを与え、入力データを与えることにより関数近似器が出力する推定振幅値＾ｐｎ，ｋを振幅誤差算出部２３に出力する。 Hereinafter, as an amplitude value p n, estimated amplitude value estimates of k ^ p n, k represented by the formula (3). The amplitude prediction unit 21 reads a coefficient from the first coefficient storage unit 22 and applies the read coefficient to a function approximator provided therein. The amplitude prediction unit 21 gives input data to the function approximation unit to which the coefficient is applied, and outputs the estimated amplitude values ^ pn, k output by the function approximation unit to the amplitude error calculation unit 23 by giving the input data.
　第２係数記憶部３２は、波形予測部３１が内部に備える関数近似器に適用される係数を記憶する。ここで、第２係数記憶部３２が記憶する係数とは、例えば、波形予測部３１が内部に備える関数近似器が多層パーセプトロン等のニューラルネットワークである場合、重みの値及びバイアスの値である。初期状態では、第２係数記憶部３２は、ランダム値で初期化された係数を記憶する。 The second coefficient storage unit 32 stores the coefficient applied to the function approximator internally provided in the waveform prediction unit 31. Here, the coefficient stored in the second coefficient storage unit 32 is, for example, a weight value and a bias value when the function approximation device included in the waveform prediction unit 31 is a neural network such as a multi-layer perceptron. In the initial state, the second coefficient storage unit 32 stores the coefficient initialized with a random value.
　波形予測部３１は、入力部１１が出力する学習対象地震関連データＩｎ及び学習対象地点データＬｋを入力データとして取り込み、Ｔ個の出力データを出力する関数近似器を内部に備える。ここで、波形予測部３１の関数近似器が出力するＴ個の出力データは、次式（４）で示される波形ベクトルｖｎ，ｋ（ｔ）の推定ベクトルである。 Waveform predictor 31 includes captures learning object seismic related data I n and the learning target spot data L k input unit 11 outputs as the input data, a function approximator outputs T output data therein. Here, the T output data output by the function approximator of the waveform prediction unit 31 are estimation vectors of the waveform vectors vn, k (t) represented by the following equation (4).
Figure JPOXMLDOC01-appb-M000004
Figure JPOXMLDOC01-appb-M000004
　以下、式（４）で示される波形ベクトルｖｎ，ｋ（ｔ）の推定ベクトルを推定波形ベクトル＾ｖｎ，ｋ（ｔ）として示す。なお、式（４）において、ｔが時刻を示すパラメータであることから、推定波形ベクトル＾ｖｎ，ｋ（ｔ）は、時系列のベクトルとなり、波形予測部３１の関数近似器は、＾ｖｎ，ｋ（０），＾ｖｎ，ｋ（１），…，＾ｖｎ，ｋ（Ｔ－２），＾ｖｎ，ｋ（Ｔ－１）というＴ個のベクトルを出力データとして出力する。 Hereinafter, the waveform vector v n of the formula (4), k (t) estimation vector estimated waveform vector ^ v n of the k (t). Since t is a parameter indicating the time in the equation (4), the estimated waveform vector ^ v n, k (t) is a time series vector, and the function approximator of the waveform prediction unit 31 is ^ v. Output T vectors of n, k (0), ^ v n, k (1), ..., ^ v n, k (T-2), ^ v n, k (T-1) as output data. ..
　波形予測部３１は、第２係数記憶部３２から係数を読み出し、読み出した係数を内部に備える関数近似器に適用する。波形予測部３１は、係数を適用した関数近似器に入力データを与え、入力データを与えることにより関数近似器が出力する推定波形ベクトル＾ｖｎ，ｋ（ｔ）を波形誤差算出部３３に出力する。 The waveform prediction unit 31 reads a coefficient from the second coefficient storage unit 32 and applies the read coefficient to a function approximator provided therein. The waveform predictor 31 gives input data to the function approximator to which the coefficient is applied, and outputs the estimated waveform vector ^ v n, k (t) output by the function approximator by giving the input data to the waveform error calculation unit 33. do.
　振幅誤差算出部２３は、次式（５）に示すように、振幅値ｐｎ，ｋと、推定振幅値＾ｐｎ，ｋとに基づいて振幅誤差Ｅｐを算出する。 As shown in the following equation (5), the amplitude error calculation unit 23 calculates the amplitude error E p based on the amplitude values pn and k and the estimated amplitude values ^ pn and k .
Figure JPOXMLDOC01-appb-M000005
Figure JPOXMLDOC01-appb-M000005
　波形誤差算出部３３は、次式（６）に示すように、波形ベクトルｖｎ，ｋ（ｔ）と、推定波形ベクトル＾ｖｎ，ｋ（ｔ）とに基づいて波形誤差Ｅｖを算出する。 As shown in the following equation (6), the waveform error calculation unit 33 calculates the waveform error E v based on the waveform vector v n, k (t) and the estimated waveform vector ^ v n, k (t). ..
Figure JPOXMLDOC01-appb-M000006
Figure JPOXMLDOC01-appb-M000006
　最適化部４１は、振幅誤差Ｅｐと、波形誤差Ｅｖとに基づいて定められる目的関数についての最小化問題を解くことにより、振幅予測部２１の関数近似器に適用する新たな係数と、波形予測部３１の関数近似器に適用する新たな係数とを算出する。 The optimization unit 41 has a new coefficient applied to the function approximator of the amplitude prediction unit 21 by solving a minimization problem for the objective function determined based on the amplitude error E p and the waveform error E v. A new coefficient to be applied to the function approximator of the waveform predictor 31 is calculated.
　最適化部４１は、算出した振幅予測部２１の関数近似器に適用する新たな係数を第１係数記憶部２２に上書きして係数を更新する。最適化部４１は、算出した波形予測部３１の関数近似器に適用する新たな係数を第２係数記憶部３２に上書きして係数を更新する。 The optimization unit 41 overwrites the first coefficient storage unit 22 with a new coefficient applied to the function approximator of the calculated amplitude prediction unit 21 to update the coefficient. The optimization unit 41 overwrites the second coefficient storage unit 32 with a new coefficient applied to the calculated function approximator of the waveform prediction unit 31 to update the coefficient.
（学習装置による処理）
　図２は、学習装置１による学習処理の流れを示すフローチャートである。入力部１１は、Ｎ個の学習対象地震関連データＩ０～（Ｎ－１）と、Ｋ個の学習対象地点データＬ０～（Ｋ－１）と、Ｎ×Ｋ個の地震波ベクトルｗ０～（Ｎ－１），０～（Ｋ－１）（ｔ）とを入力する（ステップＳ１０１）。入力部１１は、内部に備える学習ステップ数をカウントする学習ステップ数カウンタｒを「１」に初期化する（ステップＳ１０２）。 (Processing by learning device)
FIG. 2 is a flowchart showing the flow of learning processing by the learning device 1. The input unit 11 includes N learning target earthquake-related data I 0 to (N-1) , K learning target point data L 0 to (K-1) , and N × K seismic wave vectors w 0 to. (N-1), 0 to (K-1) (t) are input (step S101). The input unit 11 initializes the learning step number counter r that counts the number of learning steps provided internally to “1” (step S102).
　ステップＳ１０３からステップＳ１０８の処理を繰り返すループ処理が、Ｍ回繰り返し行われる。ここで、Ｍは、予め定められるバッチサイズであり、例えば、「６４」程度の値が適用される。 The loop process that repeats the process from step S103 to step S108 is repeated M times. Here, M is a predetermined batch size, and for example, a value of about "64" is applied.
　入力部１１は、０～（Ｎ－１）の整数値の中から何れか１つの「ｎ」と、０～（Ｋ－１）の整数値の中から何れか１つの「ｋ」をランダムに選択する。入力部１１は、選択した「ｎ」と「ｋ」に対応する地震波ベクトルｗｎ，ｋ（ｔ）をデータ分離部１２に出力する。入力部１１は、選択した「ｎ」と「ｋ」に対応する学習対象地震関連データＩｎ及び学習対象地点データＬｋを、学習部１３の振幅予測部２１と波形予測部３１とに出力する（ステップＳ１０３）。 The input unit 11 randomly selects any one "n" from the integer values of 0 to (N-1) and any one "k" from the integer values of 0 to (K-1). select. The input unit 11 outputs the seismic wave vectors w n, k (t) corresponding to the selected “n” and “k” to the data separation unit 12. The input unit 11 outputs the learning object seismic related data I n and the learning target spot data L k corresponding to the selected "n", "k", the amplitude prediction part 21 and the waveform predictor 31 of the learning section 13 (Step S103).
　データ分離部１２は、式（１）と式（２）に基づいて、地震波ベクトルｗｎ，ｋ（ｔ）を振幅値ｐｎ，ｋと、波形ベクトルｖｎ，ｋ（ｔ）とに分離する。データ分離部１２は、分離した振幅値ｐｎ，ｋを振幅誤差算出部２３に出力し、分離した波形ベクトルｖｎ，ｋ（ｔ）を波形誤差算出部３３に出力する（ステップＳ１０４）。 The data separation unit 12 separates the seismic wave vectors w n, k (t) into amplitude values pn, k and waveform vectors v n, k (t) based on the equations (1) and (2). .. The data separation unit 12 outputs the separated amplitude values pn and k to the amplitude error calculation unit 23, and outputs the separated waveform vectors v n and k (t) to the waveform error calculation unit 33 (step S104).
　振幅予測部２１は、入力部１１が出力した学習対象地震関連データＩｎ及び学習対象地点データＬｋを取り込む。振幅予測部２１は、第１係数記憶部２２から係数を読み出し、読み出した係数を内部に備える関数近似器に適用する（ステップＳ１０５－１）。 Amplitude prediction unit 21 takes in the learning object seismic related data I n and the learning target spot data L k is the input unit 11 and output. The amplitude prediction unit 21 reads a coefficient from the first coefficient storage unit 22 and applies the read coefficient to a function approximator internally provided (step S105-1).
　振幅予測部２１は、読み出した係数を適用した関数近似器に、学習対象地震関連データＩｎ及び学習対象地点データＬｋを入力データとして与える。振幅予測部２１の関数近似器は、与えられた入力データと、係数とに基づいて推定振幅値＾ｐｎ，ｋを算出する。振幅予測部２１の関数近似器は、算出した推定振幅値＾ｐｎ，ｋを出力データとして出力する。振幅予測部２１は、関数近似器が出力した推定振幅値＾ｐｎ，ｋを振幅誤差算出部２３に出力する（ステップＳ１０６－１）。 Amplitude prediction unit 21, a function approximator according to the read-out coefficients to provide a learning object seismic related data I n and learning object location data L k as input data. The function approximation unit of the amplitude prediction unit 21 calculates the estimated amplitude value ^ pn, k based on the given input data and the coefficient. The function approximation unit of the amplitude prediction unit 21 outputs the calculated estimated amplitude values ^ pn and k as output data. The amplitude prediction unit 21 outputs the estimated amplitude values ^ pn, k output by the function approximator to the amplitude error calculation unit 23 (step S106-1).
　振幅誤差算出部２３は、データ分離部１２が出力した振幅値ｐｎ，ｋと、振幅予測部２１が出力した推定振幅値＾ｐｎ，ｋとを取り込む。振幅誤差算出部２３は、式（５）にしたがって、振幅値ｐｎ，ｋと、推定振幅値＾ｐｎ，ｋとから振幅誤差Ｅｐを算出する。振幅誤差算出部２３は、算出した振幅誤差Ｅｐを最適化部４１に出力する（ステップＳ１０７－１）。 The amplitude error calculation unit 23 takes in the amplitude values pn and k output by the data separation unit 12 and the estimated amplitude values ^ pn and k output by the amplitude prediction unit 21. The amplitude error calculation unit 23 calculates the amplitude error E p from the amplitude values pn and k and the estimated amplitude values ^ pn and k according to the equation (5). Amplitude error calculating unit 23 outputs the calculated amplitude error E p in the optimization unit 41 (Step S107-1).
　波形予測部３１は、入力部１１が出力した学習対象地震関連データＩｎ及び学習対象地点データＬｋを取り込む。波形予測部３１は、第２係数記憶部３２から係数を読み出し、読み出した係数を内部に備える関数近似器に適用する（ステップＳ１０５－２）。 Waveform predictor 31 takes in the learning object seismic related data I n and the learning target spot data L k is the input unit 11 and output. The waveform prediction unit 31 reads a coefficient from the second coefficient storage unit 32 and applies the read coefficient to a function approximator internally provided (step S105-2).
　波形予測部３１は、読み出した係数を適用した関数近似器に、学習対象地震関連データＩｎ及び学習対象地点データＬｋを入力データとして与える。波形予測部３１の関数近似器は、与えられた入力データと、係数とに基づいて推定波形ベクトル＾ｖｎ，ｋ（ｔ）を算出する。波形予測部３１の関数近似器は、算出した推定波形ベクトル＾ｖｎ，ｋ（ｔ）を出力データとして出力する。波形予測部３１は、関数近似器が出力した推定波形ベクトル＾ｖｎ，ｋ（ｔ）を波形誤差算出部３３に出力する（ステップＳ１０６－２）。 Waveform predictor 31, the function approximator according to the read-out coefficients to provide a learning object seismic related data I n and learning object location data L k as input data. The function approximation unit of the waveform prediction unit 31 calculates the estimated waveform vector ^ v n, k (t) based on the given input data and the coefficient. The function approximator of the waveform predictor 31 outputs the calculated estimated waveform vector ^ v n, k (t) as output data. The waveform prediction unit 31 outputs the estimated waveform vector ^ v n, k (t) output by the function approximator to the waveform error calculation unit 33 (step S106-2).
　波形誤差算出部３３は、データ分離部１２が出力する波形ベクトルｖｎ，ｋ（ｔ）と、波形予測部３１が出力する推定波形ベクトル＾ｖｎ，ｋ（ｔ）とを取り込む。波形誤差算出部３３は、式（６）にしたがって、波形ベクトルｖｎ，ｋ（ｔ）と、推定波形ベクトル＾ｖｎ，ｋ（ｔ）とから波形誤差Ｅｖを算出する。波形誤差算出部３３は、算出した波形誤差Ｅｖを最適化部４１に出力する（ステップＳ１０７－２）。 The waveform error calculation unit 33 takes in the waveform vector v n, k (t) output by the data separation unit 12 and the estimated waveform vector ^ v n, k (t) output by the waveform prediction unit 31. The waveform error calculation unit 33 calculates the waveform error E v from the waveform vector v n, k (t) and the estimated waveform vector ^ v n, k (t) according to the equation (6). Waveform error calculating unit 33 outputs the calculated waveform error E v optimization unit 41 (Step S107-2).
　最適化部４１は、振幅誤差算出部２３が出力した振幅誤差Ｅｐと、波形誤差算出部３３が出力した波形誤差Ｅｖとを取り込む。ここで、ループＬａ１ｓ～Ｌａ１ｅの処理における処理の回数をｍで表すとする。ｍは、１～Ｍまでの間の整数値となり、以下の説明ではｍ回目の振幅誤差ＥｐをＥｐ，ｍとして示し、ｍ回目の波形誤差ＥｖをＥｖ，ｍとして示す。最適化部４１は、振幅誤差Ｅｐ，ｍと、波形誤差Ｅｖ，ｍと内部の記憶領域に書き込んで記憶させる（ステップＳ１０８）。 Optimization unit 41 takes in the amplitude error E p for the amplitude error calculating unit 23 outputs, and a waveform error E v waveform error calculating unit 33 is outputted. Here, it is assumed that the number of processes in the processes of the loops La1s to La1e is represented by m. m is an integer value between 1 and M, and in the following description, the m-th amplitude error E p is shown as E p, m , and the m-th waveform error E v is shown as E v, m. The optimization unit 41 writes and stores the amplitude error E p, m , the waveform error E v, m, and the internal storage area (step S108).
　ｍが、Ｍ未満である場合、すなわちＭ回の繰り返しが終わっていない場合、最適化部４１は、処理の継続を示す処理継続指示信号を入力部１１に出力する。入力部１１は、最適化部４１から処理継続指示信号を受けると、再びステップＳ１０３の処理を行い、それに伴いステップＳ１０４～Ｓ１０８の処理が行われる。一方、ｍが、Ｍに一致した場合、すなわちＭ回の繰り返しが終了した場合、ループＬａ１ｓ～Ｌａ１ｅの処理は終了する（ループＬａ１ｅ）。 When m is less than M, that is, when the repetition of M times has not been completed, the optimization unit 41 outputs a processing continuation instruction signal indicating the continuation of processing to the input unit 11. When the input unit 11 receives the processing continuation instruction signal from the optimization unit 41, the processing of step S103 is performed again, and the processing of steps S104 to S108 is performed accordingly. On the other hand, when m matches M, that is, when the repetition of M times is completed, the processing of loops La1s to La1e ends (loop La1e).
　ループ処理Ｌａ１ｓ～Ｌａ１ｅが終了した場合、最適化部４１は、内部の記憶領域が記憶するＭ回分の振幅誤差Ｅｐ，１～Ｍ及び波形誤差Ｅｖ，１～Ｍを読み出す。最適化部４１は、読み出した振幅誤差Ｅｐ，１～Ｍ及び波形誤差Ｅｖ，１～Ｍに基づいて、次式（７）を目的関数とする最小化問題を解くことにより、振幅予測部２１の関数近似器に適用する新たな係数と、波形予測部３１の関数近似器に適用する新たな係数を算出する。最小化問題の解法としては、例えば最急降下法等の勾配法が適用される。 When the loop processing La1s to La1e is completed, the optimization unit 41 reads out the amplitude errors E p, 1 to M and the waveform errors E v, 1 to M for M times stored in the internal storage area. The optimization unit 41 solves the minimization problem using the following equation (7) as the objective function based on the read amplitude errors E p, 1 to M and the waveform errors E v, 1 to M, and thereby the amplitude prediction unit. A new coefficient applied to the function approximation device of 21 and a new coefficient applied to the function approximation device of the waveform prediction unit 31 are calculated. As a method for solving the minimization problem, a gradient method such as the steepest descent method is applied.
Figure JPOXMLDOC01-appb-M000007
Figure JPOXMLDOC01-appb-M000007
　最適化部４１は、算出した振幅予測部２１の関数近似器に適用する新たな係数を第１係数記憶部２２に上書きして係数を更新する。最適化部４１は、算出した波形予測部３１の関数近似器に適用する新たな係数を第２係数記憶部３２に上書きして係数を更新する（ステップＳ１０９）。 The optimization unit 41 overwrites the first coefficient storage unit 22 with a new coefficient applied to the function approximator of the calculated amplitude prediction unit 21 to update the coefficient. The optimization unit 41 overwrites the second coefficient storage unit 32 with a new coefficient applied to the calculated function approximator of the waveform prediction unit 31 to update the coefficient (step S109).
　最適化部４１は、係数を更新したことを通知する係数更新通知信号を入力部１１に出力する。入力部１１は、最適化部４１から係数更新通知信号を受けると、学習ステップ数カウンタｒが、予め定められる学習ステップ上限回数に一致するか否かを判定する（ステップＳ１１０）。ここで、予め定められる学習ステップ上限回数には、式（７）の目的関数によって示される誤差Ｅが十分に収束する程度の学習回数の値が適用され、例えば、「１００００」程度の値が適用される。 The optimization unit 41 outputs a coefficient update notification signal for notifying that the coefficient has been updated to the input unit 11. Upon receiving the coefficient update notification signal from the optimization unit 41, the input unit 11 determines whether or not the learning step number counter r matches the predetermined learning step upper limit number (step S110). Here, a value of the number of learning times to which the error E represented by the objective function of the equation (7) sufficiently converges is applied to the predetermined upper limit number of learning steps, and for example, a value of about "10000" is applied. Will be done.
　入力部１１は、学習ステップ数カウンタｒが学習ステップ上限回数に一致していないと判定した場合（ステップＳ１１０－Ｎｏ）、学習ステップ数カウンタｒに１を加算する（ステップＳ１１１）。その後、再びループＬａ１ｓ～Ｌａ１ｅの処理が行われる。 When the input unit 11 determines that the learning step number counter r does not match the learning step upper limit number (step S110-No), 1 is added to the learning step number counter r (step S111). After that, the loops La1s to La1e are processed again.
　一方、入力部１１は、学習ステップ数カウンタｒが学習ステップ上限回数に一致していると判定した場合（ステップＳ１１０－Ｙｅｓ）、処理を終了する。処理が終了した段階で、第１係数記憶部２２と、第２係数記憶部３２とには、式（７）の目的関数によって示される誤差Ｅが十分収束した学習済みの係数が記憶されることになる。 On the other hand, when the input unit 11 determines that the learning step number counter r matches the upper limit number of learning steps (step S110-Yes), the input unit 11 ends the process. At the stage when the processing is completed, the first coefficient storage unit 22 and the second coefficient storage unit 32 store the learned coefficients in which the error E represented by the objective function of the equation (7) is sufficiently converged. become.
　なお、図２のフローチャートにおいて、ステップＳ１０４の処理と、ステップＳ１０５－１，Ｓ１０６－１，Ｓ１０７－１の一連の処理と、ステップＳ１０５－２，Ｓ１０６－２，Ｓ１０７－２の一連の処理とは並列に行われ、ステップＳ１０３の処理は、少なくともステップＳ１０７－１，Ｓ１０７－２の処理が開始されるまでに完了するように行われる。 In the flowchart of FIG. 2, what is the process of step S104, the series of processes of steps S105-1, S106-1, and S107-1, and the series of processes of steps S105-2, S106-2, and S107-2? It is performed in parallel, and the processing of step S103 is performed so as to be completed by at least the processing of steps S107-1 and S107-2 is started.
　ステップＳ１０４の処理、ステップＳ１０５－１，Ｓ１０６－１，Ｓ１０７－１の一連の処理及びステップＳ１０５－２，Ｓ１０６－２，Ｓ１０７－２の一連の処理は、必ずしも並列に行われなくてもよい。例えば、ステップＳ１０４の処理、ステップＳ１０５－１，Ｓ１０６－１，Ｓ１０７－１の一連の処理、ステップＳ１０５－２，Ｓ１０６－２，Ｓ１０７－２の一連の処理の順に行われてもよく、ステップＳ１０５－１，Ｓ１０６－１，Ｓ１０７－１の一連の処理と、ステップＳ１０５－２，Ｓ１０６－２，Ｓ１０７－２の一連の処理の順番が入れ替わってもよい。 The process of step S104, the series of processes of steps S105-1, S106-1, and S107-1 and the series of processes of steps S105-2, S106-2, and S107-2 do not necessarily have to be performed in parallel. For example, the process of step S104, the series of processes of steps S105-1, S106-1, and S107-1 may be performed, and the series of processes of steps S105-2, S106-2, and S107-2 may be performed in this order. The order of the series of processes of -1, S106-1, S107-1 and the series of processes of steps S105-2, S106-2, and S107-2 may be exchanged.
　ステップＳ１０５－１，Ｓ１０５－２の係数を関数近似器に適用する処理は、ループ処理Ｌａ１ｓ～Ｌａ１ｅのＭ回の処理の間、係数は更新されない。そのため、係数を関数近似器に適用する処理は、ループ処理Ｌａ１ｓ～Ｌａ１ｅの毎回において行うのではなく、初回に一度だけ行われるようにしてもよい。 In the process of applying the coefficients of steps S105-1 and S105-2 to the function approximator, the coefficients are not updated during the M times of loop processing La1s to La1e. Therefore, the process of applying the coefficient to the function approximation device may be performed only once at the first time, instead of being performed each time of the loop processes La1s to La1e.
（予測装置の構成）
　図３は、予測装置２の構成を示すブロック図である。なお、予測装置２において、学習装置１と同一の構成については同一の符号を付し、以下、異なる構成について説明する。予測装置２は、入力部５１と、予測部５２とを備える。入力部５１は、式（８）の記号で示される予測対象地震関連データと、式（９）の記号で示される所望地点データとを入力する。以下、式（８）の記号を“～Ｉ”として示し、式（９）の記号を“～Ｌ”として示す。 (Configuration of prediction device)
FIG. 3 is a block diagram showing the configuration of the prediction device 2. In the prediction device 2, the same configuration as that of the learning device 1 is designated by the same reference numerals, and different configurations will be described below. The prediction device 2 includes an input unit 51 and a prediction unit 52. The input unit 51 inputs the predicted earthquake-related data represented by the symbol of the formula (8) and the desired point data represented by the symbol of the formula (9). Hereinafter, the symbol of the formula (8) is shown as “~ I”, and the symbol of the formula (9) is shown as “~ L”.
Figure JPOXMLDOC01-appb-M000008
Figure JPOXMLDOC01-appb-M000008
Figure JPOXMLDOC01-appb-M000009
Figure JPOXMLDOC01-appb-M000009
　予測対象地震関連データ“～Ｉ”は、予測の対象となる地震に関するデータであり、例えば予測の対象となる地震の震源の位置を示す震源位置データと、当該地震のマグニチュード等の地震の規模を示す地震規模データを含んでいる。 The earthquake-related data "~ I" to be predicted is data related to the earthquake to be predicted, for example, the epicenter position data indicating the position of the epicenter of the earthquake to be predicted and the magnitude of the earthquake. Includes seismic scale data shown.
　所望地点データ“～Ｌ”は、予測対象地震関連データ“～Ｉ”の地震によって発生する地震波の予測を所望する地点の座標を示す座標データであり、例えば二次元の座標データである。 The desired point data "-L" is coordinate data indicating the coordinates of the desired point for predicting the seismic wave generated by the earthquake of the prediction target earthquake-related data "-I", and is, for example, two-dimensional coordinate data.
　予測部５２は、振幅予測部２１、学習済み第１係数記憶部６２、波形予測部３１、学習済み第２係数記憶部７２及びデータ合成部８１を備える。 The prediction unit 52 includes an amplitude prediction unit 21, a learned first coefficient storage unit 62, a waveform prediction unit 31, a learned second coefficient storage unit 72, and a data synthesis unit 81.
　学習済み第１係数記憶部６２は、図２に示した学習装置１による学習処理において最終的に第１係数記憶部２２に書き込まれている学習済みの係数を記憶する。最終的に第１係数記憶部２２に書き込まれている学習済みの係数は、ステップＳ１１０において入力部１１が、「Ｙｅｓ」の判定を行って処理を終了した時点の係数である。 The learned first coefficient storage unit 62 stores the learned coefficient finally written in the first coefficient storage unit 22 in the learning process by the learning device 1 shown in FIG. The learned coefficient finally written in the first coefficient storage unit 22 is a coefficient at the time when the input unit 11 determines “Yes” in step S110 and finishes the process.
　学習済み第２係数記憶部７２は、図２に示した学習装置１による学習処理において最終的に第２係数記憶部３２に書き込まれている学習済みの係数を記憶する。最終的に第２係数記憶部３２に書き込まれている学習済みの係数は、ステップＳ１１０において入力部１１が、「Ｙｅｓ」の判定を行って処理を終了した時点の係数である。 The learned second coefficient storage unit 72 stores the learned coefficient finally written in the second coefficient storage unit 32 in the learning process by the learning device 1 shown in FIG. The learned coefficient finally written in the second coefficient storage unit 32 is a coefficient at the time when the input unit 11 determines “Yes” in step S110 and finishes the process.
　データ合成部８１は、振幅予測部２１の出力データと、波形予測部３１の出力データとに基づいて、予測対象地震関連データ“～Ｉ”の地震によって発生する地震波であって所望地点データ“～Ｌ”が示す地点に到達する地震波を算出する。 Based on the output data of the amplitude prediction unit 21 and the output data of the waveform prediction unit 31, the data synthesis unit 81 is a seismic wave generated by the earthquake of the earthquake-related data “~ I” to be predicted, and the desired point data “~. Calculate the seismic wave that reaches the point indicated by "L".
（予測装置による処理）
　図４は、予測装置２による予測処理の流れを示すフローチャートである。
　入力部５１は、予測対象地震関連データ“～Ｉ”及び所望地点データ“～Ｌ”を入力し、入力した予測対象地震関連データ“～Ｉ”及び所望地点データ“～Ｌ”を振幅予測部２１と、波形予測部３１とに出力する（ステップＳ２０１）。 (Processing by predictor)
FIG. 4 is a flowchart showing the flow of prediction processing by the prediction device 2.
The input unit 51 inputs the prediction target earthquake-related data "-I" and the desired point data "-L", and inputs the input prediction target earthquake-related data "-I" and the desired point data "-L" to the amplitude prediction unit 21. Is output to the waveform prediction unit 31 (step S201).
　振幅予測部２１は、入力部５１が出力する予測対象地震関連データ“～Ｉ”及び所望地点データ“～Ｌ”を取り込む。振幅予測部２１は、学習済み第１係数記憶部６２から学習済みの係数を読み出し、読み出した学習済みの係数を内部に備える関数近似器に適用する（ステップＳ２０２－１）。 The amplitude prediction unit 21 takes in the prediction target earthquake-related data “~ I” and the desired point data “~ L” output by the input unit 51. The amplitude prediction unit 21 reads the learned coefficient from the learned first coefficient storage unit 62, and applies the read learned coefficient to the function approximation device provided therein (step S202-1).
　振幅予測部２１は、学習済みの係数を適用した関数近似器に、予測対象地震関連データ“～Ｉ”及び所望地点データ“～Ｌ”を入力データとして与える。振幅予測部２１の関数近似器は、与えられた入力データと、係数とに基づいて次式（１０）の記号で示される予測振幅値を算出する。 The amplitude prediction unit 21 gives the prediction target earthquake-related data "~ I" and the desired point data "~ L" as input data to the function approximation device to which the learned coefficients are applied. The function approximation unit of the amplitude prediction unit 21 calculates the predicted amplitude value represented by the symbol of the following equation (10) based on the given input data and the coefficient.
Figure JPOXMLDOC01-appb-M000010
Figure JPOXMLDOC01-appb-M000010
　以下、式（１０）の記号を“～ｐ”として示す。振幅予測部２１の関数近似器は、算出した予測振幅値“～ｐ”を出力データとして出力する。振幅予測部２１は、関数近似器が出力した予測振幅値“～ｐ”をデータ合成部８１に出力する（ステップＳ２０３－１）。 Hereinafter, the symbol of the formula (10) is shown as "~ p". The function approximator of the amplitude prediction unit 21 outputs the calculated predicted amplitude value “~ p” as output data. The amplitude prediction unit 21 outputs the predicted amplitude value “~ p” output by the function approximator to the data synthesis unit 81 (step S203-1).
　波形予測部３１は、入力部５１が出力する予測対象地震関連データ“～Ｉ”及び所望地点データ“～Ｌ”を取り込む。波形予測部３１は、学習済み第２係数記憶部７２から学習済みの係数を読み出し、読み出した学習済みの係数を内部に備える関数近似器に適用する（ステップＳ２０２－２）。 The waveform prediction unit 31 takes in the prediction target earthquake-related data “~ I” and the desired point data “~ L” output by the input unit 51. The waveform prediction unit 31 reads the learned coefficient from the learned second coefficient storage unit 72, and applies the read learned coefficient to the function approximator internally provided (step S202-2).
　波形予測部３１は、学習済みの係数を適用した関数近似器に、予測対象地震関連データ“～Ｉ”及び所望地点データ“～Ｌ”を入力データとして与える。波形予測部３１の関数近似器は、与えられた入力データと、係数とに基づいて次式（１１）の記号で示される予測波形ベクトルを算出する。 The waveform prediction unit 31 gives the prediction target earthquake-related data "~ I" and the desired point data "~ L" as input data to the function approximation device to which the learned coefficients are applied. The function approximation unit of the waveform prediction unit 31 calculates the prediction waveform vector represented by the symbol of the following equation (11) based on the given input data and the coefficient.
Figure JPOXMLDOC01-appb-M000011
Figure JPOXMLDOC01-appb-M000011
　以下、式（１１）の記号を“～ｖ”（ｔ）として示す。波形予測部３１の関数近似器は、算出した予測波形ベクトル“～ｖ”（ｔ）を出力データとして出力する。なお、ｔが時刻を示すパラメータであることから、予測波形ベクトル“～ｖ”（ｔ）は、時系列のベクトルであり、“～ｖ”（０），“～ｖ”（１），…，“～ｖ”（Ｔ－２），“～ｖ”（Ｔ－１）というＴ個のベクトルから構成される。波形予測部３１は、関数近似器が出力した予測波形ベクトル“～ｖ”（ｔ）をデータ合成部８１に出力する（ステップＳ２０３－２）。 Hereinafter, the symbol of the formula (11) is shown as “~ v” (t). The function approximator of the waveform prediction unit 31 outputs the calculated predicted waveform vector “~ v” (t) as output data. Since t is a parameter indicating the time, the predicted waveform vector "~ v" (t) is a time series vector, and "~ v" (0), "~ v" (1), ..., It is composed of T vectors "~ v" (T-2) and "~ v" (T-1). The waveform prediction unit 31 outputs the prediction waveform vector “~ v” (t) output by the function approximator to the data synthesis unit 81 (step S203-2).
　データ合成部８１は、振幅予測部２１が出力する予測振幅値“～ｐ”と、波形予測部３１が出力する予測波形ベクトル“～ｖ”（ｔ）とに基づいて、次式（１２）の右辺に示される演算を行い、式（１２）の左辺に示される予測地震波ベクトル“～ｗ”（ｔ）を算出する（ステップＳ２０４）。予測地震波ベクトル“～ｗ”（ｔ）は、所望の地点における地震波に関する情報の一態様である。 The data synthesis unit 81 has the following equation (12) based on the predicted amplitude value “~ p” output by the amplitude prediction unit 21 and the predicted waveform vector “~ v” (t) output by the waveform prediction unit 31. The calculation shown on the right side is performed to calculate the predicted seismic wave vector “~ w” (t) shown on the left side of the equation (12) (step S204). The predicted seismic wave vector “~ w” (t) is an aspect of information about the seismic wave at a desired point.
Figure JPOXMLDOC01-appb-M000012
Figure JPOXMLDOC01-appb-M000012
　式（１２）から分かるように、予測地震波ベクトル“～ｗ”（ｔ）は、予測波形ベクトル“～ｖ”（ｔ）に予測振幅値“～ｐ”を乗算することにより求められるベクトルである。そのため、予測地震波ベクトル“～ｗ”（ｔ）は、予測波形ベクトル“～ｖ”（ｔ）と同様に時系列のベクトルであり、“～ｗ”（０），“～ｗ”（１），…，“～ｗ”（Ｔ－２），“～ｗ”（Ｔ－１）というＴ個のベクトルから構成される。 As can be seen from the equation (12), the predicted seismic wave vector "~ w" (t) is a vector obtained by multiplying the predicted waveform vector "~ v" (t) by the predicted amplitude value "~ p". Therefore, the predicted seismic wave vector "~ w" (t) is a time-series vector like the predicted waveform vector "~ v" (t), and is "~ w" (0), "~ w" (1), ..., It is composed of T vectors of "~ w" (T-2) and "~ w" (T-1).
　なお、ステップＳ２０２－１，Ｓ２０３－１の一連の処理及びステップＳ２０２－２，Ｓ２０３－２の一連の処理は、並列に行われるように示しているが、必ずしも並列に行われなくてもよい。ステップＳ２０２－１，Ｓ２０３－１の一連の処理、ステップＳ２０２－２，Ｓ２０３－２の一連の処理の順に処理が行われてもよいし、逆の順序で処理が行われてもよい。 Although the series of processes in steps S202-1 and S203-1 and the series of processes in steps S202-2 and S203-2 are shown to be performed in parallel, they do not necessarily have to be performed in parallel. The processes may be performed in the order of the series of processes of steps S202-1 and S203-1, and the series of processes of steps S202-2 and S203-2, or may be performed in the reverse order.
（シミュレーション結果）
　図５から図１２は、８通りの異なる予測を所望する地点における８通りの異なる地震により発生した地震波の波形を示すグラフである。なお、本実施形態の学習装置１と、予測装置２との比較のために、以下に示すような構成の地震波ベクトルｗｎ，ｋ（ｔ）を振幅値ｐｎ，ｋと波形ベクトルｖｎ，ｋ（ｔ）に分離しない学習装置と、当該学習装置に対応する予測装置とを用いたシミュレーションを行っている。説明の便宜上、当該学習装置を「分離なし学習装置」といい、当該予測装置を「分離なし予測装置」という。 (simulation result)
5 to 12 are graphs showing the waveforms of seismic waves generated by eight different earthquakes at points where eight different predictions are desired. For comparison between the learning device 1 and the prediction device 2 of the present embodiment, the seismic wave vectors w n, k (t) having the configuration as shown below are set to the amplitude values pn, k and the waveform vector vn , A simulation is performed using a learning device that does not separate into k (t) and a prediction device corresponding to the learning device. For convenience of explanation, the learning device is referred to as a "learning device without separation", and the prediction device is referred to as a "prediction device without separation".
　分離なし学習装置は、学習対象地震関連データＩｎと、学習対象地点データＬｋとを入力データとし、地震波ベクトルｗｎ，ｋ（ｔ）の推定ベクトルを出力データとする関数近似器を備えている。分離なし学習装置は、地震波ベクトルｗｎ，ｋ（ｔ）の推定ベクトルと、入力データに対応する地震波ベクトルｗｎ，ｋ（ｔ）との誤差を算出し、算出した誤差を減少させるように関数近似器に適用する係数を更新する学習処理を行う。分離なし予測装置は、分離なし学習装置と同一の関数近似器を備えており、予測対象地震関連データ“～Ｉ”と、所望地点データ“～Ｌ”とを入力データとして与えることにより、関数近似器は、分離なし学習装置が学習処理によって生成した学習済みの係数を利用して、予測地震波ベクトル“～ｗ”（ｔ）を算出する。 No separation learning apparatus includes a learning object seismic related data I n, a learning object location data L k and input data, seismic vector w n, k function approximator to output data to estimate a vector of (t) There is. No separation learning device function so as to reduce the estimated vector of seismic vector w n, k (t), seismic vector w n corresponding to the input data, calculates an error between the k (t), the calculated error Performs learning processing to update the coefficients applied to the approximator. The non-separation prediction device is equipped with the same function approximation device as the non-separation learning device, and the function approximation is performed by giving the prediction target earthquake-related data "~ I" and the desired point data "~ L" as input data. The instrument calculates the predicted seismic wave vector “~ w” (t) by using the trained coefficient generated by the learning device without separation by the learning process.
　図５から図１２における（ａ）のグラフは、正解データ、すなわち実際に測定された地震波のグラフを示している。図５から図１２における（ｂ）のグラフは、上記の分離なし学習装置が生成した学習済み係数が適用された分離なし予測装置を利用したシミュレーションの結果であり、分離なし予測装置が算出した予測地震波ベクトル“～ｗ”（ｔ）のグラフである。図５から図１２における（ｃ）のグラフは、本実施形態の学習装置１と予測装置２を利用したシミュレーションの結果であり、予測装置２が算出した予測地震波ベクトル“～ｗ”（ｔ）のグラフである。なお、図５から図１２における（ｂ）と（ｃ）は、バッチサイズＭを「６４」とし、学習ステップ上限回数を「１００００」とした場合のグラフである。 The graph of (a) in FIGS. 5 to 12 shows the correct answer data, that is, the graph of the actually measured seismic wave. The graphs (b) in FIGS. 5 to 12 are the results of a simulation using the non-separation prediction device to which the learned coefficient generated by the above-mentioned non-separation learning device is applied, and the prediction calculated by the non-separation prediction device. It is a graph of the seismic wave vector "~ w" (t). The graphs (c) in FIGS. 5 to 12 are the results of simulations using the learning device 1 and the prediction device 2 of the present embodiment, and are the predicted seismic wave vectors “~ w” (t) calculated by the prediction device 2. It is a graph. Note that FIGS. 5 to 12 (b) and (c) are graphs when the batch size M is "64" and the upper limit of the number of learning steps is "10000".
　図５から図１２のグラフにおいて、横軸は、時間であり、ｔの単位は、「１０ミリ秒」である。縦軸は、地震波の振幅である。図５から図１２の（ｂ）のグラフから分かるように、地震波ベクトルｗｎ，ｋ（ｔ）を振幅値ｐｎ，ｋと、波形ベクトルｖｎ，ｋ（ｔ）に分離せずに学習処理を行った場合、予測地震波ベクトル“～ｗ”（ｔ）は全て、ほぼ同一の波形になっていることが分かる。これらの波形は、図５から図１２の（ａ）の正解データのグラフとも異なっており、学習処理が上手くいっていないことが分かる。 In the graphs of FIGS. 5 to 12, the horizontal axis is time, and the unit of t is "10 milliseconds". The vertical axis is the amplitude of the seismic wave. As can be seen from the graph of FIG. 5 to FIG. 12 (b), the learning process is performed without separating the seismic wave vectors w n, k (t) into the amplitude values pn, k and the waveform vectors vn , k (t). When the above is performed, it can be seen that the predicted seismic wave vectors "~ w" (t) all have almost the same waveform. These waveforms are also different from the graphs of the correct answer data in FIGS. 5 to 12 (a), and it can be seen that the learning process is not successful.
　これに対して、図５から図１２の（ａ）と（ｃ）のグラフの対比から分かるように、本実施形態の予測装置２が算出した予測地震波ベクトル“～ｗ”（ｔ）の波形の特徴は、正解データの波形の特徴と類似しており、学習処理が適切に行われており、予測精度が向上していることが分かる。 On the other hand, as can be seen from the comparison of the graphs of FIGS. 5 to 12 (a) and 12 (c), the waveform of the predicted seismic wave vector “~ w” (t) calculated by the prediction device 2 of the present embodiment. The characteristics are similar to the characteristics of the waveform of the correct answer data, and it can be seen that the learning process is properly performed and the prediction accuracy is improved.
　上記の実施形態の学習装置１において、入力部１１は、学習対象地震関連データＩｎと、学習対象地震関連データＩｎの地震によって発生した地震波を測定した地点を示す学習対象地点データＬｋと、学習対象地点データＬｋが示す地点において測定された地震波を示す地震波ベクトルｗｎ，ｋ（ｔ）とを入力する。データ分離部１２は、地震波ベクトルｗｎ，ｋ（ｔ）を、振幅値ｐｎ，ｋと、波形ベクトルｖｎ，ｋ（ｔ）とに分離する。学習部１３は、学習対象地震関連データＩｎと、学習対象地点データとを入力データとして振幅予測部２１が備える関数近似器に与えることにより得られる推定振幅値＾ｐｎ，ｋと、振幅値ｐｎ，ｋとの誤差Ｅｐを算出する。学習部１３は、入力データを波形予測部３１が備える関数近似器に与えることにより得られる推定波形ベクトル＾ｖｎ，ｋ（ｔ）と、波形ベクトルｖｎ，ｋ（ｔ）との誤差Ｅｖを算出する。学習部１３は、誤差Ｅｐと、誤差Ｅｖとに基づいて、振幅予測部２１が備える関数近似器の係数と、波形予測部３１が備える関数近似器の係数とを更新する。 In the learning apparatus 1 of the above embodiment, the input unit 11, a learning object seismic related data I n, a learning object location data L k indicating the points of measurement of seismic waves generated by earthquakes learning object seismic related data I n , The seismic wave vector w n, k (t) indicating the seismic wave measured at the point indicated by the learning target point data L k is input. The data separation unit 12 separates the seismic wave vector w n, k (t) into an amplitude value pn, k and a waveform vector v n, k (t). Learning unit 13, a learning object seismic related data I n, is obtained by providing the function approximator amplitude prediction unit 21 is provided as input data and a learning target spot data estimated amplitude value ^ p n, and k, the amplitude value The error E p with pn and k is calculated. The learning unit 13 has an error E v between the estimated waveform vector ^ v n, k (t) obtained by giving the input data to the function approximator included in the waveform prediction unit 31 and the waveform vector v n, k (t). Is calculated. The learning unit 13 updates the coefficient of the function approximation unit included in the amplitude prediction unit 21 and the coefficient of the function approximation unit included in the waveform prediction unit 31 based on the error E p and the error E v.
　上記の実施形態の予測装置２において、入力部５１は、予測対象の地震に関するデータである予測対象地震関連データ“～Ｉ”と、予測対象地震関連データ“～Ｉ”の地震によって発生する地震波の予測を所望する地点を示す所望地点データ“～Ｌ”とを入力する。予測部５２は、予測対象地震関連データ“～Ｉ”と、所望地点データ“～Ｌ”とを入力データとし、学習装置１による学習処理によって得られた学習済みの係数を用いて、予測振幅値“～ｐ”と、予測波形ベクトル“～ｖ”（ｔ）とを算出し、算出した予測振幅値“～ｐ”と、予測波形ベクトル“～ｖ”（ｔ）とに基づいて、予測地震波ベクトル“～ｗ”（ｔ）を算出する。予測地震波ベクトル“～ｗ”（ｔ）は、予測対象地震関連データ“～Ｉ”の地震によって発生する地震波であって所望の地点に到達する地震波の波形の特徴と類似する特徴を有する。 In the prediction device 2 of the above embodiment, the input unit 51 is the seismic wave generated by the earthquake of the prediction target earthquake-related data "-I" which is the data related to the prediction target earthquake and the prediction target earthquake-related data "-I". Enter the desired point data "~ L" indicating the desired point for prediction. The prediction unit 52 uses the prediction target earthquake-related data "-I" and the desired point data "-L" as input data, and uses the learned coefficient obtained by the learning process by the learning device 1 to predict the predicted amplitude value. The predicted seismic wave vector is calculated based on the predicted amplitude value "~ p" and the predicted waveform vector "~ v" (t) calculated by calculating "~ p" and the predicted waveform vector "~ v" (t). "~ W" (t) is calculated. The predicted seismic wave vector "-w" (t) has characteristics similar to those of the waveform of the seismic wave generated by the earthquake of the predicted earthquake-related data "-I" and reaching a desired point.
　上記の学習装置１の構成により、学習対象地震関連データＩｎと、学習対象地震関連データＩｎの地震によって発生した地震波を測定した地点を示す学習対象地点データＬｋと、学習対象地点データＬｋにおいて測定された学習対象地震関連データＩｎの地震の地震波ベクトルｗｎ，ｋ（ｔ）との関係を振幅予測部２１と波形予測部３１が備える関数近似器においてモデル化することができる。このモデルは、学習対象地震関連データＩｎに含まれている震源の位置から、学習対象地点データＬｋが示す地点まので間の地層のモデルを間接的に示していることになる。そのため、予測装置２は、学習装置１の学習処理によって得られた学習済みの係数を用いることで、簡易に地層のモデルを構築して、高い予測精度で地震波に関する情報を予測することができる。そのため、簡易に任意の地点における地震波に関する情報を高い精度で予測することが可能となる。 With the above configuration of the learning device 1, and the learning object seismic related data I n, a learning object location data L k indicating the points of measurement of seismic waves generated by earthquakes learning object seismic related data I n, learning object location data L seismic vector w n earthquake measured learning object seismic related data I n, the relation between k (t) can be modeled in the function approximator comprising the amplitude prediction part 21 and the waveform predictor 31 in k. This model would learn from the position of source included in the target seismic related data I n, which indirectly indicates the formation model between at the point until the indicated learning object location data L k. Therefore, the prediction device 2 can easily construct a stratum model and predict information on seismic waves with high prediction accuracy by using the learned coefficients obtained by the learning process of the learning device 1. Therefore, it is possible to easily predict information on seismic waves at any point with high accuracy.
　学習装置１は、地震波ベクトルｗｎ，ｋ（ｔ）を、予測が困難な振幅成分と、予測が容易な波形成分とに分離して学習処理を行っている。そのため、学習効率が向上し、上記のシミュレーション結果において示したように、地震波ベクトルを直接予測するよりも、高い精度で予測を行うことが可能になる。 The learning device 1 separates the seismic wave vectors w n and k (t) into an amplitude component that is difficult to predict and a waveform component that is easy to predict, and performs learning processing. Therefore, the learning efficiency is improved, and as shown in the above simulation result, it becomes possible to make a prediction with higher accuracy than directly predicting the seismic wave vector.
　一般的に、地震が発生した際における各地の影響は、各地に設置された地震計により計測された地震動に基づき判定されている。地震動は当該地震計に到達した地震波により発生するため、当然のことながら原則として地震計が設置された地点の地震波しか取得することができない。ここで、地震計を設置することができる場所は、細かに設定された条件が満たされた場所のみである。そのため、地震計を設置する基準を満たさない地点においては、地震波を測定することができないという問題がある。地震計等の機器を設置することができる地点であっても、地震発生後、すぐに地震計等の機器を設置することは時間的に困難である。これに対して、学習装置１及び予測装置２は、地震計等の機器を設置することなく、任意の地点における地震波に関する情報を予測することができる。これは、学習装置１において、学習対象地震関連データＩｎ、学習対象地点データＬｋ、及び地震波ベクトルｗｎ，ｋ（ｔ）という観測データから地震の伝達関数を連続空間でモデル化しているからである。それにより、予測装置２では、このモデル化された伝達関数を用いることにより任意の地震の任意の地点における地震波の予測を可能にしている。そのため、学習装置１及び予測装置２を用いることで、地震計を設置する基準を満たさない地点や、予め地震計等の機器を設置しておくことができない地点に到達することが想定される地震波を予測することができる。 In general, the impact of each region when an earthquake occurs is determined based on the seismic motion measured by seismographs installed in each region. Since seismic motion is generated by the seismic wave that reaches the seismograph, it is natural that only the seismic wave at the point where the seismograph is installed can be acquired. Here, the seismograph can be installed only in the place where the conditions set in detail are satisfied. Therefore, there is a problem that seismic waves cannot be measured at points that do not meet the criteria for installing seismographs. Even at a point where equipment such as a seismograph can be installed, it is difficult in terms of time to install equipment such as a seismograph immediately after an earthquake occurs. On the other hand, the learning device 1 and the prediction device 2 can predict information about seismic waves at any point without installing equipment such as a seismograph. This is because, in the learning apparatus 1, the learning target seismic related data I n, learning object location data L k, and seismic wave vector w n, because the observation data of k (t) models the transfer function of the earthquake continuous space Is. As a result, the prediction device 2 makes it possible to predict seismic waves at any point of any earthquake by using this modeled transfer function. Therefore, by using the learning device 1 and the prediction device 2, seismic waves are expected to reach points that do not meet the criteria for installing seismographs or where equipment such as seismographs cannot be installed in advance. Can be predicted.
　なお、上記の実施形態において、学習対象地震関連データＩｎは、震源の位置を示す震源位置データと、当該地震のマグニチュード等の地震の規模を示す地震規模データとを含んでいるとしているが、それ以外の情報を含むようにしてもよい。なお、学習対象地震関連データＩｎは、それ以外の情報として、震源の位置と学習対象地点データＬｋが示す地点との間の地形の形状の種類や海の深さ等の収集に多大なコストを要しない情報を含んでいてもよいが、震源の位置と学習対象地点データＬｋが示す地点との間の地層の情報のように収集に多大なコストを要する情報は含まないものとする。ここで、地層の情報とは、地層の性質を示す要素であり、例えば、地盤特性、伝搬特性、卓越周波数特性、インピーダンス特性などの個々の地震と無相関な情報である。ただし、地層の情報であっても、個々の地震と相関のある情報、例えば湿度や地面の温度などの個々の地震に関連付けられる情報については、学習対象地震関連データＩｎに含めるようにしてもよい。 In the above embodiment, the learning target seismic related data I n is the focal position data indicating the hypocenter location, although a and a seismic scale data indicating the magnitude of earthquake of magnitude or the like of the earthquake, Other information may be included. The learning target seismic related data I n are as other information, great collection of depth or the like of the shape of the types and sea terrain between the point indicated by the learning target location data L k hypocenter locations may contain not require information costs, but shall not include the information that requires a lot of cost to collect as information of the formation between the point indicated by the learning target location data L k hypocenter locations .. Here, the stratum information is an element indicating the properties of the stratum, and is, for example, information uncorrelated with individual earthquakes such as ground characteristics, propagation characteristics, predominant frequency characteristics, and impedance characteristics. However, even in the information strata, information correlated with the individual seismic, for information associated with each seismic such as for example humidity or ground temperature, be included in the learning target seismic related data I n good.
　上記したように、学習装置１と、予測装置２において、振幅予測部２１及び波形予測部３１の各々の関数近似器に与える入力データに含まれるデータの種類が一致している必要がある。そのため、学習対象地震関連データＩｎが、震源位置データと地震規模データ以外の種類のデータを含む場合、予測対象地震関連データ“～Ｉ”も同様に当該種類のデータを含むことになる。 As described above, in the learning device 1 and the prediction device 2, it is necessary that the types of data included in the input data given to the function approximation units of the amplitude prediction unit 21 and the waveform prediction unit 31 match. Therefore, learning object seismic related data I n is if it contains a type of data other than seismic position data and seismic scale data, the prediction target seismic related data "~ I" also will contain a similarly the type of data.
　上記の実施形態において、地震の規模として、例えば、マグニチュードを示しているが、マグニチュード以外の地震の規模を示す指標、例えば、地震モーメントなどを適用してもよい。 In the above embodiment, the magnitude is shown as the magnitude of the earthquake, but an index showing the magnitude of the earthquake other than the magnitude, for example, the seismic moment may be applied.
　上記の実施形態において、学習装置１は、バッチサイズＭを「６４」程度の値とし、学習ステップ上限回数を「１００００」程度の値とする、いわゆるミニバッチ学習を行っているが、これらの値は任意に変更してもよい。式（７）に示される誤差Ｅが十分収束した際に図２に示した学習処理を終了するようにしてもよい。図２に示す学習処理は、バッチサイズＭを「６４」としているが、全ての「ｎ」と「ｋ」の組み合わせが終了するまでループＬａ１ｓ～Ｌａ１ｅの処理を繰り返し行うバッチ学習を行ってもよい。最適化部４１が、ステップＳ２０９に替えて、ステップＳ２０８のタイミングで得られた振幅誤差Ｅｐと、波形誤差Ｅｖとに基づいて、ステップＳ２０８の処理の中で、係数を更新するオンライン学習を行うようにしてもよい。 In the above embodiment, the learning device 1 performs so-called mini-batch learning in which the batch size M is set to a value of about "64" and the upper limit of the number of learning steps is set to a value of about "10000". It may be changed arbitrarily. The learning process shown in FIG. 2 may be terminated when the error E shown in the equation (7) is sufficiently converged. In the learning process shown in FIG. 2, the batch size M is set to "64", but batch learning may be performed in which the processes of loops La1s to La1e are repeated until all combinations of "n" and "k" are completed. .. Optimization unit 41, in place of the step S209, the amplitude error E p obtained at the timing of step S208, on the basis of the waveform error E v, in the processing in step S208, the online learning to update the coefficients You may do it.
　上記の実施形態において、振幅予測部２１及び波形予測部３１の各々が備える関数近似器の例として、多層パーセプトロン等のニューラルネットワークであるとしているが、多層パーセプトロン等のニューラルネットワーク以外の機械学習で用いられる手段が適用されてもよく、係数を含んだ数式で示される関数を適用してもよい。なお、ニューラルネットワークを用いる場合、学習処理が終了した関数近似器は学習済みモデルとなる。また、振幅と波形をそれぞれ非線形関数で表現してもよい。要は、学習対象地震関連データＩｎと、学習対象地点データＬｋと、学習対象地点データＬｋが示す位置で観測された地震波を示す地震波ベクトルｗｎ，ｋ（ｔ）を用いて所望の地点に到来する地震波を予測しようとする場合、分離した振幅と波形を個別に予測する点がポイントである。ここで、所望の地点とは、学習対象地点データＬｋが示す地点を含む任意の地点である。 In the above embodiment, as an example of the function approximation device provided in each of the amplitude prediction unit 21 and the waveform prediction unit 31, it is assumed that the neural network is a multi-layer perceptron or the like, but it is used in machine learning other than the neural network such as the multi-layer perceptron. The means may be applied, or the function represented by the mathematical formula including the coefficient may be applied. When a neural network is used, the function approximator for which the learning process is completed becomes a trained model. Further, the amplitude and the waveform may be expressed by non-linear functions, respectively. In short, a learning object seismic related data I n, the learning target and the point data L k, seismic vector w n indicating the seismic waves observed at the position indicated by the learning target location data L k, k the desired use (t) When trying to predict the seismic wave that arrives at a point, the point is to predict the separated amplitude and waveform individually. Here, the desired point is an arbitrary point including the point indicated by the learning target point data L k.
　上記の実施形態では、学習装置１の振幅予測部２１及び波形予測部３１の各々が関数近似器を備えるようにしているが、２つの関数近似器ではなく、１つの関数近似器を用いてもよい。すなわち、入力データとして学習対象地震関連データＩｎと学習対象地点データＬｋを取り込み、出力データとして、推定振幅値＾ｐｎ，ｋと、推定波形ベクトル＾ｖｎ，ｋ（ｔ）とを出力する関数近似器を用いるようにしてもよい。この場合、学習装置１による学習処理によって得られる係数は、１つの関数近似器に適用する係数となる。そのため、予測装置２も学習装置１と同一の関数近似器を１つ備えて、学習済みの係数を当該関数近似器に適用し、入力データとして予測対象地震関連データ“～Ｉ”と所望地点データ“～Ｌ”を関数近似器に与えることにより、出力データとして予測振幅値“～ｐ”と、予測波形ベクトル“～ｖ”（ｔ）とが得られることになる。 In the above embodiment, each of the amplitude prediction unit 21 and the waveform prediction unit 31 of the learning device 1 is provided with a function approximation device, but even if one function approximation device is used instead of two function approximation devices. good. That takes a learning object seismic associated data I n and learning object location data L k as the input data, as output data, the output estimated amplitude value ^ p n, and k, the estimated waveform vector ^ v n, and k (t) You may also use a function approximator. In this case, the coefficient obtained by the learning process by the learning device 1 is a coefficient applied to one function approximation device. Therefore, the prediction device 2 also has one function approximation device that is the same as the learning device 1, applies the trained coefficient to the function approximation device, and inputs the prediction target earthquake-related data “~ I” and the desired point data. By giving "~ L" to the function approximation device, the predicted amplitude value "~ p" and the predicted waveform vector "~ v" (t) can be obtained as output data.
　上述した実施形態における学習装置１及び予測装置２をコンピュータで実現するようにしてもよい。その場合、この機能を実現するためのプログラムをコンピュータ読み取り可能な記録媒体に記録して、この記録媒体に記録されたプログラムをコンピュータシステムに読み込ませ、実行することによって実現してもよい。なお、ここでいう「コンピュータシステム」とは、ＯＳや周辺機器等のハードウェアを含むものとする。また、「コンピュータ読み取り可能な記録媒体」とは、フレキシブルディスク、光磁気ディスク、ＲＯＭ、ＣＤ－ＲＯＭ等の可搬媒体、コンピュータシステムに内蔵されるハードディスク等の記憶装置のことをいう。さらに「コンピュータ読み取り可能な記録媒体」とは、インターネット等のネットワークや電話回線等の通信回線を介してプログラムを送信する場合の通信線のように、短時間の間、動的にプログラムを保持するもの、その場合のサーバやクライアントとなるコンピュータシステム内部の揮発性メモリのように、一定時間プログラムを保持しているものも含んでもよい。また上記プログラムは、前述した機能の一部を実現するためのものであってもよく、さらに前述した機能をコンピュータシステムにすでに記録されているプログラムとの組み合わせで実現できるものであってもよく、ＦＰＧＡ（Field Programmable Gate Array）等のプログラマブルロジックデバイスを用いて実現されるものであってもよい。 The learning device 1 and the prediction device 2 in the above-described embodiment may be realized by a computer. In that case, a program for realizing this function may be recorded on a computer-readable recording medium, and the program recorded on the recording medium may be read by a computer system and executed. The term "computer system" as used herein includes hardware such as an OS and peripheral devices. Further, the "computer-readable recording medium" refers to a portable medium such as a flexible disk, a magneto-optical disk, a ROM, or a CD-ROM, and a storage device such as a hard disk built in a computer system. Further, a "computer-readable recording medium" is a communication line for transmitting a program via a network such as the Internet or a communication line such as a telephone line, and dynamically holds the program for a short period of time. It may also include a program that holds a program for a certain period of time, such as a volatile memory inside a computer system that is a server or a client in that case. Further, the above program may be for realizing a part of the above-mentioned functions, and may be further realized for realizing the above-mentioned functions in combination with a program already recorded in the computer system. It may be realized by using a programmable logic device such as FPGA (Field Programmable Gate Array).
　以上、この発明の実施形態について図面を参照して詳述してきたが、具体的な構成はこの実施形態に限られるものではなく、この発明の要旨を逸脱しない範囲の設計等も含まれる。 As described above, the embodiment of the present invention has been described in detail with reference to the drawings, but the specific configuration is not limited to this embodiment, and the design and the like within a range not deviating from the gist of the present invention are also included.
　任意の地点に到達する地震の地震波の予測に用いることができる。 It can be used to predict the seismic wave of an earthquake that reaches any point.
１…学習装置、１１…入力部、１２…データ分離部、１３…学習部、２１…振幅予測部、２２…第１係数記憶部、２３…振幅誤差算出部、３１…波形予測部、３２…第２係数記憶部、３３…波形誤差算出部、４１…最適化部、２…予測装置、５１…入力部、５２…予測部、６２…学習済み第１係数記憶部、７２…学習済み第２係数記憶部、８１…データ合成部 1 ... learning device, 11 ... input unit, 12 ... data separation unit, 13 ... learning unit, 21 ... amplitude prediction unit, 22 ... first coefficient storage unit, 23 ... amplitude error calculation unit, 31 ... waveform prediction unit, 32 ... 2nd coefficient storage unit, 33 ... waveform error calculation unit, 41 ... optimization unit, 2 ... prediction device, 51 ... input unit, 52 ... prediction unit, 62 ... learned first coefficient storage unit, 72 ... learned second Coefficient storage unit, 81 ... Data synthesis unit

Claims (8)

  1. 　所望の地点の地震波に関する情報を予測する予測方法であって、
    　所望の地点を示す所望地点情報を入力する入力ステップと、
    　少なくとも前記所望地点情報と、震源の位置情報と、地震の規模情報とを用いて前記所望の地点における地震波に関する情報を予測する予測ステップと、
    　を有し、
    　前記予測ステップにおいて、前記震源の位置と前記所望の地点との間の地層の情報を用いない予測方法。     It is a prediction method that predicts information about seismic waves at a desired point.
    An input step for inputting desired point information indicating a desired point, and
    A prediction step for predicting information about a seismic wave at the desired point using at least the desired point information, the location information of the epicenter, and the magnitude information of the earthquake.
    Have,
    A prediction method that does not use geological information between the location of the epicenter and the desired point in the prediction step.
  2. 　地震波に関する情報の予測の学習に用いられる学習対象地震関連データであって、少なくとも震源の位置情報及び地震の規模情報を含み前記震源の位置と前記所望の地点との間の地層の情報を含まない学習対象地震関連データと、前記学習対象地震関連データの地震によって発生した地震波を測定した地点を示す学習対象地点データと、前記学習対象地点データが示す地点において測定された前記地震波を示す地震波ベクトルとを入力する入力ステップと、
    　前記地震波ベクトルを、振幅値と、波形ベクトルとに分離するデータ分離ステップと、
    　前記学習対象地震関連データと、前記学習対象地震関連データに対応する前記学習対象地点データとを入力データと、学習により更新される係数とに基づいて得られる前記振幅値の推定値及び前記波形ベクトルの推定ベクトルと、前記入力データに対応する前記地震波ベクトルから得られた前記振幅値及び前記波形ベクトルとに基づいて、前記係数を更新する学習ステップと、
    　を含む学習方法。     Learning target earthquake-related data used for learning the prediction of information related to seismic waves, including at least location information of the epicenter and magnitude information of the earthquake, and does not include information on the geological formation between the location of the epicenter and the desired point. The learning target earthquake-related data, the learning target point data indicating the point where the seismic wave generated by the earthquake of the learning target earthquake-related data was measured, and the seismic wave vector indicating the seismic wave measured at the point indicated by the learning target point data. And the input step to enter
    A data separation step for separating the seismic wave vector into an amplitude value and a waveform vector,
    The estimated value of the amplitude value and the waveform vector obtained based on the input data of the learning target earthquake-related data and the learning target point data corresponding to the learning target earthquake-related data, and the coefficient updated by learning. A learning step of updating the coefficients based on the estimated vector of, the amplitude value obtained from the seismic wave vector corresponding to the input data, and the waveform vector.
    Learning methods including.
  3. 　前記学習ステップは、
    　前記学習対象地震関連データと、前記学習対象地点データとを入力データとして第１の関数近似器に与えることにより得られる前記振幅値の推定値と、前記入力データに対応する前記地震波ベクトルから得られた前記振幅値との誤差である第１の誤差を算出し、前記入力データを第２の関数近似器に与えることにより得られる前記波形ベクトルの推定ベクトルと、前記入力データに対応する前記地震波ベクトルから得られた前記波形ベクトルとの誤差である第２の誤差とを算出し、前記第１の誤差と、前記第２の誤差とに基づいて、前記第１の関数近似器の係数と、前記第２の関数近似器の係数とを更新する、
    　請求項２に記載の学習方法。     The learning step is
    Obtained from the estimated value of the amplitude value obtained by giving the learning target earthquake-related data and the learning target point data as input data to the first function approximator, and the seismic wave vector corresponding to the input data. The estimation vector of the waveform vector obtained by calculating the first error, which is an error from the amplitude value, and giving the input data to the second function approximator, and the seismic wave vector corresponding to the input data. A second error, which is an error from the waveform vector obtained from the above, is calculated, and based on the first error and the second error, the coefficient of the first function approximator and the coefficient of the first function approximator are calculated. Update with the coefficient of the second function approximator,
    The learning method according to claim 2.
  4. 　請求項３に記載の学習方法により得られた学習済みの前記第１の関数近似器の係数を、請求項２に記載の前記第１の関数近似器と同一の第１の関数近似器に適用するステップと、
    　請求項３に記載の学習方法により得られた学習済みの前記第２の関数近似器の係数を、請求項２に記載の前記第２の関数近似器と同一の第２の関数近似器に適用するステップと、を含み、
    　前記予測ステップは、
    　予測対象の地震に関するデータである予測対象地震関連データであって、少なくとも前記予測対象の地震の震源の位置情報及び前記予測対象の地震の規模情報を含み前記震源の位置と前記所望の地点との間の地層の情報を含まない予測対象地震関連データと、前記所望地点情報とを入力データとして前記第１の関数近似器と前記第２の関数近似器に与えることにより、振幅値の予測値と、波形ベクトルの予測ベクトルとを取得し、
    　取得した前記振幅値の予測値と、前記波形ベクトルの予測ベクトルとに基づいて、予測地震波ベクトルを算出する、
    　請求項１に記載の予測方法。     The coefficient of the first function approximation device that has been trained obtained by the learning method according to claim 3 is applied to the same first function approximation device as the first function approximation device according to claim 2. Steps to do and
    The coefficient of the second function approximation device that has been trained obtained by the learning method according to claim 3 is applied to the same second function approximation device as the second function approximation device according to claim 2. Steps to do, including
    The prediction step is
    Prediction target earthquake-related data that is data related to the prediction target earthquake, including at least the position information of the source of the prediction target earthquake and the scale information of the prediction target earthquake, and the position of the source and the desired point. By giving the predicted earthquake-related data that does not include the information of the geological formation between the earthquakes and the desired point information as input data to the first function approximation device and the second function approximation device, the predicted value of the amplitude value can be obtained. , Get the prediction vector of the waveform vector and
    A predicted seismic wave vector is calculated based on the acquired predicted value of the amplitude value and the predicted vector of the waveform vector.
    The prediction method according to claim 1.
  5. 　所望の地点の地震波に関する情報を予測する予測装置であって、
    　所望の地点を示す所望地点情報を入力する入力部と、
    　少なくとも前記所望地点情報と、震源の位置情報と、地震の規模情報とを用いて前記所望の地点における地震波に関する情報を予測する予測部と、
    　を備え、
    　前記予測部は、前記地震波を予測する際、前記震源の位置と前記所望の地点との間の地層の情報を用いない予測装置。     A predictor that predicts information about seismic waves at a desired location.
    An input unit for inputting desired point information indicating a desired point,
    A prediction unit that predicts information about seismic waves at the desired point using at least the desired point information, the location information of the epicenter, and the magnitude information of the earthquake.
    Equipped with
    The prediction unit is a prediction device that does not use information on the stratum between the position of the epicenter and the desired point when predicting the seismic wave.
  6. 　地震波に関する情報の予測の学習に用いられる学習対象地震関連データであって、少なくとも震源の位置情報及び地震の規模情報を含み前記震源の位置と前記所望の地点との間の地層の情報を含まない学習対象地震関連データと、前記学習対象地震関連データの地震によって発生した地震波を測定した地点を示す学習対象地点データと、前記学習対象地点データが示す地点において測定された前記地震波を示す地震波ベクトルとを入力する入力部と、
    　前記地震波ベクトルを、振幅値と、波形ベクトルとに分離するデータ分離部と、
    　前記学習対象地震関連データと、前記学習対象地震関連データに対応する前記学習対象地点データとを入力データと、学習により更新される係数とに基づいて得られる前記振幅値の推定値及び前記波形ベクトルの推定ベクトルと、前記入力データに対応する前記地震波ベクトルから得られた前記振幅値及び前記波形ベクトルとに基づいて、前記係数を更新する学習部と、
    　を備える学習装置。     Learning target earthquake-related data used for learning the prediction of information related to seismic waves, including at least location information of the epicenter and magnitude information of the earthquake, and does not include information on the geological formation between the location of the epicenter and the desired point. The learning target earthquake-related data, the learning target point data indicating the point where the seismic wave generated by the earthquake of the learning target earthquake-related data was measured, and the seismic wave vector indicating the seismic wave measured at the point indicated by the learning target point data. Input section to input and
    A data separator that separates the seismic wave vector into an amplitude value and a waveform vector.
    The estimated value of the amplitude value and the waveform vector obtained based on the input data of the learning target earthquake-related data and the learning target point data corresponding to the learning target earthquake-related data, and the coefficient updated by learning. A learning unit that updates the coefficient based on the estimation vector of the above, the amplitude value obtained from the seismic wave vector corresponding to the input data, and the waveform vector.
    A learning device equipped with.
  7. 　コンピュータに、
    　所望の地点を示す所望地点情報を入力する入力ステップと、
    　少なくとも前記所望地点情報と、震源の位置情報と、地震の規模情報とを用いて前記所望の地点における地震波に関する情報を予測する予測ステップと、
    　を実行させ、
    　前記予測ステップにおいて、前記震源の位置と前記所望の地点との間の地層の情報を用いない予測プログラム。     On the computer
    An input step for inputting desired point information indicating a desired point, and
    A prediction step for predicting information about a seismic wave at the desired point using at least the desired point information, the location information of the epicenter, and the magnitude information of the earthquake.
    To execute,
    A prediction program that does not use geological information between the location of the epicenter and the desired point in the prediction step.
  8. 　コンピュータに、
    　地震波に関する情報の予測の学習に用いられる学習対象地震関連データであって、少なくとも震源の位置情報及び地震の規模情報を含み前記震源の位置と前記所望の地点との間の地層の情報を含まない学習対象地震関連データと、前記学習対象地震関連データの地震によって発生した地震波を測定した地点を示す学習対象地点データと、前記学習対象地点データが示す地点において測定された前記地震波を示す地震波ベクトルとを入力する入力ステップと、
    　前記地震波ベクトルを、振幅値と、波形ベクトルとに分離するデータ分離ステップと、
    　前記学習対象地震関連データと、前記学習対象地震関連データに対応する前記学習対象地点データとを入力データと、学習により更新される係数とに基づいて得られる前記振幅値の推定値及び前記波形ベクトルの推定ベクトルと、前記入力データに対応する前記地震波ベクトルから得られた前記振幅値及び前記波形ベクトルとに基づいて、前記係数を更新する学習ステップと、
    　を実行させるための学習プログラム。     On the computer
    Learning target earthquake-related data used for learning the prediction of information related to seismic waves, including at least location information of the epicenter and magnitude information of the earthquake, and does not include information on the geological formation between the location of the epicenter and the desired point. The learning target earthquake-related data, the learning target point data indicating the point where the seismic wave generated by the earthquake of the learning target earthquake-related data was measured, and the seismic wave vector indicating the seismic wave measured at the point indicated by the learning target point data. And the input step to enter
    A data separation step for separating the seismic wave vector into an amplitude value and a waveform vector,
    The estimated value of the amplitude value and the waveform vector obtained based on the input data of the learning target earthquake-related data and the learning target point data corresponding to the learning target earthquake-related data, and the coefficient updated by learning. A learning step of updating the coefficients based on the estimated vector of, the amplitude value obtained from the seismic wave vector corresponding to the input data, and the waveform vector.
    A learning program to execute.
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