Analysis method, program and ground resistivity monitoring system

Abstract

To provide an analysis method, a program and a ground resistivity monitoring system capable of estimating an amount of electrode movement together in addition to resistivity.SOLUTION: An analysis method for analyzing a change in ground includes: a measurement result acquisition step of setting a pair of current electrodes and a pair of potential electrodes using a plurality of electrodes installed at prescribed intervals on the ground, and acquiring a measurement result obtained by measuring a potential difference between the pair of potential electrodes due to a current of the pair of current electrodes using any combination of the plurality of electrodes; and an estimation step of calculating distribution of resistivity of the ground and a displacement amount of the electrode relative to a reference electrode by solving an optimization problem using sparse modeling on the basis of data of the measurement result measured at different times.SELECTED DRAWING: Figure 6

Description

[Technical Field]

[0001] The present disclosure relates to an analysis method, a program, and a ground resistivity monitoring system. [Background technology]

[0002] Non-Patent Document 1 describes a technique for estimating the resistivity of ground using sparse modeling. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Hiroshi Kisanuki and Ken Sakurai (2022): Study on resistivity monitoring analysis method using sparse modeling, Japan Geoscience Union Meeting 2022 Summary of the Invention [Problem to be solved by the invention]

[0004] In ground monitoring, it is necessary to estimate not only resistivity but also ground movement (specifically, the amount of electrode movement).

[0005] In view of the above, the purpose of the present disclosure is to provide an analysis method, a program, and a ground resistivity monitoring system that can estimate not only resistivity but also the amount of electrode movement. [Means for solving the problem]

[0006] An analysis method according to a first aspect of the present disclosure includes: (1) In the analytical method for analyzing changes in the ground, a measurement result acquisition step of setting a pair of current electrodes and a pair of potential electrodes using a plurality of electrodes installed at predetermined intervals on the ground, and acquiring a measurement result of measuring a potential difference between the pair of potential electrodes due to a current of the pair of current electrodes using any combination of the plurality of electrodes; and an estimation step of determining the distribution of resistivity of the ground and the amount of displacement of the electrode relative to a reference electrode by solving an optimization problem using sparse modeling based on the data of the measurement results measured at different times.

[0007] An analysis method according to one embodiment of the present disclosure includes: (2) A distribution of resistivity of the ground at a first time among the different times is obtained by solving an optimization problem based on data of a measurement result measured at the first time; determining a distribution of resistivity of the ground and a displacement of the electrode at a second time that is later than the first time by solving an optimization problem using sparse modeling based on data of the measurement results measured at the second time and the distribution of resistivity of the ground determined by solving an optimization problem at the first time; The analysis method described in (1) above.

[0008] An analysis method according to one embodiment of the present disclosure includes: (3) The distribution of resistivity of the ground and the displacement of the electrode at a third time next to the second time among the different times are used as an initial model, and the distribution of resistivity of the ground and the displacement of the electrode obtained by solving an optimization problem at the second time are used as an initial model. and solving an optimization problem using sparse modeling based on the data and the distribution of resistivity of the ground obtained by solving the optimization problem at the first time. (2) The analysis method described above.

[0009] An analysis method according to one embodiment of the present disclosure includes: (4) Using the L1 norm, the distribution of the resistivity change of the ground and the displacement of the electrode are obtained. The analysis method according to any one of (1) to (3) above.

[0010] A program according to a second aspect of the present disclosure includes: (5) A program for analyzing ground changes, On the computer, a measurement result acquisition function that sets a pair of current electrodes and a pair of potential electrodes using a plurality of electrodes installed at predetermined intervals on the ground, and acquires measurement results of the potential difference between the pair of potential electrodes due to the current of the pair of current electrodes measured with any combination of the plurality of electrodes; an estimation function that estimates the distribution of resistivity of the ground and the displacement amount of the electrode relative to a reference electrode by solving an optimization problem using sparse modeling based on the data of the measurement results measured at different times; It is a program for executing the above.

[0011] A ground resistivity monitoring system according to a third aspect of the present disclosure includes: (6) an acquisition means for setting a pair of current electrodes and a pair of potential electrodes using a plurality of electrodes installed on the ground at predetermined intervals, and acquiring a measurement result of measuring a potential difference between the pair of potential electrodes due to a current of the pair of current electrodes using any combination of the plurality of electrodes; an analysis means for solving an optimization problem using sparse modeling to determine the distribution of resistivity of the ground and the displacement of the electrode relative to a reference electrode based on the data of the measurement results measured at different times; Equipped with. [Effects of the Invention]

[0012] According to the present disclosure, the accuracy of estimating the resistivity and the amount of electrode movement can be further improved. [Brief explanation of the drawings]

[0013] [Figure 1] FIG. 1 is a diagram showing a first example of a measurement system for electrical exploration measurement used in the present invention. [Figure 2] FIG. 2 is a diagram showing an example of a measurement procedure using the two-pole method with the measurement system of FIG. [Figure 3] FIG. 10 is a diagram showing a second example of a measurement system for electrical exploration measurement used in the present invention. [Figure 4] FIG. 4 is a diagram showing an example of a measurement procedure using the dipole-dipole method with the measurement system of FIG. 3. [Figure 5] 1 is a block diagram showing a schematic configuration of a computer according to an embodiment of the present invention. [Figure 6] 6 is a flowchart showing an analysis method executed by the computer of FIG. 5. [Figure 7] 7 is a flowchart showing step S2 of FIG. 6 in more detail. [Figure 8] 8 is a flowchart showing step S21 of FIG. 7 in more detail. [Figure 9] FIG. 10 is a diagram showing data of the measurement results of measuring the potential difference between a pair of potential electrodes due to the current of a pair of current electrodes with an arbitrary combination of multiple electrodes. [Figure 10] FIG. 10 is a diagram showing the initial value of resistivity in each cell of the grid. [Figure 11] FIG. 6 shows the computer-implemented resistivity model of FIG. 5. [Figure 12] 8 is a flowchart showing step S21 of FIG. 7 in more detail. [Figure 13] FIG. 1 is a diagram showing a model ground created to verify the analysis method of the present invention. [Figure 14] FIG. 10 is a diagram showing the distribution of resistivity of the ground obtained by the analysis method according to the embodiment. [Figure 15] 10 is a diagram showing actual measured values ​​and estimated values ​​of displacement amounts of an electrode in the X direction and Z direction relative to a reference electrode. FIG. DETAILED DESCRIPTION OF THE INVENTION

[0014] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. In the following drawings, the same components are designated by the same reference numerals.

[0015] The procedure for measuring the apparent resistivity of the ground using electrical exploration measurements may be basically the same as known methods. Figure 1 shows an example of a measurement system using a two-pole arrangement using a ground resistivity monitoring system 100. Remote electrodes are installed at the outermost ends of each measurement line, one as a current electrode (C∞) and the other as a potential electrode (P∞). A measurement line is set on the ground surface, and multiple electrodes 10 are installed at equal intervals (e.g., 1 m intervals) within the measurement line. Electrodes 10 are switched using a measuring device 14, which passes current through the electrodes and measures the potential at the selected electrode. The measuring device 14 constitutes an acquisition means 16 that acquires measurement results obtained by measuring the potential difference between a pair of potential electrodes due to the current of the current electrode using any combination of multiple electrodes.

[0016] The resistivity monitoring system 100 further includes an analysis means 18 that uses sparse modeling to solve an optimization problem to determine the distribution of resistivity in the ground and the amount of displacement of the electrodes relative to the reference electrode, based on data from measurements taken at different times. The analysis method will be described later.

[0017] Figure 2 shows an example of the measurement procedure using the two-electrode method. A current is passed between the far electrode (C∞) and electrode C, and the potential between electrode P and the far electrode (P∞) is measured. This measurement is repeated while changing the distance between electrode C and electrode P to the exploration depth. Here, five potential measurement electrodes (represented by P1, P2, P3, P4, and P5) are used, and the underground measurement positions are indicated by circles with diagonal lines from the upper left to the lower right. Several hundred electrodes may be installed. The number of measurement positions measured at one time depends on the performance of the measuring device 14. The longer the distance between electrode C and the potential measurement electrodes, the deeper the information obtained. From the initial state, the current electrode C and potential electrodes P1, ..., P5 are switched so that they are shifted one by one along the measurement line in the direction of the arrow. By changing the location where the current is passed and the location where the potential is measured, the number of measurement positions increases in the depth and axial directions. By carrying out such electrical exploration measurements along the survey line and continuing until the end, actual measurement data for that survey line at that point in time can be obtained.

[0018] An example of a measurement system using the dipole-dipole method is shown in Figure 3. A measurement line is set on the ground surface, and multiple electrodes 10 are placed at equal intervals (for example, 1 m intervals) along the measurement line. The electrodes are switched using a measuring device 14, which then passes current through the electrodes and measures the potential at the selected electrode.

[0019] An example of the measurement procedure using the dipole-dipole method is shown in Figure 4. A measurement line is set on the Earth's surface, and multiple electrodes 10 are placed at equal intervals (for example, 1 m intervals) along the measurement line. Measurements are performed using only the electrodes on the measurement line. A current is passed between electrodes C1 and C2, and the potential of adjacent electrodes (i.e., P1 and P2, P2 and P3, and P3 and P4) is measured. From the initial state, measurements are performed by shifting the current electrodes C1, C2 and potential electrodes P1, ..., P4 one by one along the measurement line in the direction of the arrow. The electrode spacing may be changed. For example, the distance between the transmitting dipole and receiving dipole may be increased. By performing various measurements, data can be obtained along the measurement line and in the depth direction.

[0020] The data from the dipole method is used to generate data from the dipole-dipole method, and both data are used to generate data from the dipole-dipole method. The analysis may be performed using only the dipole or dipole-dipole method. Other methods may also be used.

[0021] The apparent resistivity ρ is expressed by the following equation: ρ=KV / I (where K is the electrode arrangement coefficient) In actual uneven ground, this value does not represent the true resistivity, but reflects the distribution of resistivity underground, and can be considered a kind of average value of resistivity over a fairly wide area around the electrode, so it is called apparent resistivity. By carrying out electrical exploration measurements as described above, apparent resistivity data (distribution of apparent resistivity) can be obtained in a vertical cross section in the survey line direction.

[0022] The data processing flow according to the method of the present invention will now be described. As described above, apparent resistivity data of the ground is acquired by conducting electrical exploration measurements. Next, the apparent resistivity is used as measurement result data.

[0023] The above steps are repeated at any time interval (for example, every hour) to accumulate apparent resistivity data for multiple periods. The accumulated data is observed over time to monitor the ground.

[0024] Electrical exploration requires the placement of many electrodes. The placement of the electrodes can be arbitrary, but in the method of the present invention, measurements are taken over time, so it is desirable to install the electrodes in fixed positions, and it is preferable to drive each electrode into the ground to reduce noise and prevent fluctuations in the measurement position.

[0025] In the above example, many electrodes are arranged one-dimensionally on one measurement line, but they may also be arranged on multiple measurement lines. If they are arranged two-dimensionally, not only can vertical cross sections of resistivity change rates be obtained on multiple measurement lines, but also horizontal cross sections of resistivity change rates at different depths in the ground can be obtained.

[0026] Ground resistivity depends on various parameters such as the degree of saturation, porosity, fine particle content, and temperature, but repeated measurements enable evaluation focusing on specific parameters. For example, monitoring during rainfall allows evaluation of changes in the volumetric water content of the ground. Furthermore, monitoring ground improvement allows evaluation of the extent of ground improvement.

[0027] The resistivity monitoring system 100 further includes an analysis means 18. The analysis means 18 obtains the distribution of resistivity of the ground and the displacement of the electrode relative to a reference electrode by solving an optimization problem using sparse modeling based on the data of the measurement results measured at different times. The analysis means 18 may be connected to the acquisition means 16. The analysis means 18 may be realized by a computer 200. The analysis means 18 may be a device separate from the acquisition means 16. Alternatively, the analysis means 18 and the acquisition means 16 may be implemented in the same device.

[0028] (Computer hardware configuration) The resistivity monitoring system 100 may be implemented by a computer 200 shown in Fig. 5. The hardware configuration of the computer 200 will be described in detail below. The computer 200 includes a display unit 210, an operation unit 220, a storage unit 230, a control unit 240, and a communication unit 250.

[0029] The display unit 210 may be a display device, such as a liquid crystal display or an OEL (organic electroluminescence) display, but is not limited to these and may be any display device.

[0030] The operation unit 220 is an input interface that accepts user operations. The input interface may be, for example, a pointing device such as a mouse, physical keys, or a touch panel that is integral with the display unit 210, but is not limited to these and may be any input interface.

[0031] The storage unit 230 is a storage device including one or more memories. The memory may be, for example, a semiconductor memory, a magnetic memory, an optical memory, or the like, but is not limited to these, and may be any memory. The storage unit 230 functions as, for example, a primary storage device or a secondary storage device. The storage unit 230 is, for example, built into the computer 200, but may also be configured to be externally connected to the computer 200 via any interface.

[0032] The storage unit 230 stores the measurement results of the acquisition means 16 .

[0033] The control unit 240 is one or more processors. The processor may be, for example, a general-purpose processor or a dedicated processor specialized for a particular process, but is not limited to these and may be any processor. The control unit 240 controls the overall operation of the resistivity monitoring system 100.

[0034] The communication unit 250 is one or more interfaces for communicating with external devices wirelessly or via wires.

[0035] (Computer software configuration) Next, the software configuration of the computer 200 will be described. A program used to control the operation of the computer 200 is stored in the storage unit 230. When the program is loaded by the control unit 240, it causes the control unit 240 to execute a measurement result acquisition function, an estimation function, and an output function. The control unit 240 may include the analysis means 18 of the resistivity monitoring system 100.

[0036] The measurement result acquisition function is a function that acquires measurement results by setting a pair of current electrodes and a pair of potential electrodes using multiple electrodes installed in the ground at predetermined intervals, and measuring the potential difference between the pair of potential electrodes due to the current of the pair of current electrodes with any combination of multiple electrodes. The computer 200 acquires and stores the measurement results via the communication unit 250 or an input unit (not shown), and can use the measurement result data for subsequent inference processing.

[0037] The prediction function uses sparse modeling to solve an optimization problem and estimate the distribution of ground resistivity and the amount of electrode displacement relative to a reference electrode based on measurement data taken at different times.

[0038] The output function is to output the distribution of resistivity of the ground and the displacement of the electrode relative to the reference electrode.

[0039] An example of the operation of the resistivity monitoring system 100 will be described. The operation described below corresponds to the analysis method for analyzing ground changes according to this embodiment. That is, the analysis method for analyzing ground changes according to the present disclosure includes steps S1 to S2 shown in FIG. 6.

[0040] Before performing S1 in Fig. 6, the acquisition means 16 of the resistivity monitoring system 100 sets a pair of current electrodes and a pair of potential electrodes using a plurality of electrodes installed in the ground at predetermined intervals. Specifically, referring to Fig. 1 and Fig. 3, the measuring instrument 14 switches the electrodes. Next, referring to Fig. 1 and Fig. 3, the measuring instrument 14 applies current to the electrodes and measures the potential at the selected electrodes.

[0041] 6, the computer 200 acquires measurement result data. Specifically, the acquired measurement result data is input to the computer 200. The input measurement result data may be data on the measured potential and current, or may be data on the apparent resistivity calculated from the potential and current data.

[0042] In S2 of Figure 6, the analysis means 18 of the resistivity monitoring system 100 estimates the distribution of resistivity in the ground and the amount of displacement of the electrodes relative to the reference electrode based on the data of measurement results measured at different times by solving an optimization problem using sparse modeling.

[0043] S2 will be described in more detail with reference to FIG. 7. In S21, the resistivity monitoring system 100 performs analysis using the reference data to generate a resistivity model. The resistivity model indicates the resistivity structure of the ground. The reference data is the measurement result data at any time (first time) other than the last measurement result obtained, among the measurement result data obtained at multiple times in step S1. The first measurement result data obtained does not necessarily become the reference data. It is desirable that the reference data be the data obtained immediately before an event occurs that changes the resistivity of the ground. For example, if it rains at 12:10, the measurement result data obtained at 12:00 (first time) immediately before the rain falls may be used as the reference data. This step will be described in detail later.

[0044] In S22, the resistivity distribution and the displacement of the electrode relative to the reference electrode are estimated using measurement result data acquired after the reference data (second time). For example, measurement result data acquired at 1:00 PM (second time) and 2:00 PM (third time) are used. Details of this step will be described later.

[0045] S21 will be described in more detail with reference to Fig. 8. Note that in S1 before S21, data on the measurement results (apparent resistivity) obtained by measuring the potential difference between a pair of potential electrodes due to the current of a pair of current electrodes using any combination of multiple electrodes is acquired, as shown in Fig. 9. The data on the measurement results is denoted as d (the number of data is N).

[0046] In S211, an initial model is set. First, as shown in Figure 10, the ground is divided into a grid (rectangles). The number of cells is M. Each cell is not the same size, and the deeper the cell, the thicker the depth direction. This is because the sensitivity decreases as the depth decreases. The horizontal length of each cell corresponds to the spacing between the measurement electrodes. Through S21, the resistivity (m0 - m) in each cell of the grid is calculated. M-1 ) is inferred.

[0047] Referring to FIG. 10, the initial resistivity value (temporary value) in each grid cell is set to m based on the data d. i For cells corresponding to positions not measured in S1, an initial resistivity value is set based on the value of a cell at the same depth or an adjacent cell. The number of initial values ​​to be set is M. In other words, resistivity m is a matrix with M rows and 1 column.

[0048] The estimated resistivity is m that minimizes the following equation. Note that ||·||2 indicates the L2 norm. ||·||1, which will be described later, indicates the L1 norm.

number

[0049] where G is the Jacobian, m is the resistivity, d is the measured data (apparent resistivity), and C is the smoothing filter. The analysis is preferably performed in the logarithmic domain.

[0050] In S212, the difference d[i] between the observed data d and the set model is calculated. In other words, the difference (residual) between the response (apparent resistivity) ρcalc[i] obtained from the given model and the response (apparent resistivity) ρa[i] obtained by measurement is calculated. If the difference between the model used to calculate the theoretical response and the actual resistivity distribution of the ground is small, the residual will be close to 0. On the other hand, if the actual resistivity distribution differs from the calculated model, the residual will be large. TIFF2025177511000003.tif18166

[0051] If the residual is equal to or smaller than a predetermined threshold, for example, if the norm of the residual is equal to or smaller than 1% of the norm of the measurement data, the process ends. Otherwise, the process proceeds to step S213.

[0052] Analyze the Jacobian G.

number

[0053] The above optimization problem can be solved by repeatedly calculating while changing m by the correction parameter Δm, as shown in the following equation: In S213, the model is corrected.

number

[0054] Expanding the above formula, we obtain the following formula:

number

[0055] Here, F may be set to make the boundary surface clear using weights Wx and Wz as shown in the following equation.

number

[0056] In the above equation (Equation 4), Δd is the difference between the measured value and Gm i This is the difference between

[0057] Solve the above equation (Equation 4) to find Δm.

[0058] Update the parameters.

number

[0059] The theoretical calculation is performed again on the model corrected above, and the residual from the measured value is calculated again in S212. This model correction and residual calculation process is repeated until the residual becomes sufficiently small, or until no reduction in the residual is observed even after correction, or until the number of repetitions set during analysis (e.g., 8 times) has been performed.

[0060] By performing S21, a resistivity model such as that shown in FIG. 11 is generated.

[0061] S22 will be explained in more detail with reference to FIG.

[0062] In S221, the variable n indicating the measurement time is set to 2. That is, first, the distribution of the resistivity of the ground and the displacement of the electrodes at the second time are obtained.

[0063] In S222, an initial model is set. If n is 2, the resistivity generated in S21 (first time) is set as the initial value mref. The electrode displacement is set as an initial value of 0. As will be described later, if n is 3 or more, the resistivity and electrode displacement calculated for the (n-1)th time are set as the initial value mref. The electrode displacement here refers to the displacement of electrodes other than the reference electrode and the far electrode (FIG. 1) relative to the reference electrode 10S located at the starting point, with reference to FIGS. 1 and 3.

[0064] The estimated resistivity and electrode displacement are m that minimize the following equation. The direction of the measurement line is the X direction, and the up-down direction is the Z direction. The estimated electrode displacement may be the displacement in the X and Z directions (two directions). In this case, if the number of electrodes is a, unknowns are set for (a-1) electrodes. Since the displacement in the X direction and the displacement in the Z direction each have (a-1) unknowns, m and mref are matrices with (M+2(a-1)) rows and 1 column.

number

[0065] where G is the Jacobian, m is the resistivity and electrode displacement, d is the measurement data (apparent resistivity), C is the smoothing filter, m ini (=m ref ) is the reference model.

[0066] Equation 7 is solved using the ADMM method (alternating direction multiplier method). The ADMM method uses an extended Lagrangian function, so the following seven parameters are set in the analysis. λ Resistivity λ2 ·γ_rho used in the Lagrangian function λ2 in the X direction ·γ_x used in the Lagrangian function λ2 in Z direction ·γ_z used in the Lagrangian function

[0067] In S223, the difference between the observed data and the set model is calculated. This procedure is The same as 12. However, even if the residual is small, the process does not have to be terminated.

[0068] If the number of repetitions is less than the threshold value, the process proceeds to S224. If the number of repetitions is equal to or greater than the threshold value, the process proceeds to S225.

[0069] Calculate the Jacobian G. The resistivity part can be calculated in the same way as in S212. The electrode displacement part can be calculated using central differences.

[0070] The above optimization problem can be solved by giving initial values ​​and performing repeated calculations as described above, and can be expressed as follows: In S224, the model is corrected.

number

[0071] In the above equation (Equation 8), a solution is found in which the difference from the reference model obtained in S21 is sparse.

[0072] The L1 norm is used in equation (8). By solving the optimization problem using the L1 norm, it is possible to analyze the distribution of ground resistivity and the displacement of the electrodes (unknowns) using sparse modeling. Therefore, the number of unknowns that change is small. The displacement of electrodes that do not displace is calculated as 0.

[0073] Spark modeling increases the independence of each unknown parameter, resulting in higher accuracy. In addition, since no smoothing constraints are imposed on the displacement, only electrodes where displacement occurs are extracted.

[0074] The theoretical calculation is performed again on the model corrected below, and the residual from the measured value is calculated again in S223. This process of model correction and residual calculation is repeated until the number of repetitions set during analysis (e.g., 8 times) has been reached.

[0075] In S225, n is incremented by 1. Then, the process proceeds to step S211.

[0076] By carrying out the above-mentioned procedure, the distribution of resistivity in the ground and the displacement of the electrode relative to the reference electrode can be obtained. [Example]

[0077] Next, an analysis method according to an embodiment of the present invention was implemented, which will be described below.

[0078] In this example, the ground shown in Figure 13 was measured. The upper figure shows the ground before the first time. The lower figure shows the ground after the first time and before the second time. The resistivity of the ground from the surface to a depth of 1.5 m dropped from 300 to 150. In addition, the electrode at a distance of 5 m rose 10 cm. Figure 13 shows a model ground created to verify the analysis method of the present invention.

[0079] FIG. 14 is a diagram showing the distribution of the resistivity of the ground at the second time, which is determined in the estimation step of the analysis method.

[0080] From Figure 14, it was estimated that the resistivity of the ground from the surface to a depth of approximately 1.5 m at time 2 was approximately 150. It was also estimated that the ground surface was uplifted at a distance of approximately 5 m. Therefore, it was found that the resistivity of the ground was accurately estimated.

[0081] FIG. 15 is a diagram showing the measured values ​​and estimated values ​​of the displacement amounts of the electrodes in the X direction and Z direction relative to the reference electrode at the second time.

[0082] From Figure 15, it can be seen that the displacement in the X and Z directions at a distance of 5 m was accurately estimated.

[0083] Although the present invention has been described based on the drawings and examples, it should be noted that those skilled in the art can easily make various modifications or alterations based on the present disclosure. Therefore, it should be noted that these modifications and alterations are included in the scope of the present invention. For example, the functions included in each means, step, etc. can be rearranged so as not to be logically inconsistent, and multiple means or steps can be combined or divided into one.

[0084] In the above-described embodiment, an example of the operation of the resistivity monitoring system 100 has been described with reference to the drawings. However, a configuration in which some steps included in the above-described operation, or some operations included in one step, are omitted within a range that is not logically inconsistent is also possible. Also, a configuration in which the order of multiple steps included in the above-described operation is reversed within a range that is not logically inconsistent is also possible.

[0085] Furthermore, in the above-described embodiment, the various means realized by the control unit 240 of the computer 200 are described as software configurations, but at least some of the means may be a concept that includes software resources and / or hardware resources. [Explanation of symbols]

[0086] 100: Resistivity monitoring system 10,10S: Electrode 14: Measuring instrument 16: Acquisition means 18: Analysis means 200: Computer 210: Display section 220:Operation unit 230: Storage section 240: Control unit 250: Communications Department

Claims

1. In the analytical method for analyzing changes in the ground, a measurement result acquisition step of setting a pair of current electrodes and a pair of potential electrodes using a plurality of electrodes installed at predetermined intervals on the ground, and acquiring a measurement result of measuring a potential difference between the pair of potential electrodes due to a current of the pair of current electrodes using any combination of the plurality of electrodes; an estimation step of solving an optimization problem using sparse modeling to determine the distribution of resistivity of the ground and the displacement of the electrode relative to a reference electrode based on the data of the measurement results measured at different times; An analysis method including:

2. A distribution of resistivity of the ground at a first time among the different times is obtained by solving an optimization problem based on data of a measurement result measured at the first time; determining a distribution of resistivity of the ground and a displacement of the electrode at a second time that is later than the first time by solving an optimization problem using sparse modeling based on data of the measurement results measured at the second time and the distribution of resistivity of the ground determined by solving an optimization problem at the first time; The analysis method according to claim 1 .

3. The distribution of resistivity of the ground and the displacement amount of the electrode at a third time next to the second time among the different times are obtained by solving an optimization problem using sparse modeling based on the data of the measurement results measured at the third time and the distribution of resistivity of the ground obtained by solving the optimization problem at the first time, with the distribution of resistivity of the ground and the displacement amount of the electrode obtained by solving the optimization problem at the second time as an initial model. The analysis method according to claim 2 .

4. Using the L1 norm, the distribution of the resistivity change of the ground and the displacement of the electrode are obtained. The analysis method according to any one of claims 1 to 3.

5. A program for analyzing ground changes, On the computer, a measurement result acquisition function that sets a pair of current electrodes and a pair of potential electrodes using a plurality of electrodes installed at predetermined intervals on the ground, and acquires measurement results of the potential difference between the pair of potential electrodes due to the current of the pair of current electrodes measured with any combination of the plurality of electrodes; an estimation function that estimates the distribution of resistivity of the ground and the displacement amount of the electrode relative to a reference electrode by solving an optimization problem using sparse modeling based on the data of the measurement results measured at different times; A program to execute.

6. an acquisition means for setting a pair of current electrodes and a pair of potential electrodes using a plurality of electrodes installed on the ground at predetermined intervals, and acquiring a measurement result of measuring a potential difference between the pair of potential electrodes due to a current of the pair of current electrodes using any combination of the plurality of electrodes; an analysis means for solving an optimization problem using sparse modeling to determine the distribution of resistivity of the ground and the displacement of the electrode relative to a reference electrode based on the data of the measurement results measured at different times; A ground resistivity monitoring system equipped with

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