JP2010217036A - Sensitivity-adapted backward analysis method in numerical analysis of resistivity method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To improve the analysis resolution and the analysis efficiency in a backward analysis of the resistivity in physical probing. <P>SOLUTION: Each grid in a forward analysis grid and a backward analysis grid is composed of a triangular or tetrahedral unstructured grid. The backward analysis grid is composed so as to variably control a density of grid nodes. A sensitivity statistical value S<SB>S</SB>of each parameter is obtained from a formed sensitivity matrix. A function F<SB>S</SB>for controlling the density of the nodes in the backward analysis grid is obtained based on the obtained sensitivity statistical value S<SB>S</SB>. A sparseness of the density of the grid nodes in the backward analysis grid is corrected in response to the magnitude of the sensitivity and a change in a property value based on the function F<SB>S</SB>. The backward analysis grid is set again. The sensitivity matrix is formed again based on the backward analysis grid set again. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a sensitivity-adapted inverse analysis method in numerical analysis of a specific resistance method.

In recent years, geological disasters due to geological conditions have occurred over a relatively wide range, such as large-scale landslides covering several square kilometers and frequent slope failures during heavy rains, and geology due to pollutants such as heavy metals and volatile organic compounds Contamination is increasing. In addition, there is an increasing need for highly accurate ground surveys when constructing civil engineering structures in areas with complex topography and geological structures. Conventionally, as an investigation method to elucidate such a wide-area underground structure three-dimensionally accurately and at low cost, a physical exploration method of the underground structure by measuring a physical quantity of the ground and estimating the physical property value distribution of the underground It has been known. In this geophysical exploration method analysis, the ground is divided into small areas, and a ground model obtained by assigning physical properties to each small area is set, and theoretical values calculated theoretically for this ground model. Inverse analysis is performed in which the physical property value of the small region is changed so that the square sum of the difference between the actual measured value and the actually measured value is minimized, and the physical property distribution of the ground is estimated (see, for example, Patent Document 1). .) In the inverse analysis of geophysical exploration, there is a forward analysis grid for theoretical calculation of physical property values and a model grid that is divided more roughly than this forward analysis grid and defines physical property values for each group of cells in multiple forward analysis grids. used.
Japanese Patent Laying-Open No. 2005-337746 (page 10, FIG. 6)

  However, in the above model grid (parameter grid), the grid is divided into a lattice pattern, or mesh division is automatically performed by the inverse of the cube of the distance from the current source, and is constant according to the distance from the observation point. The division is performed so as to enlarge the division area according to the rule. In the inverse analysis, physical property values assigned to individual model grids are repeatedly corrected, but the model grid division state itself is not changed in the process. As a result, there is a problem that the division of the actual physical property value distribution is inappropriate and the convergence of the analysis is deteriorated. For this reason, conventionally, in order to prevent the convergence of the analysis from deteriorating, constraints such as smoothing and flattening between adjacent grids must be applied, and the obtained information can be used effectively for measurement data. There was a problem that the underground information contained therein could not be extracted sufficiently. In particular, three-dimensional exploration and analysis have the problem that the number of unknown physical property values is enormous for two-dimensional exploration and analysis, which increases the calculation time for solving this and significantly reduces the stability of the analysis. It was.

  The present invention has been made to solve the above-described problem, and can appropriately set an analysis region in which a change in physical property value is involved with respect to a measured physical property value data group without excess or deficiency, and determine an analysis range. The purpose of this study is to provide a sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method that can improve the resolution and analysis efficiency of the analysis by changing the parameter grid according to the physical property value distribution of the underground structure. Is.

  The sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to claim 1 of the present invention is based on the input terrain information data, the electrode source position data, and the observation data obtained by actual measurement. Set up a forward analysis grid with a high grid node density and a reverse analysis grid with a lower grid node density than this forward analysis grid, as well as the average of the physical properties obtained based on the observation data actually measured in each small area Set a ground model with physical properties added to the grid obtained by giving values, compare the theoretical value theoretically calculated from the set ground model with the observed data, and perform reverse analysis if within the error range Output the analysis results of the grid and the physical property values defined in the grid to estimate the physical property value distribution of the ground. Determine the sensitivity of the parameter to form a sensitivity matrix, perform a reverse analysis based on the difference between the theoretical value of the observed data and the actual measurement value, and the sensitivity matrix, obtain a new parameter value, and reversely analyze the calculated parameter value An analysis method in which the analysis is performed by repeatedly applying the ground model to the grid, and each of the forward analysis grid and the reverse analysis grid is constituted by a triangular or tetrahedral unstructured grid, and the inverse analysis is performed. A function that configures the grid so that the grid node density is variably controlled, calculates the sensitivity statistics of each parameter from the formed sensitivity matrix, and controls the node density of the inverse analysis grid based on the obtained sensitivity statistics Based on this function, the grid node density of the inverse analysis grid is corrected according to the change in the physical property value and the sensitivity, and the inverse analysis grid is set again. , It is characterized in that the re-forming the sensitivity matrix based on the inverse analysis grids set again.

  In the sensitivity-adaptive inverse analysis method in the numerical analysis of the resistivity method according to claim 1 of the present invention, the underground space is made into a small region based on the input topographic information data, the electrode source position data, and the observation data obtained by actual measurement. Set up a forward analysis grid with a high grid node density and a reverse analysis grid with a lower grid node density than this forward analysis grid, as well as the average of the physical properties obtained based on the observation data actually measured in each small area Set a ground model with physical properties added to the grid obtained by giving values, compare the theoretical value theoretically calculated from the set ground model with the observed data, and perform reverse analysis if within the error range Output the analysis results of the grid and the physical property values defined in the grid to estimate the physical property value distribution of the ground, and if it is outside the error range, The sensitivity of the parameter is calculated to form a sensitivity matrix, and the inverse analysis is performed based on the difference between the theoretical value and the actual measurement value of the observation data and the sensitivity matrix, the parameter value is newly determined, and the calculated parameter value is inversely analyzed. An analysis method in which the analysis is performed by repeatedly applying the ground model to the grid, and each of the forward analysis grid and the reverse analysis grid is constituted by a triangular or tetrahedral unstructured grid, and the inverse analysis is performed. A function that configures the grid so that the grid node density is variably controlled, calculates the sensitivity statistics of each parameter from the formed sensitivity matrix, and controls the node density of the inverse analysis grid based on the obtained sensitivity statistics Based on this function, the grid node density of the inverse analysis grid is corrected according to the change in the physical property value and the sensitivity, and the inverse analysis grid is set. Since the sensitivity matrix is recreated based on the reconfigured inverse analysis grid, the sensitivity matrix is recreated based on the reconfigured inverse analysis grid, and then the physical properties of the inverse analysis grid Since the inverse analysis is performed to correct the values, as the analysis progresses, the underground area can be divided into grids that match the observation data actually used and the underground resistivity distribution, and changes in physical properties are involved. The analysis area to be performed can be set appropriately without excess and deficiency, and the resolution and efficiency of analysis are improved.

  The sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to claim 2 of the present invention is a part where the change in physical property value and sensitivity at the nodes of the reverse analysis grid are large when the density of the grid nodes of the inverse analysis grid is set. Then, the node density is increased, and correction is made so that the node density is lowered at a portion where the change in physical property value and sensitivity are small.

  In the sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to claim 2 of the present invention, when the density of the grid nodes of the inverse analysis grid is set, the physical property value change and the sensitivity at the nodes of the reverse analysis grid are large. Then, by increasing the nodal density and reducing the nodal density in areas where the physical property value change and sensitivity are small, the nodal density is increased and the physical property value changes in areas where the physical property value change is large and the sensitivity is high. Since the density of nodes is small and the node density is low, it is corrected so that the node density is low. By performing this inverse analysis, it is possible to appropriately set the analysis area in which changes in physical property values are involved, resulting in excess or deficiency. Hard to do. In addition, since the small region is finely divided in the region where the physical property value change is large, the resolution of the analysis can be improved, and the underground information contained in the data can be sufficiently extracted without waste. In the region where the change in the physical property value is not large, the small region is not divided finely and remains divided roughly, so that the calculation load is reduced and the analysis efficiency and stability are improved.

  The sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to claim 3 of the present invention corresponds to a grid whose sensitivity to the observation data is equal to or lower than a predetermined threshold when obtaining the sensitivity of each parameter for each observation data. The analysis region is determined by removing the parameter from the analysis parameter.

  In the sensitivity adaptive inverse analysis method in the numerical analysis of the resistivity method according to claim 3 of the present invention, when the sensitivity of each parameter is obtained for each observation data, the sensitivity to the observation data corresponds to a grid having a predetermined threshold value or less. By removing the parameters from the analysis parameters and determining the analysis area, grids with sensitivity below the specified threshold or no sensitivity are removed from the analysis area, so only the effective analysis range for the observation data is available. Based on the analysis.

  The sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to claim 4 of the present invention is based on the input topographic information data, the electrode source position data, and the observation data obtained by actual measurement. A forward analysis grid having a grid with a high node density of the grid and a reverse analysis grid having a grid with a node density lower than that of the forward analysis grid are generated, and each grid of the forward analysis grid and the reverse analysis grid is generated. Is composed of a triangular or tetrahedral unstructured grid, and the inverse analysis grid is configured to have a grid node density variably controlled, and observation data obtained by a combination of transmitting and receiving electrodes The average physical property value of the basement is calculated based on the above, and the physical property average value is calculated on the line or plane connecting the nodes of the mesh of the generated inverse analysis grid. A second step of setting an initial model by setting an initial physical property parameter to the cell, and a third step of setting a physical property model by assigning a physical parameter to each cell of the forward analysis grid based on the set initial model; The forward analysis is performed based on the set physical property model, and the theoretical value of the physical response to the observation data is obtained based on the physical property model with the electrode transmission / reception arrangement that matches the actual measurement in the physical property model. A fourth step for obtaining a model theoretical solution at the node, a fifth step for comparing the model theoretical solution and the observation data, and determining whether or not it is within the error range, and an error range in the fifth step In the sixth step and the fifth step in which the inverse analysis grid and the physical property value defined in the grid are output and the analysis is terminated, If it is determined that the difference is out of the range, the sensitivity of each parameter for each observation data is obtained for each node of the inverse analysis grid, and a sensitivity matrix corresponding to the inverse analysis grid is formed in the seventh step and the seventh step. The sensitivity statistic of each parameter is obtained from the formed sensitivity matrix, the function corresponding to the inverse analysis grid corresponding to the sensitivity analysis is obtained from the sensitivity statistics, and the grid node density of the inverse analysis grid is calculated based on the sensitivity adaptation function. Correct the density according to the physical property value change and the sensitivity and re-set the inverse analysis grid, re-form the sensitivity matrix based on the inverse analysis grid re-set according to the sensitivity adaptation function, An eighth step of determining an analysis region by removing a parameter corresponding to a grid whose sensitivity is equal to or less than a predetermined threshold from the analysis parameter, and the difference and formation between the model theoretical solution and the observation data Inverse analysis is performed on the basis of the revised sensitivity matrix, the physical property parameter is corrected to obtain a new physical property parameter, and the newly obtained physical property parameter is assigned to each cell of the inverse analysis grid to update the model. And a ninth step of returning to the third step instead of the updated model as an initial model of the third step.

  In the sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to claim 4 of the present invention, a large number of subsurface spaces are reduced based on the input topographic information data, electrode source position data, and observation data obtained by actual measurement. A forward analysis grid having a grid with a high node density of the grid and a reverse analysis grid having a grid with a node density lower than that of the forward analysis grid are generated, and each grid of the forward analysis grid and the reverse analysis grid is generated. Is composed of a triangular or tetrahedral unstructured grid, and the inverse analysis grid is configured to have a grid node density variably controlled, and observation data obtained by a combination of transmitting and receiving electrodes The average physical property value of the basement is calculated based on this, and the physical property average value is obtained by connecting the nodes of the mesh of the generated inverse analysis grid to the line or surface. A second step of setting an initial model by setting an initial physical property parameter to a surrounding cell, and a third step of setting a physical property model by assigning a physical parameter to each cell of the forward analysis grid based on the set initial model; The forward analysis is performed based on the set physical property model, and the theoretical value of the physical response to the observation data is obtained based on the physical property model with the electrode transmission / reception arrangement that matches the actual measurement in the physical property model. A fourth step for obtaining a model theoretical solution at the node, a fifth step for comparing the model theoretical solution and the observation data, and determining whether or not it is within the error range, and an error range in the fifth step In the sixth step and the fifth step, the analysis is finished by outputting the inverse analysis grid and the physical property value defined in the grid when it is determined that If it is determined that the error is out of the range, the sensitivity of each parameter for each observation data is obtained for each node of the inverse analysis grid, and a sensitivity matrix corresponding to the inverse analysis grid is formed in the seventh step and the seventh step. The sensitivity statistic of each parameter is obtained from the formed sensitivity matrix, the function corresponding to the inverse analysis grid corresponding to the sensitivity analysis is obtained from the sensitivity statistics, and the grid node density of the inverse analysis grid is calculated based on the sensitivity adaptation function. Correct the density according to the physical property value change and the sensitivity and re-set the inverse analysis grid, re-form the sensitivity matrix based on the inverse analysis grid re-set according to the sensitivity adaptation function, An eighth step of determining an analysis region by removing a parameter corresponding to a grid having a sensitivity of a predetermined threshold value or less from the analysis parameter, and a difference and a shape between the model theoretical solution and the observation data Inverse analysis is performed on the basis of the reconstructed sensitivity matrix, the physical property parameter is corrected to obtain a new physical property parameter, and the newly obtained physical property parameter is assigned to each cell of the inverse analysis grid to update the model. And the 9th step of returning to the 3rd step instead of the updated model as the initial model of the 3rd step, the inverse analysis grid obtained in the 7th step. The latest inverse analysis grid, which is derived from the sensitivity matrix corresponding to, changes the density of the grid nodes of the inverse analysis grid according to the physical property value change and the sensitivity, and is reconfigured according to this sensitivity Based on, the sensitivity matrix is re-formed and the analysis is performed. For this reason, as the analysis progresses, the subsurface area can be divided into grids that match the observation data actually used and the subsurface resistivity distribution, so that the analysis area involved in the change in physical property values can be completed without excess or deficiency. It can be set appropriately, improving the resolution and efficiency of analysis.

  The sensitivity-adapted inverse analysis method in the numerical analysis of the specific resistance method according to claim 5 of the present invention is a portion where the physical property value change and sensitivity at the nodes of the inverse analysis grid are large when setting the density of the grid nodes of the inverse analysis grid. Then, the node density is increased, and correction is made so that the node density is lowered at a portion where the change in physical property value and sensitivity are small.

  In the sensitivity-adaptive inverse analysis method in the numerical analysis of the resistivity method according to claim 5 of the present invention, when setting the density of the grid nodes of the inverse analysis grid, the property value change and the sensitivity at the nodes of the inverse analysis grid are large. Then, by increasing the node density and modifying the physical property value change and sensitivity so that the node density is lowered, each parameter has sufficient sensitivity during reverse analysis, and causes unstable factors. The parameter with excessive sensitivity that becomes one is reduced, and the underground information included in the observation value can be stably and maximized. Since the inverse analysis is performed while repeating this, it is possible to appropriately set the analysis region in which the physical property value change is involved, and it is difficult for excess and deficiency to occur. In addition, since the small area is finely divided in the area where the physical property value change is large, the resolution of the analysis is improved. In the region where the change in physical property value is not large, the small region is not divided finely and remains divided roughly, so that the calculation load is reduced and the analysis efficiency and stability are improved.

In the sensitivity adaptation inverse analysis method in the numerical analysis of the resistivity method according to claim 6 of the present invention, the sensitivity adaptation function is an optimal node density function of the inverse analysis grid in the resistivity method,
The following formula,
F _S = a (1 + b | S _S | ^C )
Where F _S : sensitivity adaptation function,
S _S : Sensitivity statistic obtained from the sensitivity matrix, and the sensitivity statistic is also a function of all transmission / reception electrode sets and underground space coordinates through the sensitivity matrix.
c: constant related to dimension,
a: a constant related to the set maximum resolution and the range of the analysis area,
b: It is obtained by a constant related to the set relative resolution.

In the sensitivity adaptation inverse analysis method in the numerical analysis of the resistivity method according to claim 6 of the present invention, the sensitivity adaptation function is an optimal node density function of the inverse analysis grid in the resistivity method,
The following formula,
F _S = a (1 + b | S _S | ^C )
Where F _S : sensitivity adaptation function,
S _S : Sensitivity statistic obtained from the sensitivity matrix, and the sensitivity statistic is also a function of all transmission / reception electrode sets and underground space coordinates through the sensitivity matrix.
c: constant related to dimension,
a: a constant related to the set maximum resolution and the range of the analysis area,
b: Since it is determined by a constant related to the set relative resolution, the grid node density of the inverse analysis grid can be optimally changed according to the sensitivity, so that the analysis resolution and analysis efficiency are improved.

  In the sensitivity-adaptive inverse analysis method in the numerical analysis of the resistivity method according to claim 7 of the present invention, when the sensitivity adaptation function is obtained, the density of the grid nodes is proportional to the sensitivity adaptation function using the immediately preceding inverse analysis grid as the background grid. The sensitivity matrix is re-formed based on the latest inverse analysis grid having the re-created grid.

  In the sensitivity-adaptive inverse analysis method in the numerical analysis of the resistivity method according to claim 7 of the present invention, when the sensitivity adaptation function is obtained, the density of the grid nodes is proportional to the sensitivity adaptation function using the immediately preceding inverse analysis grid as the background grid. In order to generate a new grid by preparing the sensitivity matrix based on the latest inverse analysis grid with the re-created grid, a grid for defining the spatial function is prepared in advance. However, by using the immediately preceding inverse analysis grid as the background grid, it is not necessary to generate a new grid according to another spatial function, so that the analysis work is made efficient.

  The sensitivity-adapted inverse analysis method in the numerical analysis of the specific resistance method according to claim 8 of the present invention excludes a parameter corresponding to a grid whose sensitivity is equal to or lower than a predetermined threshold from the analysis target from among the regenerated sensitivity matrix. The analysis region is determined, a sensitivity matrix is determined, and analysis is performed based on the determined sensitivity matrix.

  In the sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to claim 8 of the present invention, a parameter corresponding to a grid whose sensitivity is equal to or lower than a predetermined threshold is excluded from the analysis target in the regenerated sensitivity matrix. Since the analysis region is determined and the sensitivity matrix is calculated, and the analysis is performed based on the calculated sensitivity matrix, the sensitivity is equal to or lower than the predetermined threshold value or the grid having no sensitivity is removed from the analysis region. The analysis is performed based only on the effective analysis range for the measured value.

  The sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to claim 1 of the present invention is based on the input terrain information data, the electrode source position data, and the observation data obtained by actual measurement. Set up a forward analysis grid with a high grid node density and a reverse analysis grid with a lower grid node density than this forward analysis grid, as well as the average of the physical properties obtained based on the observation data actually measured in each small area Set a ground model with physical properties added to the grid obtained by giving values, compare the theoretical value theoretically calculated from the set ground model with the observed data, and perform reverse analysis if within the error range Output the analysis results of the grid and the physical property values defined in the grid to estimate the physical property value distribution of the ground. Determine the sensitivity of the parameter to form a sensitivity matrix, perform a reverse analysis based on the difference between the theoretical value of the observed data and the actual measurement value, and the sensitivity matrix, obtain a new parameter value, and reversely analyze the calculated parameter value An analysis method in which the analysis is performed by repeatedly applying the ground model to the grid, and each of the forward analysis grid and the reverse analysis grid is constituted by a triangular or tetrahedral unstructured grid, and the inverse analysis is performed. A function that configures the grid so that the grid node density is variably controlled, calculates the sensitivity statistics of each parameter from the formed sensitivity matrix, and controls the node density of the inverse analysis grid based on the obtained sensitivity statistics Based on this function, the grid node density of the inverse analysis grid is corrected according to the change in the physical property value and the sensitivity, and the inverse analysis grid is set again. Since the sensitivity matrix is re-formed based on the reconfigured inverse analysis grid, the subsurface area is adapted to the actually used observation data and the subsurface resistivity distribution as the analysis progresses. It is possible to divide the grid into the grids, and to appropriately set the analysis area in which the physical property value change is concerned without excess or deficiency, improving the resolution of the analysis and reducing the calculation load and improving the analysis efficiency.

  The sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to claim 4 of the present invention is based on the input topographic information data, the electrode source position data, and the observation data obtained by actual measurement. A forward analysis grid having a grid with a high node density of the grid and a reverse analysis grid having a grid with a node density lower than that of the forward analysis grid are generated, and each grid of the forward analysis grid and the reverse analysis grid is generated. Is composed of a triangular or tetrahedral unstructured grid, and the inverse analysis grid is configured to have a grid node density variably controlled, and observation data obtained by a combination of transmitting and receiving electrodes The average physical property value of the basement is calculated based on the above, and the physical property average value is calculated on the line or plane connecting the nodes of the mesh of the generated inverse analysis grid. A second step of setting an initial model by setting an initial physical property parameter to the cell, and a third step of setting a physical property model by assigning a physical parameter to each cell of the forward analysis grid based on the set initial model; The forward analysis is performed based on the set physical property model, and the theoretical value of the physical response to the observation data is obtained based on the physical property model with the electrode transmission / reception arrangement that matches the actual measurement in the physical property model. A fourth step for obtaining a model theoretical solution at the node, a fifth step for comparing the model theoretical solution and the observation data, and determining whether or not it is within the error range, and an error range in the fifth step In the sixth step and the fifth step in which the inverse analysis grid and the physical property value defined in the grid are output and the analysis is terminated, If it is determined that the difference is out of the range, the sensitivity of each parameter for each observation data is obtained for each node of the inverse analysis grid, and a sensitivity matrix corresponding to the inverse analysis grid is formed in the seventh step and the seventh step. The sensitivity statistic of each parameter is obtained from the formed sensitivity matrix, the function corresponding to the inverse analysis grid corresponding to the sensitivity analysis is obtained from the sensitivity statistics, and the grid node density of the inverse analysis grid is calculated based on the sensitivity adaptation function. Correct the density according to the physical property value change and the sensitivity and re-set the inverse analysis grid, re-form the sensitivity matrix based on the inverse analysis grid re-set according to the sensitivity adaptation function, An eighth step of determining an analysis region by removing a parameter corresponding to a grid whose sensitivity is equal to or less than a predetermined threshold from the analysis parameter, and the difference and formation between the model theoretical solution and the observation data Inverse analysis is performed on the basis of the revised sensitivity matrix, the physical property parameter is corrected to obtain a new physical property parameter, and the newly obtained physical property parameter is assigned to each cell of the inverse analysis grid to update the model. Since the initial model of the third step has a ninth step for returning to the third step instead of the updated model, the density of the grid nodes of the inverse analysis grid is changed by changing the physical property value. The analysis can be performed based on the latest inverse analysis grid that has been reconfigured according to the sensitivity, and the subsurface area is actually used as the analysis progresses. Can be divided into grids suitable for the observed observation data and the distribution of underground resistivity, the analysis area involved in the change in physical property values can be set appropriately without excess and deficiency, and the resolution of the analysis can be improved. Moni, calculation load is reduced analysis efficiency is improved.

FIG. 1 is a flowchart for explaining a sensitivity-adapted inverse analysis method in numerical analysis of a specific resistance method according to an embodiment of the present invention in the order of steps. (Example 1) 2A and 2B are respectively an explanatory diagram of a two-dimensional ground model and an explanatory diagram of an electrode system arrangement thereof according to an example of analysis used in the method of FIG. 3A and 3B are an explanatory diagram showing an example of analysis by the sensitivity adaptive analysis method (Sensitivity Adaptive Inversion, SAI method) and an explanatory diagram of a forward analysis grid, respectively. 4A and 4B are an explanatory diagram showing an example of analysis by the sensitivity matching analysis method (SAI method) and an explanatory diagram of an initial inverse analysis grid, respectively. FIG. 5 is an explanatory diagram showing an example of a sensitivity matching function and an example of a range in which a parameter grid having no sensitivity is removed. FIGS. 6A and 6B are explanatory diagrams showing a state in which the inverse analysis grid changes as the analysis by the sensitivity matching analysis method (SAI method) proceeds. FIGS. 7A and 7B are an explanatory diagram and an analysis result diagram showing a state in which the inverse analysis grid changes as the analysis by the sensitivity matching analysis method (SAI method) proceeds. FIG. 8 is an explanatory diagram of a three-dimensional ground model according to another example of analysis used in the method of FIG. (Example 2) FIG. 9 is a cross-sectional view showing the contact distribution of the model grid projected on the YZ cross section at x = 7.5 m in the state of the initial inverse analysis grid of the analysis of the ground model of FIG. FIG. 10 is a cross-sectional view showing the contact distribution of the model grid projected on the YZ cross section at x = 7.5 m in the state where the reverse analysis grid is changed from the state of FIG. 9 with the progress of analysis for the ground model of FIG. FIG. FIG. 11 is a cross section showing the distribution of contact points of the model grid projected on the YZ cross section at x = 7.5 m in the state where the reverse analysis grid is changed from the state of FIG. FIG. FIG. 12 is a cross-sectional view showing a point distribution of a model grid projected on the XZ cross section at y = 7.5 m in the state of FIG. 9 in the ground model of FIG. FIG. 13 is a cross-sectional view showing a point distribution of a model grid projected on the XZ cross section at y = 7.5 m in the state of FIG. 10 for the ground model of FIG. 14 is a cross-sectional view showing a point distribution of a model grid projected on the XZ cross section at y = 7.5 m in the state of FIG. 11 in the ground model of FIG. 15 is a cross-sectional view showing a point distribution of a model grid projected on the XY cross section at z = −7.5 m in the state of FIG. 9 in the ground model of FIG. 16 is a cross-sectional view showing the point distribution of the model grid projected on the XY cross section at z = −7.5 m in the state of FIG. 10 for the ground model of FIG. 17 is a cross-sectional view showing a point distribution of a model grid projected on the XY cross section at z = −7.5 m in the state of FIG. 11 for the ground model of FIG. FIG. 18 is a reverse analysis result diagram showing the result of the reverse analysis in the cross section of x = 7.5 m with respect to FIG. FIG. 19 is a reverse analysis result diagram showing the result of the reverse analysis in the cross section of y = 7.5 m with respect to FIG. FIG. 20 is a reverse analysis result diagram showing the result of the reverse analysis in the cross section of z = −7.5 m with respect to FIG. FIG. 21 is a flowchart for explaining the inverse analysis method in the numerical analysis of the conventional specific resistance method in the order of steps. FIG. 22 is a grid diagram of the inverse analysis in which the three-dimensional ground model of FIG. 8 is projected onto the YZ section at x = 7.5 m with the progress of analysis using the conventional inverse analysis method shown in FIG. FIG. 23 is a grid diagram of inverse analysis projected on the XZ section at y = 7.5 m in the state of FIG. FIG. 24 is a grid diagram of inverse analysis projected on the XY cross section at z = −7.5 m in the state of FIG. 22. FIG. 25 is a reverse analysis result diagram showing the result of the reverse analysis in the cross section of x = 7.5 m with respect to FIG. FIG. 26 is a reverse analysis result diagram showing the result of the reverse analysis in the cross section of y = 7.5 m with respect to FIG. FIG. 27 is a reverse analysis result diagram showing the result of reverse analysis in the cross section of z = −7.5 m with respect to FIG. FIGS. 28A to 28C are explanatory diagrams showing examples of nonconformity in the conventional model grid arrangement. FIGS. 29A and 29B show analysis results analyzed using the method according to the present invention and the analysis results analyzed using the conventional method of fixing the model grid in searching for a known cavity, respectively. It is a comparison figure of the analysis result shown by comparing. (Example 3) FIGS. 30A and 30B are explanatory views for explaining the unstructured lattice of the present invention. FIG. 31 is a change diagram showing a change in the relative mean square error RMS of each iteration.

  Based on the input terrain information data and electrode source position data, the forward analysis grid with a high node density and grid nodes divided into small areas based on the input topographic information data and electrode source position data, Set up a reverse analysis grid with a grid node density lower than that of the forward analysis grid, and set up a ground model obtained by giving the average value of physical properties obtained based on actually measured observation data to each small area The theoretical values calculated theoretically from the obtained ground model are compared with the observed data, and if it is within the error range, the analysis results of the inverse analysis grid and the physical property values defined in the grid are output to output the physical properties of the ground Estimate the value distribution, and if it is out of the error range, find the sensitivity of each parameter for each observation data, form a sensitivity matrix, and calculate the theoretical and actual values of the observation data This is an analysis method that performs inverse analysis based on the difference between the two and the sensitivity matrix, obtains a new parameter value, assigns the obtained parameter value to the inverse analysis grid, and performs analysis by repeatedly updating the ground model. Each analysis grid and inverse analysis grid is composed of a triangular or tetrahedral unstructured grid, and the inverse analysis grid is configured so that the grid node density is variably controlled. From the obtained sensitivity statistics, a function for controlling the nodal density of the inverse analysis grid is obtained, and based on this function, the density of the grid nodal density of the inverse analysis grid is calculated. Modify according to the magnitude of change and sensitivity, reset the inverse analysis grid, and re-form the sensitivity matrix based on the reset inverse analysis grid When setting the density of the grid nodes of the inverse analysis grid, increase the node density in the part where the physical property value change is large and the part where the sensitivity is strong, and the node is small in the part where the physical property value change is small and the part where the sensitivity is weak Modified to reduce the density, and when determining the sensitivity of each parameter for each observation data, the analysis area is determined by removing the grid whose sensitivity to the measurement value of the observation data is below the predetermined threshold from the analysis parameters. It was realized by doing.

Hereinafter, the present invention will be described with reference to embodiments shown in the drawings. FIG. 1 is a flowchart for explaining the sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to the present invention in the order of steps, and FIG. 2 is an explanatory diagram showing an example of the model ground used in the method of FIG. As shown in FIG. 2A, the specific resistance model ground is a ground model in which three types of specific resistance abnormal bodies are embedded in the ground having a specific resistance of 100 Ωm. The observation data measured by the electrode system shown in FIG. 2B is obtained by numerical analysis, and 5% random noise is given to these data and analyzed as actual measurement data.
First, the purpose of exploration is to elucidate the resistivity structure assuming a two-dimensional ground resistivity model as shown in FIG. In order to elucidate the resistivity structure by the resistivity method, as shown in FIG. 2B, an electrode system composed of electrodes el (see FIGS. 2A and 2B) on the ground surface and underground Set elsys. The electrode position coordinates and the surface topographic coordinates are known, and the transmission current and the reception potential difference are observed by actual measurement with a set of four electrodes selected from this electrode system (two transmission electrodes and two reception electrodes). It is assumed that the four electrode groups selected in this way have a total of n, and the transmission current and the reception potential difference are observed for each of them.

  Hereinafter, a sensitivity-adapted inverse analysis method in the numerical analysis of the specific resistance method according to the first embodiment will be described according to the analysis procedure shown in FIG. When starting the analysis, first, topographical coordinate data, electrode position data, and observation data (transmission current and reception potential difference) by actual measurement are input (see S1 of Step A (first step) shown in FIG. 1).

  In order to discretize the underground space based on these data, the underground space is divided into a large number of small regions cl (in this embodiment, triangular small regions, see FIGS. 3A and 3B) by an unstructured grid. ) And a forward analysis grid having a high density grid of grid nodes nl as shown in FIGS. 3A and 3B, and a sequence as shown in FIGS. 4A and 4B. Each of the inverse analysis grids having a grid having a node density lower than that of the analysis grid is set, so that the grid density of the inverse analysis grid is variably controlled, that is, the distance between adjacent nodes is variably controlled. (Refer to S2 and S3 of Step A shown in FIG. 1).

  Next, using the input data, the apparent resistivity is obtained, and the average underground resistivity is calculated. The average underground resistivity is expressed by the following equation.

In the above mathematical formula (1), ρ _mean : average specific resistance, n: number of observation data, ρ _ai : i-th apparent specific resistance. Apparent specific resistance is expressed by the following equation.

In the above mathematical expression (2), ΔU _i : potential difference (V) observed between the receiving electrodes of the i-th electrode group, I _i : current (A) flowing between the transmitting electrodes of the i-th electrode group, K _i : i-th It is an electrode coefficient of an electrode set. The calculated subsurface average resistivity is assigned as an initial physical property parameter to the initial inverse analysis grid, and an initial ground model is set (see Step B (second step) in FIG. 1).

  Note that mesh and grid are conceptually similar terms and are also called lattices. In this embodiment, the grid refers to a local mesh, and the mesh refers to the entire network (connected relationship) that connects the grids. The composition is composed of three elements. It consists of a node (a grid point) and a line (two-dimensional) or surface (three-dimensional) connecting the nodes and a cell. The simplest spatial range that encloses mesh nodes with connecting lines (surfaces) is called a cell. There are usually many ways to connect even if the nodes do not change. The method of connecting the nodes is based on the mesh generation method. The lattice generation method is roughly classified into a structural generation method and an unstructured generation method. The former usually creates a mesh with a quadrilateral (2D) or hexahedron (3D) as a basic cell. In the latter case, a mesh is usually created with a triangular (two-dimensional) or tetrahedron (three-dimensional) as a basic cell. The problem of obtaining physical field responses from a known underground physical property model, boundary and source is called a forward problem. Analysis that solves a forward problem is called forward analysis. The problem of estimating the underlying physical property distribution from known sources, boundaries, and measured physical field data is called an inverse problem. Analysis that solves the inverse problem is called inverse analysis. The reverse analysis process usually includes forward analysis. When solving the inverse problem in geophysical exploration, it is necessary to divide the underground space into many cells (small areas) and give physical property values to the components of each cell. In this case, it is necessary to fill the entire analysis area without overlapping the cells. Such division of the underground region is called discretization of the underground space, and it is necessary to use an appropriate grid generation method in order to discretize correctly. The grid used for the forward analysis is called the forward analysis grid fwg, and the grid defining the parameters for the reverse analysis is called the reverse analysis grid ivg (parameter grid or model grid). In the inverse analysis, it is required that the outer edge boundaries of the two types of meshes of the forward analysis grid and the inverse analysis grid coincide with the controlled space completely.

  When the initial model is set in the second step Step B, the physical property parameter is assigned to each cell of the forward analysis grid based on the set initial model to set the physical property model (Step 1 in FIG. 1). C (see third step)). That is, the specific resistance value ρ is assigned to the forward analysis grid according to the initial model. Next, forward analysis is performed based on the set physical property model, and the theoretical value of the physical response to the observation data is obtained based on this physical property model with the electrode transmission / reception arrangement that matches the actual measurement in this physical property model, and the forward analysis grid The model theoretical solution at each node is obtained (see the fourth step Step D in FIG. 1).

  Next, the model theoretical solution is compared with the observation data to determine whether or not the error is within the error range (see the fifth step Step E in FIG. 1). Then, if it is determined in the fifth step Step E that it is within the error range, that is, the calculated model theoretical solution is compared with the actually measured observation value, and the model theoretical solution and the observed value are compared. When the difference is determined to be within the error range, that is, when it is determined that the relative mean square error RMS between the model theoretical solution and the observed value is sufficiently small (see FIG. 31), the inverse analysis grid and the grid are defined. The physical property value ρ thus output is output to complete the analysis (see the sixth step Step F in FIG. 1). As indicated by the change in the relative mean square error RMS in FIG. 31, since 5% random noise is added to the analysis data, it can be said that the RMS is sufficiently small if the RMS converges near the noise level. . The RMS discriminant standard for the data currently being searched is set for estimating the noise level of the actually measured data. Here, the relative mean square error RMS between the model theoretical solution and the observed value is expressed by the following equation.

  On the other hand, if it is determined in the fifth step Step E that it is out of the error range, that is, the calculated model theoretical solution and the actually measured observation value are compared, and the model theoretical solution is compared with the observed value. When it is determined that the mean square error RMS is not sufficiently small, the sensitivity of each parameter with respect to each observation data is obtained for each node of the forward analysis grid, and a sensitivity matrix is formed (see the seventh step Step G in FIG. 1). ). That is, a sensitivity vector for each observation data is obtained for each node of the inverse analysis grid. The sensitivity of the parameter to the observation data refers to the amount of change in the physical response to the observation data that occurs when the physical property value of the parameter for one cell created underground is changed. The sensitivity matrix is a matrix generated by placing the sensitivity of the j-th parameter for the i-th observation data in i rows and j columns of the matrix and performing this operation on all i and j. In other words, the sensitivity of the parameter to the observation data obtained in the seventh Step G in FIG. 1 is the amount of change in the physical response to the observation data that occurs when the physical property value of the parameter for one cell created underground is changed. The sensitivity matrix places the sensitivity of the j-th parameter for the i-th observation data in the i-row and j-column of the matrix, and this operation is performed from 1 to n rows and 1 to m columns (i, j, m, n are This is a sensitivity matrix generated by performing all processing on natural numbers).

Next, a sensitivity statistical value of each parameter is obtained from the sensitivity matrix formed in the seventh step Step G, and a function F _S corresponding to the inverse analysis grid and corresponding to the sensitivity is obtained from the sensitivity statistical value (first step in FIG. 1). (See S4 in Step H of Step 8). The sensitivity fitting function F _S is obtained from sensitivity statistics, and is an optimal node density function of the inverse analysis grid in the resistivity method.
It is obtained by the following equation (4).
F _S = a (1 + b | S _S | ^C ) (4)
In the equation, F _S : Sensitivity adaptation function, S _S : Sensitivity statistical value obtained from sensitivity matrix, c: Constant related to dimension, a: Constant related to the set maximum resolution and analysis region range, b: Set relative resolution Is a constant involved.
Sensitivity statistic S _S, in one model, the sensitivity of the one parameter is significantly different by the combination of transmission and reception, in order to obtain the optimum node density function, typical sensitivity values, statistics from their sensitivity value Sorted by method. The selected sensitivity value is referred to as a sensitivity statistical value S _S.

Next, based on the sensitivity adaptation function F _S , the density of the grid node density of the current inverse analysis grid is corrected according to the change in the physical property value and the sensitivity, and the inverse analysis grid is reset (see FIG. 1 (see S5 of Step H). That is, when the sensitivity adaptation function F _S is obtained, the density of the grid nodes is made proportional to the sensitivity adaptation function F _{S using} the immediately preceding inverse analysis grid as a background grid. At this time, when setting the density of the grid nodes of the inverse analysis grid, increase the node density in the part where the physical property value change at the node of the inverse analysis grid is large and the part where the sensitivity is strong. Correction is made so that the node density is low, that is, the distance between the nodes is increased, in the part where the change in the physical property value at the nodes of the grid is small and the part where the sensitivity is weak. This creates a new inverse analysis grid.

  Normally, when a new grid is generated according to a certain spatial function, a grid for defining the spatial function must be prepared in advance. The background grid is a grid that defines such a spatial function, and is a grid used for grid generation. Here, the spatial area of the background grid needs to include the spatial area of the grid to be generated.

  Next, when a new inverse analysis grid is recreated in S8 of the eighth step Step H, the sensitivity of each parameter for each observation data is obtained for each node of the inverse analysis grid based on this inverse analysis grid, and a new A sensitivity matrix corresponding to the inverse analysis grid is formed again (see S6 in the eighth step Step H in FIG. 1). That is, again, a sensitivity vector for each observation data is obtained for each node of the inverse analysis grid. Then, of the regenerated sensitivity matrix, the grid whose sensitivity is equal to or lower than a predetermined threshold is excluded from the analysis target, the analysis region is determined, and the sensitivity matrix for analysis is determined (in the eighth step Step H of FIG. 1). (See S6 and FIG. 5). Next, reverse analysis is performed using the difference between the model theoretical solution of the observed data and the actually observed data and the newly determined sensitivity matrix, and the physical parameter is corrected to obtain a new physical property parameter. An updated model is set by assigning the obtained physical property parameters to each cell of the inverse analysis grid (see the ninth step Step I in FIG. 1), and the initial model in the third step Step C is replaced with this updated model. The process returns to the third step Step C (see the return from the ninth step Step I to the third step Step C in FIG. 1).

  That is, in the ninth step Step I, the modified specific resistance is assigned to the model grid, the process returns to the third step Step C, the iterative calculation is performed again until the convergence determination, and the error range in the fifth step Step E. If it is determined to be inside, the inverse analysis grid and the physical property value ρ defined in the grid are output, and the analysis is terminated (see the sixth step Step F). If it is determined in the fifth step Step E that it is out of the error range, the seventh step Step G to the ninth step Step I are repeated. 6 (A), (B) and FIG. 7 (A) show the inverse when analyzing the data of the first embodiment shown in FIGS. 2 (A) and 2 (B) in the sensitivity adaptive inverse analysis method. The analysis grid changes. FIG. 7B shows a state in which the inverse analysis result is reproduced in the physical property model.

FIG. 5 is an explanatory diagram showing an example of a sensitivity matching function and an example of a range in which a parameter grid having no sensitivity is removed. The inside of the curve (semicircular curve) from the electrode range is an effective analysis region, The parameters corresponding to the cells of the inverse analysis grid are excluded from the actual inverse analysis parameters. For this reason, as the analysis progresses, the subsurface area can be divided into grids that match the actual observation data and the subsurface resistivity distribution, and analysis that involves changes in the physical properties of the measured data group. The area can be set appropriately without excess or deficiency. In addition, in determining the analysis range, the grid of the model grid can be changed in conformity with the distribution of physical property values of the underground structure, and the analysis resolution and analysis efficiency can be improved. As described above, in the sensitivity-adaptive inverse analysis method in the numerical analysis of the resistivity method according to the above-described embodiment, the grid node density change for controlling the density of the grid nodes of the inverse analysis grid based on the obtained sensitivity adaptation function F _S. Since the means is provided, the inverse analysis grid can be corrected to suit the sensitivity as the analysis progresses.

Next, the operation of the sensitivity adaptive inverse analysis method in the numerical analysis of the specific resistance method according to the above embodiment will be described. In the sensitivity-adaptive inverse analysis method in the numerical analysis of the specific resistance method according to the above embodiment, when the convergence of the analysis is out of the error range, the sensitivity of each parameter for each observation data is set for each node of the inverse analysis grid. Then, a sensitivity matrix corresponding to the inverse analysis grid is formed, and a sensitivity adaptation function F _S is obtained based on the sensitivity matrix. When the sensitivity adaptation function F _S is obtained, the density of the grid node density of the inverse analysis grid is corrected according to the magnitude of the physical property value change and the sensitivity, and the physical property value change and the sensitivity at the node of the inverse analysis grid are large. The part is corrected so as to increase the node density and the part having a small change in physical property value and sensitivity to decrease the node density, and the inverse analysis grid is reset. For this reason, sensitivity is reflected more accurately in the analysis. In addition, since the grid that does not reach the predetermined threshold is excluded from the analysis target, the calculation load is reduced. As described above, in the sensitivity-adapted inverse analysis method in the numerical analysis of the resistivity method according to the present embodiment, the model grid division state is corrected each time the inverse analysis parameters are corrected by applying an effective sensitivity adaptation function F _S. Then, the number of analysis parameters is optimized, and the model grid is divided according to the distribution of physical property values in the basement to automatically determine the analysis range. And the analysis precision in the area | region far from an observation point can also be improved. This reduces the subjectivity of the model grid division and automatically places necessary and sufficient grid nodes that fit the observation data at the correct location, thereby saving computational complexity and the underground data included in the observation data. Information can be extracted to the maximum.

  Next, a second embodiment of the present invention will be described. In the second embodiment, the electric exploration shown in FIG. 8 is taken as an example of the physical exploration, and the division of the model grid (parameter model grid) of the present invention shown in FIG. 1 is corrected according to the specific resistance distribution for analysis. The results obtained (see FIGS. 9 to 17) and the results according to the conventional case where the analysis was performed without modifying the model grid division mode according to the specific resistance distribution, unlike the present invention shown in FIGS. 22 to 24) will be described. As shown in FIG. 8, the specific resistance model ground is a model ground in which a cubic low specific resistance body X having a specific resistance of 1 Ωm and a side of 5 m is embedded in a ground having a specific resistance of 100 Ωm. When the resistivity model ground is set, the measured value when two-dimensional electric exploration (electrode spacing 4m) by the bipolar method is performed with the electrode system of the orthogonal two survey lines is obtained by numerical analysis. What gave random noise was used as a model measurement value, and a three-dimensional inverse analysis was performed using the model measurement value.

  9 to 11 show the point distribution of the model grid projected on the YZ cross section at x = 7.5 m obtained based on the method according to the present invention for the specific resistance model ground of FIG. 9 shows the contact distribution of the initial model grid, FIG. 10 similarly shows the contact distribution of the model grid obtained by performing the iterative calculation twice after returning to the third step Step C of the present invention, and FIG. Similarly, the distribution of the contact points of the final model grid after 8 iterations is shown. Similarly, FIG. 12 to FIG. 14 show the XZ at y = 7.5 m for each of the initial model grid, the model grid that has been subjected to two iterations, and the final model grid that has been repeated eight times. It shows the point distribution of the model grid projected on the cross section. Similarly, FIGS. 15 to 17 respectively show an initial model grid, a parameter model grid that has been subjected to iterative calculations twice, and a final parameter model grid that has also been subjected to eight iterations at z = −7.5 m. It shows the point distribution of the model grid projected on the XY cross section.

  On the other hand, in the conventional method in which the parameter model grid is fixed (see the flowchart in FIG. 21), since the underground structure is unknown, the grid is set in the range of the underground region to be examined according to the arrangement of the electrode system shown in FIG. Perform grid division with regular intervals. This grid division is subjective. Once the model grid is divided, it is fixed until the end of the analysis, and the division mode is not changed through the analysis.

  That is, in the conventional method of performing geophysical exploration of the underground structure using the inverse analysis method with the inverse analysis grid shown in FIGS. 22 to 24 fixed, first, the minimum observation electrode interval (see the electrode interval 4 m in FIG. 8). ) As a reference, set the inverse analysis grid (see FIGS. 22 to 24) and the forward analysis grid, calculate the average apparent resistivity value, and assign it as the initial parameter value to the reverse analysis grid and the forward analysis grid. Set the initial model. The forward analysis grid divides the underground space into a number of small areas to discretize the underground space based on the input terrain information data, electrode position data, and observed observation data. It is a grid having a high lattice. Each cell of the forward analysis grid is constituted by a structural grid composed of a tetrahedron having four nodes (or a hexahedron having eight nodes). Next, based on the input topographic information data, electrode position data, and observed observation data, the underground space is divided into a number of small areas, and an inverse analysis with a grid with a lower node density than the forward analysis grid. A grid is generated and set (see S1 to S3 in the first step Step a in FIG. 21). As shown in FIGS. 22 to 24, each cell of the inverse analysis grid is composed of a hexahedral hexagonal lattice having eight nodes. The inverse analysis grid is not changed through analysis once the position of the grid node is determined (see the flowchart of FIG. 21).

  Next, the average physical property value of the underground is obtained based on the observation data of the specific resistance obtained by the combination of the transmitting and receiving electrodes, and the average physical property value is surrounded by a line or plane connecting the nodes of the generated inverse analysis grid. Are set as initial physical property parameters, and an initial model is set (see the second step Step b in FIG. 21). At this time, the initial model grid is divided subjectively and regularly as shown in FIGS. 22 to 24, and the division of the grid is fixed. When the initial model grid is set in the second step Step b, a physical property model is set by assigning physical property parameters to each cell of the forward analysis grid based on the set initial model grid (FIG. 21). 3rd step of step c)). That is, the specific resistance value ρ is assigned to the forward analysis grid by the initial model grid. Next, forward analysis is performed based on the assigned physical property parameters, and the theoretical value of the physical response to the observation data is obtained based on the physical property model with the electrode transmission / reception arrangement that matches the actual measurement in this physical property model, and the forward analysis grid The model theoretical solution at each node is obtained (see the fourth step Step d in FIG. 21).

  Next, the model theoretical solution is compared with the observation data to determine whether or not the error is within the error range (see the fifth step Step e in FIG. 21). If it is determined in the fifth step Step e that it is within the error range, that is, the calculated model theoretical solution and the actually measured observation value are compared, and the model theoretical solution and the observed value are compared. When it is determined that the relative mean square error RMS has become sufficiently small, the inverse analysis grid and the physical property value ρ defined in the grid are output to complete the analysis (see the sixth step Step f in FIG. 21).

  On the other hand, if it is determined that the error is out of the error range in the fifth step Step e, that is, the calculated model theoretical solution is compared with the actually measured observation value, and the model theoretical solution and the observation value are compared. When it is determined that the mean square error RMS is not sufficiently small, the sensitivity of each parameter for each observation data is obtained for each node of the inverse analysis grid, and a sensitivity matrix corresponding to the inverse analysis grid is formed. That is, a sensitivity vector for each observation data is obtained for each node of the inverse analysis grid, and a sensitivity matrix is formed (see the seventh step Step g in FIG. 21). Inverse analysis is performed using the difference between the model theory solution of the observation data and the observation data of the measurement and the sensitivity matrix, the physical property parameter is corrected to obtain a new physical property parameter, and the newly obtained physical property parameter is obtained from the inverse analysis grid. Assigned to each cell, the initial model grid of the third step Step c is returned to the third step Step c instead of this updated model (from the eighth step Step h to the third step Step in FIG. 21). See Return to c). That is, in the eighth step Step h, the specific resistance assignment to the model grid is corrected, the process returns to the third step Step c, the calculation is repeated until the convergence determination, and the error range in the fifth step Step e. If it is determined to be inside, the inverse analysis grid and the physical property value ρ defined in the grid are output and the analysis is terminated (see the sixth step Step f). If it is determined that the error is out of the error range in the fifth step Step e, the process returns from the seventh step Step g and the eighth step Step h to the third step Step c. Since the division state of the inverse analysis grid is not changed through the analysis, if the division is performed as finely as possible, the number of physical property value parameters increases. When the number of physical property parameter parameters increases, a large amount of observation data needs to be acquired in order to determine these parameters, and calculation time increases. Furthermore, since the sensitivity to the observation value of the model grid decreases as the distance from the observation point decreases, it is preferable to roughen the division as the distance from the observation point increases. It cannot be changed, and to change the split status, you have to start over.

  22 to 24 respectively show the nodal distribution of the model grid projected on the YZ section at x = 7.5 m based on the conventional method in which the model grid is fixed for the resistivity model ground of FIG. The nodal distribution of the model grid projected on the XZ cross section at = 7.5 m and the nodal distribution of the model grid projected on the XY cross section at z = −7.5 m are shown. As is clear from these node distributions, with the conventional method with a fixed model grid, the grid is arranged up to an area that is not sensitive to observation data, or the node density is more dense than the ability to classify information contained in the data. Since it will be set, it will be useless in analysis calculation. Further, in such a conventional method, the node density is low in a range where sensitivity is sufficiently high, information included in the data is not sufficiently used, and the analysis resolution may be lowered. In addition, since the grid division is fixed until the end of the analysis, as shown in FIGS. 28A to 28C, the grid size and the boundary may not be appropriate for the specific resistance distribution. Causes a drop. 28A shows a case where the model grid is large with respect to the specific resistance distribution, and FIG. 28B shows a case where the model grid is small with respect to the specific resistance distribution. Shows the case where the resistivity distribution boundary and the model grid division do not match, and the resistivity distribution boundary and the model grid cross each other.

  On the other hand, in the second embodiment of the present invention, for example, as shown in FIGS. 9 to 11, the division state of the model grid is corrected and rearranged so as to match the specific resistance distribution for each iterative calculation. The analysis is performed by narrowing down the data to a sensitive area. That is, in the example in which the model grid shown in FIGS. 22 to 24 is fixed, the number of parameter grids included in the region of the low resistivity X remains unchanged, but the parameter model grids shown in FIGS. In the example of correction according to the sensitivity adaptation function, the number increases from 0 to 4, 4 to 20, and the reproduction accuracy of the range of the low specific resistance element X is improved. Further, as is apparent from FIGS. 9 to 11, it can be seen that the low resistivity X is subdivided in a certain region. Further, FIGS. 18 to 20 respectively show the results of the conventional inverse analysis performed with the model grid fixed (CASE1) with the result of the inverse analysis derived based on the second embodiment of the present invention as CASE1 (FIGS. 25 to 25). Fig. 27) shows the CASE2 as a comparison with each other, and the exploration data is obtained by forward analysis for a ground model with a low specific resistance X of 1 Ωm on the ground of 100 Ωm, and 3% noise is added to this. This is a reverse analysis. Even in the conventional CASE 2, the low resistivity X is reproduced in the model range, but the analyzed resistivity value is larger than that of the present invention, and the position is also shifted. Furthermore, a false image of high specific resistance is generated around the low specific resistance body X. On the other hand, when the specific resistance cross section of CASE 1 of the present invention is seen, the low specific resistance body X is analyzed more clearly and at a more accurate position than CASE 2 and has high accuracy with few false images. It can be seen that the analysis results are obtained.

  FIGS. 29A and 29B show analysis results analyzed using the method according to the present invention and the analysis results analyzed using the conventional method of fixing the model grid in searching for a known cavity, respectively. In the analysis result shown in FIG. 29A, the known cavity position Cv was analyzed by the high specific resistance distribution, but in FIG. 29B, it was unclear. .

  In the above-described embodiment, an example of electrical exploration was shown in performing geophysical exploration of the underground structure, but the present invention is not limited to this, and exploration using surface waves, reflected waves, vibration, radiation, ions, stress, or strain Needless to say, this is also applicable. In the above embodiment, when setting the forward analysis grid and the inverse analysis grid, as shown in FIG. 30A, each grid is a triangle (N1-N2-N3) with three nodes (nodes). Although it is configured by an unstructured lattice, the present invention is not limited to this. As shown in FIG. 30B, an unstructured structure consisting of tetrahedrons (n1-n2-n3-n4) having four nodes. You may comprise by a simple lattice.

fwg forward analysis grid
ivg inverse analysis grid
ivg model grid
rsm Ground model ρ Physical property (specific resistance)
N1-N2-N3 Grid nodes S _S parameter sensitivity statistics F _S sensitivity fitting function
el electrode
nl grid contact
cl Grid cell

Claims (8)

Based on the input terrain information data, electrode source position data, and observed observation data, the forward analysis grid with a high grid node density that divides the underground space into small areas, and the grid node density is lower than this forward analysis grid In addition to setting a reverse analysis grid, a ground model with physical property values added to the grid obtained by giving the average physical property values obtained based on the actually measured observation data to each small area was set and set Compare the theoretical value theoretically calculated from the ground model and the observed data, and if within the error range, output the analysis result of the inverse analysis grid and the physical property value defined in that grid, and distribute the physical property value of the ground If it is out of the error range, the sensitivity of each parameter for each observation data is obtained to form a sensitivity matrix, and the theoretical and actual measurement values of the observation data are calculated. Perform inverse analysis based on the difference between the sensitivity matrix of the newly calculated parameter values, given the determined parameter values to the inverse analysis grid, a analysis method for analyzing by repeating update of the ground model,
Each grid of the forward analysis grid and the reverse analysis grid is configured by a triangular or tetrahedral unstructured grid, and the inverse analysis grid is configured so that the grid node density is variably controlled.
The sensitivity statistic of each parameter is obtained from the formed sensitivity matrix, a function for controlling the node density of the inverse analysis grid is obtained based on the obtained sensitivity statistic, and the grid node density of the inverse analysis grid is obtained based on this function. The ratio is characterized by reconfiguring the inverse analysis grid after correcting the density of the material according to the change in the physical property value and the sensitivity, and re-forming the sensitivity matrix based on the reconfigured inverse analysis grid. Sensitivity compatible inverse analysis method in numerical analysis of resistance method.   When setting the density of the grid nodes of the inverse analysis grid, increase the node density at the part where the physical property value change and sensitivity at the node of the inverse analysis grid are large, and decrease the node density at the part where the physical property value change and sensitivity are small The sensitivity compatible inverse analysis method in the numerical analysis of the specific resistance method according to claim 1, wherein the method is modified as follows.   The analysis area is determined by removing the parameter corresponding to the grid whose sensitivity to the observation data is a predetermined threshold value or less from the analysis parameter when determining the sensitivity of each parameter for each observation data. A sensitivity-compatible inverse analysis method in the numerical analysis of the specific resistance method described in 2. Based on the input topographic information data, electrode source position data, and measured observation data, the underground space is divided into a large number of small areas, and a forward analysis grid and a forward analysis grid having a grid with a high node density. An inverse analysis grid having a grid with a low node density is generated, and each of the forward analysis grid and the inverse analysis grid is configured by a triangular or tetrahedral unstructured grid. A first step configured to variably control the grid node density;
Based on the observation data obtained by the combination of the transmitting and receiving electrodes, the average physical property value of the underground is obtained, and the initial physical property parameter is measured in a cell that is surrounded by a line or plane connecting the nodes of the mesh of the generated inverse analysis grid. And a second step of setting the initial model as
A third step of setting a physical property model by assigning physical property parameters to each cell of the forward analysis grid based on the set initial model;
The forward analysis is performed based on the set physical property model, and the theoretical value of the physical response to the observation data is obtained based on this physical property model with the electrode transmission / reception arrangement that matches the actual measurement in this physical property model. A fourth step to find a model theoretical solution in
A fifth step of comparing the model theoretical solution with the observed data and determining whether or not the error is within the error range;
A sixth step of outputting the inverse analysis grid and the physical property value defined in the grid and ending the analysis when it is determined in the fifth step that it is within the error range;
In the fifth step, when it is determined that the error is out of the range of error, the sensitivity of each parameter for each observation data is obtained for each node of the inverse analysis grid, and a sensitivity matrix corresponding to the inverse analysis grid is formed; ,
A sensitivity statistical value of each parameter is obtained from the sensitivity matrix formed in the seventh step, a function corresponding to the inverse analysis grid and matching the sensitivity is obtained from the sensitivity statistical value, and the inverse analysis grid is obtained based on the sensitivity adaptation function. The density of the node density of the grid is corrected according to the change in the physical property value and the magnitude of the sensitivity, the inverse analysis grid is reset, and the sensitivity matrix based on the inverse analysis grid reset according to the sensitivity adaptation function An eighth step of determining an analysis region by removing a parameter corresponding to a grid whose sensitivity is equal to or lower than a predetermined threshold value from the analysis parameter;
Inverse analysis is performed based on the difference between the model theoretical solution and the observed data and the reconstructed sensitivity matrix, the physical property parameter is corrected to obtain a new physical property parameter, and the newly obtained physical property parameter is inversely analyzed. A specific resistance characterized by having an updated model set by giving to each cell of the grid, and an initial model of the third step replacing the updated model with a ninth step of returning to the third step Sensitivity adaptive inverse analysis method in numerical analysis of the method.   When setting the density of the grid nodes of the inverse analysis grid, increase the node density at the part where the physical property value change and sensitivity at the node of the inverse analysis grid are large, and decrease the node density at the part where the physical property value change and sensitivity are small The sensitivity-adapted inverse analysis method in the numerical analysis of the specific resistance method according to claim 4, wherein the method is modified as follows. The sensitivity fitting function is the optimal node density function of the inverse analysis grid in the resistivity method,
The following formula,
F _S = a (1 + b | S _S | ^C )
Where F _S : sensitivity adaptation function,
S _S : Sensitivity statistic obtained from the sensitivity matrix, and the sensitivity statistic is also a function of all transmission / reception electrode sets and underground space coordinates through the sensitivity matrix.
c: constant related to dimension,
a: a constant related to the set maximum resolution and the range of the analysis area,
6. The sensitivity-adapted inverse analysis method in the numerical analysis of the specific resistance method according to claim 4, wherein b is obtained as a constant related to the set relative resolution.   When the sensitivity adaptation function is obtained, the previous inverse analysis grid is used as the background grid, and the density of the grid nodes is reconstructed in proportion to the sensitivity adaptation function, and the sensitivity matrix is calculated based on the latest inverse analysis grid having the reconstructed grid. The sensitivity-matching inverse analysis method in the numerical analysis of the specific resistance method according to claim 6, wherein the method is re-formed.   Of the regenerated sensitivity matrix, the parameter corresponding to the grid whose sensitivity is equal to or lower than the predetermined threshold is excluded from the analysis target, the analysis area is determined, the sensitivity matrix is calculated, and the inverse is performed based on the calculated sensitivity matrix. 8. The sensitivity-adapted inverse analysis method in the numerical analysis of the specific resistance method according to any one of claims 4 to 7, wherein analysis is performed.