JPH109903A - Estimation method of stratum boundary level - Google Patents

Abstract

(57) [Summary] [PROBLEMS] To make work more efficient and reduce labor by creating a system that can use a computer. A correlation between measured data of a geological boundary level obtained by survey boring and measured data of a ground surface level at a boring position is examined, and when the correlation is high, both data are used to determine a geological boundary level. Is estimated.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention belongs to the technical field of estimating a formation boundary level such as a foundation ground level using topographic information.

[0002]

2. Description of the Related Art Geological survey at a construction site is one of the important survey items related to the success or failure of a construction project. Recently, large-scale structures have been often planned with the progress of civil engineering technology, and accordingly, foundations have been enlarged and deepened. In general, the ground is composed of stratified or massive strata and rocks, in which discontinuous planes such as faults and shatter zones are distributed, and depending on the area, it has a complex structure due to the action of folding, erosion, etc. I have. The key point in geological surveys is how to efficiently obtain the geological structure from limited data.

[0003] When constructing a structure deep in the foundation ground, a pile foundation is often used. Therefore, it is very important to accurately estimate the foundation ground level of supporting piles from limited survey boring data.

[0004]

However, when constructing a substation or the like in a mountainous area with steep undulations, it may be difficult to accurately estimate the foundation ground based on the results of the survey drilling alone. Experts often make somewhat subjective estimates with reference to surface surveys and seismic surveys. Therefore, not only does it require the efforts of experts,
Efforts were also needed to make changes, such as differences in human estimates and when additional survey drilling results were incorporated.
In addition, human power was also required when calculating the pile length from the estimated foundation ground level.

[0005] In the past, attempts have been made in the field of mining engineering to estimate geological structures and the like as geostatistics. Recently, a research field called information geology, which specializes in the information science approach in geology, has been proposed, and geology has come to be positioned as a theoretical and quantitative science. In addition, there is also known an estimation method called kriging, which estimates a three-dimensionally undulating foundation ground surface from a limited survey boring data using a computer, but in order to interpolate very smoothly between boring operations. However, there is a problem that accuracy is poor.

The present invention has been made to solve the above-mentioned problem, and by creating a computer-assisted system, it is possible to improve work efficiency and reduce labor, and to estimate a geological boundary level with high accuracy. The aim is to provide a method.

[0007]

For this purpose, the method for estimating a stratum boundary level according to the present invention relates to a method of correlating measured data of a stratum boundary level obtained by survey boring with measured data of a ground surface level at a boring position. Consider,
The feature is that the stratum boundary level is estimated using both data when the correlation is high.

[0008]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a diagram illustrating an embodiment of a method for estimating a stratum boundary level according to the present invention and illustrating a flow of processing. In the present embodiment, the base ground level is taken as an example, but the same processing is performed at the geological boundary level.

In FIG. 1, the left side schematically shows the procedure of the work, and the right side shows the flow of data. First, step S
Investigation drilling was carried out in 1 and, as the data of the boring position, for the foundation ground level, the N value of the foundation ground level by standard penetration test, weathering, hardness, rock classification as crack data, velocity data by elastic wave exploration obtain. For the ground level, topographic data of contour lines is obtained.

Next, in step S2, the correlation between the base ground level and the ground level is examined with respect to the data of the base ground level obtained in step S1. For example, FIG.
In this case, the correlation coefficient is 0.93, indicating a high degree of correlation.

Next, in step S3, it is determined whether or not the correlation coefficient is larger than a predetermined value (for example, 0.7). If the correlation is small, in step S4 an estimation method using only the data of the base ground level is performed. (Hereinafter referred to as an estimation method by Kriging) is applied. If the correlation is large, an estimation method using data of both the ground surface level and the foundation ground level (hereinafter referred to as an estimation method by co-clicking) is applied in step S6. It should be noted that whether the correlation coefficient is large or not is 0.
Judgment is made between 65 and 0.75, and if it is within this range,
It is also possible to calculate by both estimation methods and compare the estimated values of both.

The present invention is characterized in that estimation is performed by co-clicking using data at both the ground surface level and the foundation ground level, and a bivariate random field of a ground surface level and a stratum boundary level is assumed. Means for setting a plurality of function models (trend function, self-covariance function, mutual variance function) when assuming the bivariate random field, and estimating parameters of the plurality of function models by a maximum likelihood method. Means, a means for selecting a best model from the plurality of function models according to an AIC criterion defined by the number of parameters and likelihood, and estimating a formation boundary level at an arbitrary point from measurement data of the level using the best model And means for performing the operation. Hereinafter, an estimation method based on kriging will be described, and then an estimation method based on co-kriging will be described.

(A) Estimation Method by Kriging (A-1) Modeling of Base Ground Surface First, the probability that the base ground level z can be expressed by the sum of a trend component and a random component as follows using plane space coordinates: Field.

[0014]

(Equation 1)

Here, b is a parameter vector expressing a trend component, and X is a plane space coordinate (x,
This is a plane space coordinate vector expressed by a polynomial regarding y), and can be expressed as follows by an order regarding plane space coordinates (x, y), for example.

[0016]

(Equation 2)

Ε is a random component associated with the second-order stationary stochastic process, and has an average value of 0 and a covariance matrix Q (θ)
(= E [εε ^T ]). Is a parameter of the covariance function. For example, the covariance between two points is a function of distance C
(Δx), σ ² and a are parameters θ
Becomes

[0018]

(Equation 3)

In addition, various covariance functions have been proposed. In geostatistics, a variogram 2γ (Δx) in which the condition of the covariance function is slightly relaxed is used. The variogram is for obtaining an unbiased estimator from N (Δx) data pairs of z (x) and z (x + Δx) as shown by the following equation.

[0020]

(Equation 4)

Of course, in the stationary case, the covariance function C
(Δx) has the following relationship.

[0022]

(Equation 5)

(A-2) Parameter estimation In order to obtain the statistical parameters b and θ of z, the maximum likelihood method is used here. The likelihood as a joint probability density function can be obtained from the N pieces of measurement data by the following equation.

[0024]

(Equation 6)

Next, a function form of the average value and the covariance is selected. The function parameter can be determined by maximizing the likelihood of the above equation, but is determined by minimizing the negative log likelihood expressed by the following equation from calculation.

[0026]

(Equation 7)

Further, the coefficient vector b of the trend component is obtained by the least square method of the following equation.

[0028]

(Equation 8)

That is, b and θ that minimize the negative log likelihood are obtained by iterative calculation.

(A-3) Selection of Best Model In the statistic estimation by the maximum likelihood method, parameters are determined so as to maximize the log likelihood for a preset model. Prior to estimation, there is the problem of choosing the best model to apply. In geostatistics, a plurality of statistical models generally required are proposed. In the present invention, AIC (Akaike Information Criterion: Akaike Information Criterion) is introduced as a criterion for evaluating these models.

As can be seen from the theory of the maximum likelihood method, the parameters in a particular model can be evaluated by the mean log likelihood.
That is, it can be said that the larger the value of the average log likelihood is, the better the value of the parameter is. Here, the average log likelihood is an expected value of the log likelihood regarding the measurement data z, and therefore, the log likelihood may be taken as the unbiased estimator.

When a plurality of models are conceivable, a maximum likelihood model (a model using a maximum likelihood estimated value as a parameter) is used as an evaluation criterion for comparing the models.
And an expected value (referred to as expected average log likelihood) of the measured data z of the average log likelihood can be considered.
That is, it can be said that the larger the value of the expected mean log likelihood is, the better the model is.

Although the maximum log likelihood of the model can be considered as one estimator of the expected average log likelihood, the maximum log likelihood itself is not an unbiased estimator of the expected average log likelihood. The maximum log likelihood of a model depends on the number of free parameters of the model, and generally increases as the number of free parameters increases. However, in the present invention, since the actual distribution is obtained by statistical estimation from the measured data, the free parameter is set when the matching with the data is almost the same (the value of the maximum log likelihood is the same). It is reasonable that a model with a small number is a better model. Since the value obtained by subtracting the number of free parameters from the maximum log likelihood of the model is approximately an unbiased estimator of the expected mean log likelihood, AIC = −2 × (maximum log likelihood of the model) + 2 × (model The number of free parameters) is the basis for model selection. The model obtained by minimizing the AIC is called minimum AIC estimation (MAICE),
It can be considered that it gives a more optimal model.

(A-4) Estimation of Spatial Distribution One of the techniques for estimating the spatial distribution at the base ground level from limited survey boring measurement data is kriging. Kriging is a method of estimating a value at an arbitrary position by a linear sum of measured data, and can be expressed by an estimated value, which is a conditional probability of z when the measured data z ₀ is obtained, and an estimated error covariance matrix. Assume an estimate can be expressed by a linear sum of the measurement data z ₀ by weight coefficient λ as follows. Then, the weight coefficient λ is obtained from the condition that the unbiasedness of the estimation amount and the estimation error are minimized.

[0035]

(Equation 9)

The estimation error is as follows.

[0037]

(Equation 10)

From the unbiasedness of the estimator,

[0039]

[Equation 11]

Under this constraint, the estimation error variance represented by the following equation is minimized.

[0041]

(Equation 12)

Here, the following equation using the Lagrange's undetermined coefficient μ is minimized.

[0043]

(Equation 13)

From this, μ is determined as follows.

[0045]

[Equation 14]

The weight coefficient λ is as follows.

[0047]

(Equation 15)

Therefore, when this is substituted into (Equation 11) and (Equation 12), the estimated value and the estimated error covariance matrix, which are the conditional probability of the foundation ground level z when the measured data z ₀ is obtained, are Can be expressed as

[0049]

(Equation 16)

(B) Estimation Method by Co-Kriging Co-Kriging is a method of estimating a spatial distribution from a cross-correlation relationship with respect to a random field having two or more variables having strong correlation with each other. When the number of data is limited, if another data having a strong correlation with the data can be easily obtained, more accurate estimation can be performed. In the present invention, co-kriging is applied by focusing on the fact that the foundation ground level has a strong correlation with the ground surface level.

(B-1) Modeling of Bivariate Random Field The spatial distribution of _two measurement data z ₁ , z _{2 in} a certain area S is represented by a trend component obtained by macro-capturing the overall behavior as follows. It is assumed that it can be represented by the sum of random components handled in a statistically uniform random field. Here, “statistically uniform” means a stationarity in which the probability characteristic does not change depending on the position.

[0052]

[Equation 17]

Now, two measurement data z ₁ (x), z ₂ (x)
Is measured at the position of the measurement point x,
These measurement data are considered as one realization data of the random fields Z ₁ (x) and Z ₂ (x). These random fields Z ₁ (x), Z
Assuming stationarity up to the second moment of ₂ (x), the following equation can be defined.

[0054]

(Equation 18)

These are represented by a distance vector h between two points, and various covariance function models have been generally proposed.

In such a random field estimation, the parameters θ of the set model are obtained from the measured data z ₁ (x) and z ₂ (x). In general, the semivariogram and the mutual semivariogram shown in the following equations It is often performed using.

[0057]

[Equation 19]

That is, when N (h) pairs of measurement data [z ₁ (x), z ₁ (x + h)] and [z ₂ (x), z ₂ (x + h)] at a point separated by h are given. , The semivariogram is estimated as follows:

[0059]

(Equation 20)

As described above, since the semivariogram estimation does not need to assume statistical homogeneity or probability distribution of a population, it is possible to make a somewhat powerful estimation and is widely used in general. However, it is necessary to obtain N (h) pieces of measurement data pairs z ₁ and z ₂ at points distant from each other by h, and when trying to obtain a value between any two points, a function approximation such as a least square method is used. Therefore, there is a problem in estimation accuracy. In addition, since the semivariogram and the mutual semivariogram are estimated independently of each other, there is a possibility that the condition for modeling the correlation characteristic described later may not be satisfied. Therefore, in the present invention, the following estimation method using the maximum likelihood method is used.

(B-2) Statistical Estimation of Parameters From the limited data, the random field Z ₁ (x),
In order to determine the trend component and the random component of Z ₂ (x), the parameters are estimated by the maximum likelihood method assuming a model of the self-covariance function and the cross-covariance function. In order to obtain a correlation characteristic from the _two measurement data z ₁ (x _i ) and z ₂ (x _i ), N common sample values of the measurement points x _i are used. The likelihood represented by the joint probability density function is given by the following equation from the set of N measurement data.

[0062]

(Equation 21)

Q in (Equation 21) is a matrix obtained by integrating the self-covariance matrix and the mutual covariance matrix as shown in the following equation.

[0064]

(Equation 22)

The parameter θ is estimated by maximizing the likelihood of (Equation 21). It is determined from the calculation by minimizing the negative log likelihood represented by the following equation.

[0066]

(Equation 23)

In order to minimize the above equation, the Gauss-Newton method is used here. The first derivative for the parameter θ _{j in} (Equation 23) is represented by the following equation.

[0068]

(Equation 24)

Here, the above equation uses the following relationship.

[0070]

(Equation 25)

The basic calculation for minimizing the log likelihood is performed using the following equation.

[0072]

(Equation 26)

The Hessian matrix is approximated and expressed as follows.

[0074]

[Equation 27]

If the primary search method is not performed at each iteration, ρ _i is fixed at = 1, and the iteration calculation is as follows.

[0076]

[Equation 28]

The trend component is modeled by a polynomial in spatial coordinates as follows, and is obtained simultaneously by the least squares method in the above iterative calculation. First, the average value function μ is expressed as the following equation.

[0078]

(Equation 29)

For example, in the case of a one-dimensional case, it is expressed as follows by an order relating to the spatial coordinates x.

[0080]

[Equation 30]

Now, combine the two variables into one

[0082]

(Equation 31)

The estimated value of the coefficient vector b by the least squares method is obtained by the following equation.

[0084]

(Equation 32)

[0085] (B-3) co-kriging by estimation method for example, the measurement of the variables Z ₂ as compared to the variable Z ₁ is required difficulties in economic or other reasons, consider the case that the number of data is limited . In such a case, if the estimated variables Z ₂ from the measured data with these cross-correlation function of the variables Z ₁ and Z _2, thereby enabling more accurate estimate while suppressing the measurement cost variables Z _2. Such an estimation method is an estimation method by co-kriging. In co-kriging, the estimated value of an arbitrary point is represented by a linear sum of the measured data as shown in the following equation.

[0086]

[Equation 33]

The weighting factors λ ₁ and λ ₂ in the above equation are

[0088]

(Equation 34)

By substituting (Equation 33) into (Equation 34),

[0090]

(Equation 35)

Considering that E [Z (x)] = μ (x),

[0092]

[Equation 36]

Is obtained. Therefore,

[0094]

(37)

The estimated error variance σ _E ^{2 in} (Equation 34) is
Expanded as follows:

[0096]

(38)

## EQU10 ## Under the condition of (Equation 37), (Equation 3)
If Lagrange's undetermined coefficient method is used to minimize 8), λ ₁ and λ ₂ satisfying the following equations can be determined.

[0098]

[Equation 39]

When this is expanded,

[0100]

(Equation 40)

This is a linear equation of unknown constants λ ₁ , λ ₂ and η ₁ , η ₂ and is a formulation of co-kriging. Then, the minimized estimated error variance is expressed by the following equation.

[0102]

[Equation 41]

[0103]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment to which co-kriging according to the present invention is applied will be described below. FIG. 2 shows an arrangement of a symmetric construction site, a survey boring, and a position of an elastic wave exploration survey line. The base ground surface having an N value of 50 or more from the elastic wave velocity value at the boring position has an elastic wave velocity of 1.2 to 1..
It corresponds to 7 km / sec or more, and this upper limit surface of the speed band may be considered as the foundation ground level. Therefore, as an evaluation of the applicability of this method, the estimation results were compared with the estimation level of the foundation ground surface obtained by elastic wave exploration as a true value. Estimation using data of outcrop survey and elastic wave exploration was also performed.
FIG. 3 shows the evaluation points of the estimation result in the symmetric construction site area (200 × 200 m). ● marks indicate the estimated points of the foundation ground surface by elastic wave survey. Exposure of CL and CM-grade rocks is recognized along the swamp, and the ○ mark is used as the measurement data of the base ground outcrop along the swamp as input data of the foundation ground surface.

(1) Modeling of the foundation ground surface The boundary of the foundation ground surface of this site is geologically the boundary between the weathered zone from the ground surface and the rock which has not received much weathering. It is considered that the surface is distributed almost according to the undulation of the ground surface. Figure 4 plots the ground surface level and the foundation ground surface level based on the survey boring data. It is apparent from this figure that the two data have a strong positive correlation with a correlation coefficient of 0.9 or more by linear approximation. Is recognized.

Therefore, as a modeling of the base ground surface, a bivariate random field in which Z ₁ (x) in (Equation 17) is set to the ground surface level and Z ₂ (x) is set to the base ground surface level is assumed. In estimating the random field, several function models of the trend component and the random component are set, and the best model is selected based on the AIC criteria defined by the log likelihood and the number of parameters. Here, the following model was set.

[0106]

(Equation 42)

A total of four types of models are obtained by combining the above two types. Here, the self-covariance function and the mutual covariance function of the random component set a model having a common parameter a _i representing the spatial correlation. This results in the constraint that the mutual correlation will be small if the two variables are assumed to have different spatial correlations,
If the correlation between the two variables is strong and at the same time the spatial correlation of the two variables is almost the same, it is better to use the same correlation parameter from the viewpoint of reducing the number of parameters. Table 1 shows the results of estimating the parameters of the best model that minimizes the AIC by setting a model assuming that the ground surface and the foundation ground surface are independent random fields.

[0108]

[Table 1]

From these results, the best model shows a trend of 1
Next, the covariance function is a one-dimensional Expornential model. An estimate of the spatial correlation parameter a (sometimes called the correlation distance) is 38.55 m above ground level,
There is no significant difference from the base ground surface of 46.99m. From such a result, modeling was performed in which the self-covariance function and the cross-covariance function have the same spatial correlation parameter a.

(2) Parameter Estimation and Model Selection In the model of (Expression 42), the parameters to be estimated are the parameter vector b of the trend component and the variance σ ₁ ² ,
σ ₂ ² , the spatial correlation parameter a and the cross-correlation coefficient ρ. The data used for the estimation is a set of ground surface data and foundation ground surface data at 27 survey boring positions. Table 2 shows the parameter estimation results for each model.

[0111]

[Table 2]

Table 2 shows the results of obtaining the AIC. As in the case of obtaining the AIC with an independent random field of univariate, the best model has a first-order trend and a covariance function of a one-dimensional Exporn.
The ential type model was selected. The difference between the 0th trend (constant average value) and the 1st order AIC is close to 30. It can be seen that the 1st order trend is indispensable to capture the slope inclined in the northeast direction. Although the random component is one-dimensional and two-dimensional, the AIC is not much different, about 1.5 to 2,
One-dimensional is smaller, indicating that there is no worthwhile effect of increasing the parameters by expanding the spatial correlation to two-dimensional. The cross-correlation coefficient ρ of the best model estimate is 0.8
It is quite large at 89, suggesting that the estimation of the foundation ground surface by co-kriging is very effective.

(3) Estimation of Foundation Ground Surface The spatial distribution of the foundation ground surface due to co-clicking was estimated using the above-mentioned statistics. It was necessary to use a set of the ground surface and the foundation ground surface data at the survey boring position for estimation of the statistics, but the spatial distribution estimation by co-kriging, as understood from (Equation 33), required It is not necessary that the number of data on the foundation ground surface and the measurement position match. Here, as the data on the ground surface, 10 m
The data obtained by reading the positions of the grid points and the elevations of a total of 441 points from the topographic map were used.

For comparison, the result of estimating the foundation ground level by univariate kriging described in the section (A) is also shown. FIG. 5 is a contour diagram showing an estimation result using only survey boring data by kriging.
(A) is the estimated value of the foundation ground level, and FIG. 5 (B) is the estimation error. The inclination to the northeast is well understood, but the distribution is smooth throughout and does not reflect the undulation of the ground surface. The estimation error is 4 to 5 m near the survey boring position (the top of the contour line), but becomes 8 m or more when the distance is 30 m or more.

On the other hand, FIG. 6 is a contour diagram showing an estimation result using survey drilling data and ground surface data by co-kriging, and FIG. 6 (A) is an estimated value of the base ground level, and FIG. (B) is an estimation error. Looking at the contour map of the estimated values, it is very similar to the undulation of the ground surface, and roughly -10
m, the foundation ground surface is distributed about -5 m on the north side. The distribution of the estimation error is the same as the distribution of the estimation error of kriging due to boring only, since the data of the ground surface is given uniformly to the entire target area, but the value of the estimation error is near the survey boring position. Is 2 to 4 m, and the entire target area is within 5 to 6 m, which is about 60 to 70% of the estimated error of kriging.

In order to examine the validity of the result of estimation by co-kriging, comparison was made between basic ground surface data obtained by elastic wave exploration, which is considered to be a true value, and basic ground outcrop data along a river. The elastic wave survey line (C shown in FIG. 3)
-1 to C-5) and a comparison between the true value and the estimated value for a total of 8 cross sections of the foundation ground outcrop (S-1 to S-3) along the shore.
Shown in FIG. 7A shows an estimation result by kriging only by boring, and FIG. 8B shows an estimation result by co-kriging. Further, a shaded portion surrounded by a broken line indicates a range of the estimation error.

First, of the cross section of the elastic wave survey line, FIG.
In the cross section in the slope direction (northeast) as shown in FIG. 10, the difference from the true value is almost within 5 m for both estimation by kriging and co-krigging, and the estimation is very good. This is probably because the effect of the slope direction is large and the effect of the terrain is small.
On the other hand, in the cross section in the direction crossing the swamp terrain shown in FIGS. 7, 8, and 11, the estimation by the kriging smoothly interpolates the undulating terrain, while the difference from the true value is 15 m or more. , Co-Kriging estimates the true value very accurately. Because of the swamp terrain, the base ground plane is actually lower than the average trend, and there is a contradiction that the base ground plane is estimated higher than the ground surface by kriging without considering the influence of the terrain.

As described above, the estimation result of co-kriging was more accurate than the estimation result by kriging in all the cross sections, and the validity of the estimation by co-krigging with the ground surface could be confirmed. FIG. 15 shows a histogram of the difference between the estimation result by co-krigging and the true value. The difference between the true value and the estimation value is 1.7 m on average and almost within 2 to 3 m. It is thought that it is made. For the purpose of application to actual design, it is necessary to accurately estimate the foundation ground surface using all the given data. Therefore, estimation by co-kriging using all of the drilling data, elastic wave exploration result data and outcrop data was performed. FIG. 16 shows the estimation result as a perspective view simultaneously with the ground surface.

[0119]

As is apparent from the above description, according to the present invention, a mathematical model for expressing a stratum boundary level and a foundation ground level by a linear sum of measured data such as survey boring is introduced, and the estimation work is systematized. By doing so, work efficiency and labor can be reduced. In addition, data at the ground surface level that cannot be directly input, which must be relied on by an expert, can be objectively incorporated into the estimation using a statistic called correlation. As a result, it is possible to easily perform almost the same estimation as that of the expert even if the expert is not the expert.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating an embodiment of a method for estimating a stratum boundary level according to the present invention and illustrating a flow of processing.

FIG. 2 is a diagram showing an arrangement of a symmetric site and a survey boring and a position of an elastic wave exploration survey line.

FIG. 3 is a diagram showing evaluation points of an estimation result in a symmetric site region.

FIG. 4 is a diagram in which a ground surface level and a foundation ground surface level based on survey boring data are plotted.

FIG. 5 is a contour diagram showing an estimation result using only survey boring data by kriging, FIG. 5 (A) shows an estimated value of a foundation ground level, and FIG. 5 (B) shows an estimation error.

FIG. 6 is a contour map showing an estimation result using survey drilling data and ground surface data by co-kriging, FIG. 6 (A) is an estimated value of a foundation ground level, and FIG. 6 (B).
Is the estimation error.

FIG. 7 is a diagram showing a comparison between a true value and an estimated value for kriging and co-kriging.

FIG. 8 is a diagram showing a comparison between a true value and an estimated value for kriging and co-kriging.

FIG. 9 is a diagram showing a comparison between a true value and an estimated value for kriging and co-kriging.

FIG. 10 is a diagram showing a comparison between a true value and an estimated value for kriging and co-kriging.

FIG. 11 is a diagram showing a comparison between a true value and an estimated value for kriging and co-kriging.

FIG. 12 is a diagram showing a comparison between a true value and an estimated value for kriging and co-kriging.

FIG. 13 is a diagram showing a comparison between a true value and an estimated value for kriging and co-kriging.

FIG. 14 is a diagram showing a comparison between a true value and an estimated value for kriging and co-kriging.

FIG. 15 is a diagram showing a histogram of a difference between an estimation result by co-kriging and a true value.

FIG. 16 is a perspective view (halftone image displayed on a display) showing an estimation result by co-clicking using all of boring data, elastic wave exploration result data, and outcrop data together with the ground surface.

Continued on the front page (72) Inventor Makoto Honda Shimizu Corporation, 2-3-2 Shibaura, Minato-ku, Tokyo

Claims (4)

[Claims] The correlation between the measurement data of the geological boundary level obtained by the survey drilling and the measurement data of the ground surface level at the boring position is examined, and when the correlation is high, the data of the geological boundary is used by using both data. A method for estimating a stratum boundary level, comprising estimating a level. 2. A means for assuming a bivariate random field at a ground surface level and a stratum boundary level; a means for setting a plurality of function models when assuming the bivariate random field; Means for estimating by a maximum likelihood method, means for selecting a best model from the plurality of function models based on an AIC criterion defined by the number of parameters and likelihood, and an arbitrary point from the measurement data of the level using the best model. 2. A method for estimating a stratum boundary level according to claim 1, further comprising: means for estimating the stratum boundary level. 3. A method for estimating a stratum boundary level according to claim 2, further comprising means for inputting additional data of a stratum boundary level such as an outcrop survey or an elastic wave exploration to said best model. 4. The method for estimating a stratum boundary level according to claim 1, wherein when the correlation is low, the stratum boundary level is estimated only from the measurement data of the stratum boundary level obtained by the survey drilling.