JP2018128929A - Subsurface structure estimating device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a subsurface structure estimating device capable of estimating a subsurface structure using earthquake observational data.SOLUTION: A subsurface structure estimating device 10 receives, as an input, time sequential observation data of an earthquake at each point in time at a location corresponding to a subsurface structure model and repeatedly corrects parameters of the subsurface structure model according to a difference between earthquake data predicted from the parameters of the subsurface structure model and an earthquake prediction model and the observation data of the earthquake.SELECTED DRAWING: Figure 1

Description

  The present invention relates to an underground structure estimation apparatus.

  Conventionally, a technique for estimating a hydraulic conductivity in the ground / rock is known (for example, see Patent Document 1).

JP 2001-32419 A

  In Patent Document 1, the permeability coefficient in the ground / rock mass is estimated from the measurement of only the pore water pressure without requiring the flow rate measurement from the test borehole. However, in the technique of Patent Document 1, it is necessary to measure the pore water pressure, and only the hydraulic conductivity can be estimated as the underground structure.

  In consideration of the above facts, an object of the present invention is to provide an underground structure estimation apparatus capable of estimating an underground structure using earthquake observation data.

  In order to achieve the above object, the underground structure estimation apparatus of the present invention receives an underground structure model and a time series of observation data of earthquakes at each time at a point corresponding to the underground structure model, and the underground structure model According to the difference between the earthquake data obtained from the earthquake state at the time predicted from the parameters and the earthquake prediction model and the observed data of the earthquake at the time, the earthquake state at the time and the parameters of the underground structure model It is comprised including the estimation part which repeats correcting. As a result, the underground structure can be estimated using the observation data of the earthquake.

  The parameter of the underground structure model of the present invention may include the parameter relating to each layer located in the underground direction of the lattice point with respect to each lattice point of the ground surface of the underground structure model. This can reduce the amount of calculation when estimating the underground structure.

  The parameter relating to the layer of each lattice point of the present invention can be set in advance so that a correlation corresponding to the position of the lattice point is set between the lattice points. Thereby, the underground structure can be accurately estimated in consideration of the continuity of the underground structure.

  The parameter relating to the layer of the present invention may include a layer thickness of the layer, and the layer thickness may be set in advance so as to have a correlation corresponding to the position of the lattice point between the lattice points. Accordingly, the underground structure can be accurately estimated in consideration of the continuity of the layer thickness of the underground structure.

  In the present invention, for each of the lattice points of the underground structure model, the closer the distance between the lattice points, the more the parameters related to each layer positioned in the underground direction of one lattice point and the underground direction of the other lattice point It is possible to set in advance so that the parameters relating to each layer located at the position correspond to each other. Thereby, the underground structure can be accurately estimated in consideration of the distance between the lattice points of the underground structure.

  The underground structure estimation apparatus of the present invention includes an expanded state vector having a parameter vector representing the parameter of the underground structure model, a state vector including the velocity and stress of each lattice point due to the earthquake, and each time representing the observation data. And the estimation unit predicts the expanded state vector at time t based on the expanded state vector at time t-1 and the earthquake prediction model, and A correction unit that corrects the expanded state vector at time t based on the earthquake data generated from the expanded state vector at time t predicted by the prediction unit and the earthquake motion data of the earthquake at time t; Until the end time T of the observation data, the prediction by the prediction unit and the correction by the correction unit are repeated, and the correction unit obtained at each time Smoothing the parameter of the underground structure model included in the estimation result to obtain the parameter of the underground structure model included in the expanded state vector. it can. Thereby, an underground structure can be estimated accurately using a sequential filtering technique.

  According to the present invention, the time series of the observation data of the earthquake at the point corresponding to the underground structure model is input, and the difference between the earthquake data predicted from the parameters of the underground structure model and the earthquake prediction model and the observation data of the earthquake is obtained. Accordingly, it is possible to obtain an effect that the underground structure can be estimated using the earthquake observation data by repeatedly correcting the earthquake state and the parameters of the underground structure model.

It is a block diagram which shows schematic structure of the underground structure estimation apparatus which concerns on embodiment of this invention. It is explanatory drawing for demonstrating an underground structure model. It is a figure which shows an example of the detailed structure of the estimation part of the underground structure estimation apparatus which concerns on embodiment of this invention. It is a figure which shows an example when a correlation is set with respect to the variance covariance matrix used in sequential data assimilation. It is a figure which shows an example of each ensemble of an ensemble Kalman filter when not correlating with a layer of an underground structure model, and an example of each ensemble of an ensemble Kalman filter when a correlation is given to a layer of an underground structure model . It is a figure which shows an example of an underground structure estimation process routine. It is a figure which shows an example of a data assimilation processing routine. It is explanatory drawing for demonstrating a simulation experiment. It is a figure which shows the experimental result of a simulation experiment.

  Hereinafter, embodiments of the present invention will be described in detail.

<System configuration of underground structure estimation device>

  FIG. 1 is a block diagram illustrating an example of a configuration of an underground structure estimation apparatus according to an embodiment of the present invention. As shown in FIG. 1, the underground structure estimation apparatus 10 can be functionally represented by a configuration including a reception unit 12, a computer 14, and a display unit 16.

  The reception unit 12 receives information input from the outside of the underground structure estimation apparatus. For example, when a new earthquake occurs, the accepting unit 12 accepts earthquake source parameters, which are examples of earthquake observation data, and earthquake speed data at each observation point at each observation point. The epicenter parameter is input based on earthquake information from the Japan Meteorological Agency or the like. And the reception part 12 stores the epicenter parameter and the velocity data of the earthquake of each time in each observation point in the observation data storage part 18 mentioned later. The earthquake speed data is an example of earthquake motion data.

  The computer 14 includes a CPU (Central Processing Unit), a ROM (Read Only Memory) that stores a program for realizing each processing routine, a RAM (Random Access Memory) that temporarily stores data, and a memory as storage means. And a network interface and the like.

  As shown in FIG. 1, the computer 14 is functionally configured to include an observation data storage unit 18, a model storage unit 20, an information acquisition unit 22, and an estimation unit 24.

  The observation data storage unit 18 stores the earthquake source parameters and the earthquake speed data at each observation point at each observation point for each earthquake. Each time a new earthquake occurs, the observation data of the earthquake is stored in the observation data storage unit 18.

  The model storage unit 20 stores an underground structure model representing the underground structure and a parameter vector representing the parameters of the underground structure model.

  In this embodiment, the parameters of the underground structure model are estimated by data assimilation. Therefore, in this embodiment, the difference between the earthquake velocity data stored in the observation data storage unit 18 and the earthquake vector predicted from the parameter vector of the underground structure model and the earthquake prediction model stored in the model storage unit 20 is calculated. Estimate the parameters of the underground structure model to correct.

  The underground structure model and parameters used in this embodiment will be described below.

  In simulations using the finite difference method used in earthquake motion prediction, by substituting parameters representing physical properties (for example, propagation velocity, density, and attenuation constant) at each lattice point of the underground structure model, Express.

For example, as in the underground structure model 25 in FIG. 2, each lattice point (i, j, k) of the underground structure model 25 has a density ρ, an S wave shear wave velocity V _S , and a P wave shear wave velocity V. Physical properties of _{P 1} , S wave attenuation constant Q _S , and P wave attenuation constant Q _P are assigned as parameters.

  However, when a parameter is assigned to each lattice point of the underground structure model and each parameter is estimated by data assimilation, the number of parameters to be estimated increases, and the amount of calculation increases. In addition, the parameter estimation accuracy may decrease due to an increase in parameters.

Therefore, in the present embodiment, in the underground structure model used for data assimilation, a parameter is assigned to each layer located in the underground direction of each lattice point on the ground surface. Specifically, as in the underground structure model 26 in FIG. 2, the layer thickness H of each layer is assigned as a parameter to each layer of the underground structure model 26 for each lattice point on the ground surface. Further, physical property values (ρ, V _S , V _P , Q _S , Q _P ) are assigned as parameters to each layer.

  Here, assuming that the number of grid partitions in the x direction is I, the number of grid partitions in the y direction is J, and the number of grid partitions in the z direction is K, in the case of the underground structure model 25 in FIG. The following equation (1) is obtained.

Total number of parameters = number of parameters per grid point x number of grid points
= 5 x I x J x K [pieces] (1)

  On the other hand, in the case of the underground structure model 26 according to the present embodiment shown in FIG.

Total number of parameters = number of parameters per layer × number of layers + 1 number of layers per grid point × number of grid points on the ground surface = 5 × L + I × J × (L−1) [pieces] (2)

In the underground structure model 25, as can be seen from the above equation (1), when physical property parameters (ρ, V _S , V _P , Q _S , Q _P ) are assigned to each lattice point, the number of parameters to be estimated Is a huge number. On the other hand, in the underground structure model 26 of this embodiment, as can be seen from the above equation (2), the physical property value parameters (ρ, V _S , V _P , Q _S , Q _P ) are given for each layer, and the layer thickness The parameter H is given for each grid point on the ground surface. Therefore, in the underground structure model 26 of this embodiment, the number of parameters to be estimated is reduced, and the amount of calculation at the time of parameter estimation by data assimilation is suppressed.

  The information acquisition unit 22 acquires observation data stored in the observation data storage unit 18. Then, the information acquisition unit 22 determines whether or not to use the earthquake velocity data of the observation data for estimating the parameters of the underground structure model based on information such as the hypocenter position included in the epicenter parameter of the observation data.

  For example, the information acquisition unit 22 is not within the region of the underground structure model when the distance between the location of the earthquake source included in the earthquake source parameter and the point corresponding to the underground structure model is equal to or greater than a preset threshold value. It is determined that it is not used for estimating the parameters of the underground structure model.

  On the other hand, if the distance between the location of the epicenter included in the epicenter parameter and the point corresponding to the underground structure model is less than a preset threshold, the information acquisition unit 22 is within the region of the underground structure model. It is determined that it is used for estimating the parameters of the underground structure model. Seismic velocity data in an area unrelated to the location corresponding to the underground structure model is excluded because it is not appropriate when estimating the underground structure parameters.

  Further, the information acquisition unit 22 uses the earthquake speed data of the observation data for estimation of the parameters of the underground structure model according to whether or not the SN ratio of the earthquake speed data as the observation data satisfies a predetermined condition. It is determined whether or not. Whether the S / N ratio satisfies a predetermined condition is determined based on the shape of the Fourier amplitude spectrum calculated from the earthquake velocity data.

  When the low-frequency component of the earthquake velocity data that is the observation data is below the noise level, the information acquisition unit 22 determines that the parameter of the underground structure is not appropriate and determines the earthquake velocity data as the underground It is determined that the structural model is not used for parameter estimation. On the other hand, when the low frequency component of the earthquake speed data exceeds the noise level, the information acquisition unit 22 determines to use the earthquake speed data for estimating the parameters of the underground structure model.

  In addition, the information acquisition unit 22 acquires a parameter vector representing the parameters of the underground structure model stored in the model storage unit 20. The parameter vector of the underground structure model acquired by the information acquisition unit 22 is obtained by data assimilation based on the earthquake speed data up to the previous time.

  According to the difference between the parameter vector of the underground structure model acquired by the information acquisition unit 22 and the earthquake data predicted from the earthquake prediction model, and the earthquake velocity data acquired by the information acquisition unit 22, the estimation unit 24 Repeat the modification of the parameter vector of the underground structure model.

  More specifically, data assimilation is performed according to the difference between the earthquake data obtained from the earthquake state predicted by the finite difference simulation, which is an example of an earthquake prediction model, and the earthquake velocity data that is the observation data. Estimate the parameters of the structural model.

  In this embodiment, as an example of data assimilation, a case where an ensemble Kalman filter that is a sequential data method is used will be described as an example. In the sequential data method, assimilation is performed every time time-series data is obtained.

  The flow of data assimilation processing is shown below. In this embodiment, the system model used for data assimilation is represented by the following equations (3) and (4).

(3)

(4)

In the above formula (3) and (4), t represents time, x _t represents an enlarged state vector at time t, y _t denotes the observed data at time t. f _t represents a simulation which is a system model. Further, the observation noise w _t follows a normal distribution N (0, R _t ), and the system noise v _t follows an arbitrary distribution. H _t is an observation matrix.

  When the above expressions (3) and (4) are expressed by conditional distribution, a general state space model as shown in the following expressions (5) to (7) is obtained.

(5)

(6)

(7)

Here, x ₀ represents the expansion state vector prior to assimilate the seismic observation data. The parameter vector θ of the underground structure model is set according to the existing model, the structure exploration result, and the geological information.

  Next, referring to the references (Daido Nagao, “Basic theory of data assimilation and its application”, Automatic Tuning Study Group, 6th Symposium on Current Status and Applications of Automatic Tuning Technology (ATTA2014) slide material), the ensemble Kalman filter Will be described.

[1] In an stage forward prediction of Ichiki destination prediction ensemble Kalman filter, each ensemble ^x _{(i) t-1} corresponding to the expanded state vector _{x t |} is the time evolution by _t-1 simulation _{f t,} Ichiki destination prediction Obtain an ensemble of distributions x ⁽ⁱ⁾ _{t | t−1} .

The filter distribution at time t−1 is approximately expressed by the following equation (9). Note that δ (·) represents a delta function. Table _t-1 is by the following equation (10) _| Each ensemble ^x _{(i) t-1 |} a _t-1, the ensemble ^x obtained by time development by simulation _{f t} is a system model _{(i) t} Is done. Further, the one-prediction predicted distribution is approximated by the following equation (11) by each ensemble x ⁽ⁱ⁾ _{t | t−1} in equation (10).

(8)

(9)

(10)

(11)

[2] Filtering Next, in the filtering of the ensemble Kalman filter, the ensemble x ⁽ⁱ⁾ _{t | t of the} filter distribution is obtained from the ensemble x ⁽ⁱ⁾ _{t |}

Ichiki destination prediction distribution ensemble _{^{x (i) t | t-}} 1 of the variance-covariance matrix _{V ^ t | t-1} is expressed by the following equation (12). Note that “′” in the expression represents transposition of a matrix. Further, the variance-covariance matrix R ^ _t of the observation noise w ⁽ⁱ⁾ _t is expressed by the following equation (13).

Further, the Kalman gain K ^ _t is expressed by the following equation (14). An ensemble x ⁽ⁱ⁾ _{t | t} of the filter distribution is expressed by the following equation (15). It should be noted, _{y t} represents the observation data at time t.

(12)

(13)

(14)

(15)

[3] Smoothing In the smoothing of the ensemble Kalman filter, the ensemble obtained by repeating the one-time prediction and filtering is smoothed. Specifically, an expanded state vector is estimated by calculating a smoothed distribution p (x ₀ | y _{1: T} ) based on each ensemble obtained from observation data up to time step t = T.

  Each process using the ensemble Kalman filter in the present embodiment will be specifically described below.

The expanded state vector x _t in the present embodiment includes state vectors x ^to _t whose elements are the speeds v _{i, j, k} and stresses τ _{i, j, k} of the lattice points of the underground structure model obtained by simulation, The parameters (ρ _l , V _{S, l} , V _{P, l} , Q _{S, l} , Q _{P, l} ) and the layer thickness H _{i, j, l} of each layer l are expressed as elements. And a parameter vector θ.

Further, the state vectors x ^to _t of the present embodiment are represented by the following formula (16). Q _{i, j, k} of the state vectors x ^to _t represent the velocity of each lattice point obtained by simulation. Further, τ _{i, j, k} of the state vectors x ^to _t represent the stress of each lattice point obtained by simulation. The state vectors x ^to _t are examples of earthquake states.

The parameter vector θ of the present embodiment is expressed by the following equation (17). The parameter vector θ includes parameters (ρ _l , V _{S, l} , V _{P, l} , Q _{S, l} , Q _{P, l} ) of layer _l , and layer thickness parameters H _{i, j, l} , Is included.

Moreover, the enlarged state vector xt of this embodiment which is an example of earthquake data is represented by the following formula _| equation (18). The velocity data y _t seismic time t for the M observation point is represented by the following equation (19). Each element a _m speed data y _t seismic represent velocity data observed seismic at the point m.

  As shown in FIG. 3, the estimation unit 24 includes a prediction unit 240, a correction unit 242, and a smoothing unit 244.

The prediction unit 240 acquires the parameter vector θ of the underground structure model acquired by the information acquisition unit 22. Also, the prediction unit 240 acquires the velocity data y _t seismic acquired by the information acquisition unit 22.

Next, the prediction unit 240 sets an initial value of each value. Specifically, the prediction unit 240 in accordance with the conditional probability distribution of the above formula (6), sets the initial value x ₀ of the expanded state vector. Also, the prediction unit 240, when setting the initial value x ₀ of expanding the state vector, the thickness H of the parameter vector theta, among lattice points, setting the correlation in accordance with the position of the grid point. Specifically, the prediction unit 240 determines the layer thickness of each layer located in the underground direction of one lattice point and the other lattice point as the distance between the lattice points is shorter for each of the lattice points of the underground structure model. It is set so that the layer thickness of each layer located in the underground direction is close. More specifically, the layer thickness correlation is set by setting the correlation according to the position of the lattice point for the term relating to the layer thickness H of the variance-covariance matrix V ^ _{t | t-1 in} the above equation (12). To do.

FIG. 4 shows an example of the variance-covariance matrix V ^ _{t | t−1} for the term relating to the layer thickness H. In FIG. 4A, the horizontal axis α and the vertical axis β represent the position of each element of the matrix. The brighter region has a higher correlation value and the darker region has a lower correlation value. FIG. 4B is a three-dimensional representation of FIG. 4A. The horizontal axis α and the vertical axis β in the horizontal plane represent the position of each element of the matrix, and the vertical direction represents the correlation value.

As shown in FIGS. 4A and 4B, in this embodiment, for each grid point, the smaller the distance between the grid points, the higher the correlation value and the greater the distance between the grid points. A variance-covariance matrix V ^ _{t | t-1} with respect to the layer thickness H is set so that the correlation value becomes low. Then, each ensemble is generated according to the variance-covariance matrix V ^ _{t | t−1} for which the correlation is set. This reflects the continuity of the underground structure.

  In the underground structure, the shape of the layer changes smoothly unless there is a fault. In the present embodiment, in consideration of this point, the layer thickness corresponding to the same layer is correlated.

  FIG. 5 shows an example of ensembles 1 to 5 when no correlation is set and an example of ensembles 1 to 5 when a correlation is set. In the figure, Xgrid corresponds to the x direction in FIG. 2, and Zgrid corresponds to the z direction in FIG. As shown in FIG. 5A, in ensembles 1 to 5 when no correlation is set, the value of Zgrid takes a random value regardless of the position of Xgrid. However, the layers in the underground structure are considered to be continuous in the horizontal direction. Therefore, if data assimilation is performed while the layer thickness of each ensemble takes a random value, the parameters of the underground structure model cannot be accurately estimated.

On the other hand, as shown in FIG. 5B, in the ensembles 1 to 5 in the case where the correlation is set, the value of Zgrid is a value corresponding to the position of Xgrid. Take. Therefore, the continuity of the layers of the underground structure is reflected by setting the correlation with respect to the variance-covariance matrix V ^ _{t | t−1} for the term relating to the layer thickness H.

Next, the prediction unit 240, the ensemble x ^{(i) _t-1} representing an enlarged state vector at time t-1 _|, based on the simulation f _t finite difference method, which is an example of a _t-1 and the earthquake prediction models Then, according to the above equation (10), each ensemble x ⁽ⁱ⁾ _{t | t−1} representing the expanded state vector at time t is predicted.

The correcting unit 242 converts the seismic data generated from each ensemble x ⁽ⁱ⁾ _{t | t−1} representing the expanded state vector predicted at the time t predicted by the predicting unit 240 and the velocity data y _t of the earthquake at the time t. Based on the above equation (15), each ensemble x ⁽ⁱ⁾ _{t | t−1} representing the expanded state vector at time t is corrected. Then, the correcting unit 242 obtains each ensemble x ⁽ⁱ⁾ _{t | t} representing the expanded state vector.

  Then, until the end time T of the earthquake speed data, the prediction by the prediction unit 240 and the filtering by the correction unit 242 are repeated.

The smoothing unit 244 obtains the parameter vector θ of the underground structure model by smoothing the parameter vector θ of the underground structure model included in the estimation result by the correction unit 242 obtained at each time. The parameter vector θ includes parameters (ρ, V _S , V _P , Q _S , Q _P ) of the physical property values of each layer and a parameter H of the layer thickness of each layer. The parameter is obtained.

  Then, the smoothing unit 244 stores the parameter vector of the underground structure model obtained by the smoothing in the model storage unit 20. The parameter vector stored in the model storage unit 20 is used in data assimilation when observation data of the next earthquake is obtained.

  The display unit 16 displays estimation results such as parameter vectors stored in the model storage unit 20. A user who operates the underground structure estimation apparatus 10 confirms the result displayed by the display unit 16.

<Operation of underground structure estimation device>
Next, the operation of the underground structure estimation apparatus 10 will be described with reference to FIG. When a new earthquake occurs, the reception unit 12 of the underground structure estimation apparatus 10 receives a new earthquake source parameter and earthquake speed data at each observation point at each time point, and stores them in the observation data storage unit 18. And the underground structure estimation apparatus 10 performs the underground structure estimation process routine shown in FIG. The underground structure estimation processing routine is executed each time new earthquake observation data is stored in the observation data storage unit 18.

  In step S100, the information acquisition unit 22 acquires the epicenter parameter of the observation data stored in the observation data storage unit 18.

  In step S <b> 102, the information acquisition unit 22 determines whether the observation data is within the region of the underground structure model based on the information on the hypocenter position included in the hypocenter parameter. If the observation data is within the region of the underground structure model, the process proceeds to step S104. On the other hand, if the observation data is not within the region of the underground structure model, the underground structure estimation processing routine is terminated.

  In step S <b> 104, the information acquisition unit 22 acquires earthquake speed data of the observation data stored in the observation data storage unit 18.

  In step S106, the information acquisition unit 22 determines whether the SN ratio of the earthquake speed data acquired in step S104 satisfies a predetermined condition. If the SN ratio of the earthquake speed data satisfies a predetermined condition, the process proceeds to step S108. On the other hand, if the SN ratio of the earthquake speed data does not satisfy the predetermined condition, the underground structure estimation processing routine is terminated.

  In step S <b> 108, the information acquisition unit 22 acquires a parameter vector representing the parameters of the underground structure model stored in the model storage unit 20.

In step S110, the estimation unit 24, and seismic data are predicted in accordance with the parameter vector θ and simulation have been subsurface structure model obtained in step S108, the velocity data y _t seismic acquired in step S104 A parameter vector θ of the underground structure model is estimated according to the difference. The process of step S110 is realized by a data assimilation process routine shown in FIG.

<Data assimilation processing routine>
In step S200, 0 is set at time t.

In step S202, the prediction unit 240 in accordance with the conditional probability distribution of the above formula (6), sets the initial value _{x 0} of the expanded state vector.

In step S <b> 204, the prediction unit 240 calculates the above formula so that the closer the distance between the lattice points, the closer the underground thickness of one lattice point and the underground thickness of the other lattice point are. Correlation corresponding to the position of the lattice point is set for the term relating to the layer thickness H of the variance-covariance matrix V ^ _{t | t−1} in (12).

In step S206, the prediction unit 240 expands the current time t according to the above equation (10) based on each ensemble x ⁽ⁱ⁾ _{t-1 | t-1} and the simulation f _{t at} the previous time t-1. Predict each ensemble x ⁽ⁱ⁾ _{t | t−1} representing the vector.

In step S208, the correction unit 242 is based on the earthquake data generated from each ensemble x ⁽ⁱ⁾ _{t | t−1} predicted in step S206 and the earthquake velocity data y _{t at} time t. Then, according to the above equation (15), each ensemble x ⁽ⁱ⁾ _{t | t−1} at time t is corrected. Then, the correcting unit 242 obtains each ensemble x ⁽ⁱ⁾ _{t | t} representing the expanded state vector.

In step S210, correction unit 242 determines to end the time T of the velocity data _{y t} earthquake, whether one stage forward prediction and filtering of the step S208 of the step S206 is repeated. If the one-term prediction and filtering are repeated until the end time T, the process proceeds to step S214. On the other hand, if the one-term prediction and filtering are not repeated until the end time T, the time is incremented by 1 in step S212, and the process returns to step S206.

  In step S214, the smoothing unit 244 obtains the parameter vector θ by smoothing the parameter vector θ of the underground structure model included in the estimation result obtained at each time in step S208.

  In step S216, the smoothing unit 244 outputs the parameter vector θ obtained in step S214 as a result.

  Next, in step S112 in FIG. 6, the smoothing unit 244 stores the parameter vector θ output in step S110 in the model storage unit 20. The parameter vector θ stored in the model storage unit 20 is used for data assimilation when observation data of the next earthquake is obtained.

  In step S114, the display unit 16 displays the estimation result such as the parameter vector θ stored in the model storage unit 20, and ends the underground structure estimation processing routine.

  As described in detail above, in this embodiment, the time series of the observation data of the earthquake at the point corresponding to the underground structure model is input, and the earthquake data predicted from the parameters of the underground structure model and the earthquake prediction model, It is possible to estimate the underground structure using the earthquake observation data by repeating the modification of the earthquake state and the parameters of the underground structure model according to the difference from the observation data.

  When applying data assimilation to parameter estimation of an underground structure model, for example, when using an ensemble Kalman filter, which is an example of a sequential filtering method, a plurality of ensembles representing expanded state vector candidates are generated. However, since the number of parameters of the underground structure model is large, there is a problem that the amount of calculation for the ensemble generated according to the parameters increases. In addition, since each ensemble is randomly generated according to the probability distribution, there is a problem that even if the parameters of the underground structure model having continuity are estimated, it cannot be accurately estimated.

  Therefore, in this embodiment, when estimating the underground structure by data assimilation, the number of parameters is reduced by assigning parameters to each layer of the underground structure model. Thereby, when estimating an underground structure by data assimilation, a calculation amount can be reduced.

  In the present embodiment, correlation is set for the parameters of the underground structure model. Thereby, the continuity of the underground structure is considered and the underground structure can be estimated with high accuracy.

  In addition, since an underground structure model with a high degree of consistency with earthquake observation data is estimated, the prediction accuracy of earthquake motion can be improved. In addition, additional drilling surveys for modifying the underground structure model are not required.

  In addition, since sequential data assimilation is used in this embodiment, even if the earthquake observation data increases, it is only necessary to modify the parameters of the underground structure model using only the increased observation data. Therefore, the calculation amount is small.

<Experimental example>
In order to confirm the effect of this embodiment, a numerical experiment in a two-dimensional SH wave field was performed. In addition, it analyzed using the ensemble Kalman filter which is one of the sequential data assimilation methods.

[Summary of experiment]
A numerical experiment was conducted on the two-dimensional underground structure model shown in FIG. First, a simulation is performed on a true model (true value) to create a simulated ground motion at a ground observation point (triangle in FIG. 8). In addition, as shown in Table 1 below, an initial model (initial value) that gives a 10% error to the true underground structure model is set. Next, we performed data assimilation between simulation and simulated ground motion for the initial model, and confirmed that the initial model approached the true model.

[Comparison between when correlation is set for a layer and when correlation is not set for a layer]

FIG. 9A shows the result of the numerical experiment when the correlation is given to the layers. In the figure, the horizontal axis indicates the time step, and the vertical axis indicates the ratio of the estimated value to the true value. The closer the ratio is to 1, the closer the value is to the true value. The layer thickness H and the shear wave velocity V _S of the S wave are successively corrected and approach the true value, and the effect of underground structure estimation using data assimilation has been confirmed.

On the other hand, FIG. 9B shows the result of a numerical experiment when no correlation is set for the layer. Compared with the case where the correlation is set, the estimation accuracy of the layer thickness H when the correlation is not set is poor. Further, the estimation accuracy is better when the correlation is set for the shear wave velocity V _S of the S wave, and it is confirmed that the correlation thickness is effective.

  The present invention is not limited to the above-described embodiment, and various modifications and applications can be made without departing from the gist of the present invention.

For example, in the above-described embodiment, a case has been described in which the physical property value parameters (ρ, V _S , V _P , Q _S , Q _P ) of each layer and the layer thickness parameter H are estimated simultaneously by data assimilation. It is not limited to this. For example, after estimating a predetermined parameter of each parameter, a parameter other than the predetermined parameter may be estimated. For example, after estimating the thickness H and the velocity V _S of the respective layers, may be estimated as the density ρ decay constant Q _S and Q _P.

In the above embodiment, the case where the correlation is set according to the horizontal distance (xy direction) between the lattice points as shown in FIG. 4 is described as an example. However, the present invention is not limited to this, and the z direction is used. A correlation may be set for. For example, the correlation may be set such that the deeper the position in the z direction is, the harder the layer is. Thereby, for example, in each ensemble generated in the ensemble Kalman filter, generation of an ensemble indicating that the layer located below the specific layer is softer than the specific layer is suppressed.

Moreover, although the case where a correlation was set with respect to layer thickness H as an example of the parameter regarding a layer was demonstrated in the said embodiment, it is not limited to this. For example, the correlation may be set for parameters other than the layer thickness H. Specifically, for example, the correlation may be set so that the velocity V _S increases as the position of the underground structure model in the z direction increases. For example, in consideration of the relationship between the speed V _S and the density ρ, the correlation may be set so that the density ρ increases as the speed V _S increases. The correlation may be set so that the attenuation coefficient Q increases as the position of the underground structure model in the z direction increases. Moreover, taking into account the relationship between the velocity V _S and the speed V _P, it may be set correlation. Further, the correlation may be set according to at least one of an actual ground survey result, a relational expression between parameters, and a past study.

In the above embodiment, the case where the physical property values (ρ, V _S , V _P , Q _S , Q _P ) and the layer thickness H of each layer are estimated by data assimilation as the parameters of the underground structure model has been described as an example. However, it is not limited to this. Only some of the parameters of the subsurface structure model of the present embodiment may be estimated, for example, it may be estimated only layer thickness H and the velocity V _S. Alternatively, the attenuation constant Q _S may be estimated after estimating only the layer thickness H and the velocity V _S.

  In the above embodiment, the case where the correlation is set for the parameter vector every time data assimilation based on new observation data is performed in the underground structure estimation processing routine has been described as an example. It is not a thing. For example, the correlation may be set for the parameter vector only when data assimilation is performed based on the earthquake observation data obtained for the first time.

  Moreover, although the case where an ensemble Kalman filter is used as an example of the sequential filtering technique for data assimilation has been described as an example in the above embodiment, the present invention is not limited to this, and other sequential filtering techniques may be used. For example, a particle filter may be used as a sequential filtering method.

  In the above description, the program is stored (installed) in a storage unit (not shown) in advance. However, the program is recorded on any recording medium such as a CD-ROM, a DVD-ROM, and a micro SD card. It is also possible to provide it in the form in which it is provided.

DESCRIPTION OF SYMBOLS 10 Underground structure estimation apparatus 12 Reception part 14 Computer 16 Display part 18 Observation data storage part 20 Model storage part 22 Information acquisition part 24 Estimation part 26 Underground structure model 240 Prediction part 242 Correction part 244 Smoothing part (theta) Parameter vector

Claims (6)

With an underground structure model and a time series of observation data of earthquakes at each time at a point corresponding to the underground structure model as inputs,
According to the difference between the earthquake data obtained from the earthquake state at the time predicted from the parameters of the underground structure model and the earthquake prediction model and the observation data of the earthquake at the time, the state of the earthquake at the time and the underground An underground structure estimation device that includes an estimation unit that repeatedly modifies the parameters of the structural model. The parameters of the underground structure model include the parameters relating to each layer located in the underground direction of the lattice point with respect to each lattice point of the ground surface of the underground structure model,
The underground structure estimation apparatus according to claim 1. As for the parameters related to the layer at each lattice point, a correlation is preset between the lattice points according to the position of the lattice points.
The underground structure estimation apparatus according to claim 2. The parameters for the layer include the layer thickness of the layer;
The layer thickness is preset with a correlation between the lattice points according to the position of the lattice points.
The underground structure estimation apparatus according to claim 3. For each of the lattice points of the underground structure model, the closer the distance between the lattice points, the more the parameters related to each layer located in the underground direction of one lattice point and the layers located in the underground direction of the other lattice point. Is preset to correspond to the parameters relating to
The underground structure estimation apparatus according to claim 3 or 4. An enlarged state vector having a parameter vector representing the parameter of the underground structure model, a state vector including the velocity and stress of each lattice point due to the earthquake, and earthquake motion data of the earthquake at each time representing the observation data are input. age,
The estimation unit includes
A prediction unit that predicts the expanded state vector at time t based on the expanded state vector at time t-1 and the earthquake prediction model;
A correction unit that corrects the expanded state vector at time t based on the earthquake data generated from the expanded state vector at time t predicted by the prediction unit and the earthquake motion data of the earthquake at time t;
The prediction by the prediction unit and the correction by the correction unit are repeated until the end time T of the observation data, and the parameters of the underground structure model included in the estimation result by the correction unit obtained at each time are smoothed. A smoothing unit for acquiring the parameters of the underground structure model included in the expanded state vector;
The underground structure estimation apparatus according to any one of claims 1 to 5, comprising: