A quantitative evaluation method for the stationarity of training images based on variogram

Abstract

The present invention discloses a quantitative evaluation method for the stationarity of training images based on a variogram, which calculates the strength of the spatial stationarity of the training image through the variogram, thereby providing an objective quantitative index for judging whether the training image is suitable for modeling. First, the variogram is used to quantify the variability differences between different spatial anchor points and other areas of the training image to obtain an anchor point distance model. Then, the stationarity coefficient of the anchor point is calculated through the anchor point distance model, and finally, the stationarity coefficients of all distance models are statistically analyzed to form a quantitative index for the stationarity of the training image. The present invention aims to solve the limitations of the quantification of the stationarity of training images, greatly improve the accuracy and efficiency of image analysis, systematically evaluate the stationarity of training images, and provide a more accurate and reliable spatial variability analysis method for geological modeling.

Description

Technical Field

[0001] The present invention relates to a quantitative evaluation method, in particular to a quantitative evaluation method for the stationarity of a training image based on a variogram, and belongs to the technical field of reservoir geological modeling. Background Art

[0002] In geostatistics, the acquired data often exhibit complex spatial variability, that is, stationarity, where the statistical characteristics of the data change with the change of location. The theoretical basis of geostatistics is the stationary assumption. However, this assumption often does not hold true in practical applications, especially when dealing with geological data with complex spatial relationships. The multi-point geostatistics (MPS) method has been proposed and widely used. The MPS method can more accurately simulate complex spatial distributions by considering high-order statistical relationships between data points. However, the existing MPS modeling method has limitations when dealing with anisotropic characteristics. Anisotropy refers to the inconsistency of the statistical characteristics of data in different directions, which is very critical for accurate modeling.

[0003] The variogram, a fundamental tool for assessing spatial variability in geostatistics, can describe the spatial autocorrelation and variability of a random field. Its core is to quantify the spatial correlation between two points through the semivariogram, providing a quantitative indicator of the spatial continuity of geological variables. Although the variogram provides a powerful theoretical framework for quantifying the structural characteristics of spatial data, its practical application faces significant challenges, especially when dealing with heterogeneous and non-stationary geological phenomena. How to effectively apply the variogram to systematically assess the stationarity and local anisotropy of training images has become a key bottleneck in improving the accuracy of geological modeling.

[0004] Existing methods usually assume the stationarity of spatial processes or adopt simplified statistical models, and mainly rely on local pattern methods for stationarity analysis. These methods have limited accuracy under stationary conditions, which limits their applicability and accuracy when dealing with complex geological structures. Summary of the Invention

[0005] In order to address the shortcomings of the above-mentioned technologies, the present invention proposes a quantitative evaluation method for the stationarity of training images based on the variogram, which aims to provide a more accurate and reliable spatial variability analysis tool for geological modeling by systematically evaluating the stationarity and local anisotropy of training images. Through refined anchor point selection and variogram calculation, it can effectively identify and quantify stationary areas and their local anisotropic characteristics, providing a new method for the accurate simulation and prediction of geological bodies.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a quantitative evaluation method for the stationarity of a training image based on a variogram, comprising the following steps:

[0007] Step S1: Define the window size of each anchor point of the training image through spatial autocorrelation analysis;

[0008] Step S2: Find the non-anchor point on the training image and calculate the experimental variation function values ​​at four directions of 0°, 45°, 90°, and 135° between the anchor point and the non-anchor point;

[0009] Step S3: Using the Euclidean distance formula, calculate the distances between the anchor point and the non-anchor point at the grid points with the same value in each direction space, and calculate the average distance.

[0010] Step S4: Calculate the average distance between the anchor point and all non-anchor points on the training image, find the maximum and minimum distances of the corresponding anchor points, and divide the normal distribution graph of the distance into equal proportion segments according to the maximum and minimum distances;

[0011] Step S5: For the segmented distance model, the stationary coefficient of the non-anchor point position is obtained by calculating the cumulative sum and average of the distances of each segment point to the non-anchor point, and the anisotropic similarity model of the anchor point position is plotted;

[0012] Step S6: Repeat the operations from step S2 to step S5 until all anchor point positions in the training image are calculated;

[0013] Step S7: averaging the stationary coefficients of all anchor point feature maps to obtain the stationary coefficient of the image;

[0014] Step S8: The stationarity calculation of the three-dimensional training image only requires adding the vertical z-axis to the operation of the two-dimensional training image, and judging whether the image is in a stationary state according to the stationarity coefficient.

[0015] Preferably, in step S2, non-anchor points are found on the training image, and experimental variogram values ​​in four directions of anchor points and non-anchor points are calculated respectively. The formula for calculating the variogram value is:

[0016]

[0017] in, is the average value of the experimental variation function, h is the distance between two points, Z(x i ) is the pixel value at x, N θ (h) is the number of pixel pairs at a given distance h, i.e., non-Null value, γ θ (h) are the experimental variogram values ​​calculated along the directions of 0°, 45°, 90°, and 135° at distance h, respectively.

[0018] Preferably, in step S3, the distances between the anchor point and the non-anchor point in the above four directions are calculated, and the cumulative sums are taken and the average value is obtained to obtain the average anchor point position distance, which is calculated as follows:

[0019]

[0020] Among them, n is the number of points corresponding to the four directions, and the experimental variation function p in each direction of the anchor point is in The corresponding coordinates are (p i1 , p i2 ,...,p in ), experimental variation function a in all directions of non-anchor points jn The corresponding coordinates are (a j1 , a j2 ,...,a jn ), D mean is the average distance between the anchor point and the non-anchor point in each corresponding direction.

[0021] Preferably, in step S4, according to the normal distribution N(μ, σ 2 ), the image is divided into k segments in equal proportion. For the kth segment (k=1, 2, ..., n-1), the corresponding segment point x k The calculation formula is:

[0022]

[0023] Among them, F(x k ) represents the normal distribution at point x k The cumulative distribution function value at x k is the value of the kth segment point, erf (z) is the error function, which is used to describe the variability of the random variable and is defined as: z is the parameter of the error function, μ is the mean of the normal distribution, and σ is the standard deviation of the normal distribution.

[0024] Preferably, in step S5, the stationary coefficient of the training image is calculated, and the calculation formula of the stationary coefficient is:

[0025]

[0026] Among them, S represents the image stability coefficient, M is the total number of anchor points in the image, m is the index of the anchor point, where the value range of m is from 1 to M, that is, traversing all anchor points, N m Indicates the number of segmentation points associated with the mth anchor point, i is the index of the segmentation point, which is used to represent the i-th segmentation point of the mth anchor point in the formula, where the value of i ranges from 1 to N m , that is, traverse all segment points of a certain anchor point, D m，iis the distance between the mth anchor point and its i-th segment point.

[0027] Preferably, in step S8, the stationary coefficients are calculated for multiple groups of two-dimensional training images and three-dimensional training images, and the critical values ​​of stationary and non-stationary of the two-dimensional training images and three-dimensional training images are divided according to the stationary coefficients, and whether the image is in a stationary state is judged according to the critical values.

[0028] The beneficial effects of the present invention are: performing image stationarity analysis based on the variogram, dividing the global stationary image into several sub-regions, first calculating the points with the same variability in each region, and then judging the stationarity of the image by statistically calculating the distance between grid points with the same value in the space, that is, if the spatial distribution is uniform, the larger the distance, the higher the image stationarity, and vice versa, the stronger the non-stationarity. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a stable training image and a segmented interval simulation display diagram of the present invention;

[0030] Figure 2 It is a non-stationary training image and segmented interval simulation display diagram of the present invention;

[0031] Figure 3 is the anisotropic similarity model of each anchor point position of the training image of the present invention;

[0032] Figure 4 It is the training image stationarity arrangement diagram of the present invention;

[0033] Figure 5 The present invention's stationarity arrangement diagram based on variogram;

[0034] Figure 6 A flow chart of the variogram algorithm of the present invention;

[0035] Figure 7 This is a two-dimensional and three-dimensional training image stationarity boundary diagram according to an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] A quantitative evaluation method for the stationarity of a training image based on a variogram includes the following steps:

[0038] 1) Define the window size of each anchor point in the training image through spatial correlation analysis; Figure 1 A and B are stationary and non-stationary training images respectively. Figure 1 A1 and B1 are the pattern similarity graphs of the training images, where the darker the color, the better the correlation at that location. Figure 1The red dot in the middle is the location of the anchor point.

[0039] 2) Find the non-anchor points on the training image and use the formula for calculating the variogram value to calculate the experimental variogram values ​​in four directions (0°, 45°, 90°, and 135°) between the anchor point and the non-anchor point.

[0040] Find the non-anchor point on the training image and calculate the experimental variogram value in the four directions of anchor point and non-anchor point respectively. The formula for calculating the variogram value is:

[0041]

[0042] Among them, γ(h) is the variogram value, h is the distance between two points, Z(x i ) is the pixel value at x, N θ (h) is the number of pixel pairs at a given distance h, i.e., non-Null value. θ (h) are the experimental variogram values ​​calculated along the 0°, 45°, 90°, and 135° directions at a distance h, respectively. Since the variogram is directionally symmetric, i.e., the range values ​​for azimuths 0° and 180° are the same, in practice, only the variograms for azimuths 0°, 45°, 90°, and 135° need to be calculated. For 3D images, the variogram calculation only requires adding the vertical coordinate component to the existing one.

[0043] 3) Using the Euclidean distance formula, calculate the distances between the anchor point and the non-anchor point at the grid points with the same value in each direction space, and calculate the average distance.

[0044] Calculate the distances between the anchor point and the non-anchor point in the four directions mentioned above, accumulate and average them to get the average distance of the anchor point position. The calculation formula is:

[0045]

[0046] Among them, n is the number of points corresponding to the four directions, and the experimental variation function p in each direction of the anchor point is in The corresponding coordinates are (p i1 , p i2 ,...,p in ), experimental variation function a in all directions of non-anchor points jn The corresponding coordinates are (a j1 , a j2 ,...,a jn ), D mean is the average distance between the anchor point and the non-anchor point in each corresponding direction.

[0047] 4) Obtain the average distance between the anchor point and all non-anchor points on the training image, find the maximum and minimum values ​​of the average distance, and obtain the normal distribution N(μ, σ) of the training image. 2 ), according to the normal distribution N(μ,σ) of the training image 2 ), the image is divided into k segments in equal proportion. For the kth segment (k=1, 2, ..., n-1), the corresponding segment point x k The calculation formula is:

[0048]

[0049] Among them, F(x k ) represents the normal distribution at point x k The cumulative distribution function value at x k is the value of the kth segment point, erf (z) is the error function, which is used to describe the variability of the random variable and is defined as: z is the parameter of the error function, μ is the mean of the normal distribution, and σ is the standard deviation of the normal distribution.

[0050] According to the normal distribution graph, the image is divided into k segments in equal proportion using the equal proportion segmentation method, such as Figure 1 As shown, Figure 1 A1 is segmented into 5 segments in equal proportions. For each segment, the distance between the same grid values ​​is calculated. Figure 1 A1 segmentation pattern similarity diagram is as follows Figure 2 As shown in a1-a5, points with the same grid value in the figure are of the same color; Figure 1 The segmentation pattern similarity graph of B1 is as follows Figure 2 As shown in b1-b5, the segment distance model is calculated based on the segment points;

[0051] 5) For the segmented distance model, the stationary coefficient of the non-anchor point position is obtained by calculating the cumulative sum of the distances of each segment point to the non-anchor point and taking the average.

[0052] Calculate the stationary coefficient of the training image. The calculation formula of the stationary coefficient is:

[0053]

[0054] Among them, S represents the image stability coefficient, M is the total number of anchor points in the image, m is the index of the anchor point, where the value range of m is from 1 to M, that is, traversing all anchor points, N m Indicates the number of segmentation points associated with the mth anchor point, i is the index of the segmentation point, which is used to represent the i-th segmentation point of the mth anchor point in the formula, where the value of i ranges from 1 to N m , that is, traverse all segment points of a certain anchor point, D m，iis the distance between the mth anchor point and its i-th segment point.

[0055] 6) Repeat steps 2) to 5) until all anchor points in the training image are calculated. Figure 3 The left image is a non-stationary training image TI8, and the right image is the corresponding anisotropic similarity model obtained after calculating the position of each anchor point. i and j are the coordinate positions corresponding to the anchor points in the anisotropic similarity model. By calculating the stationarity of each anchor point position, the average stationarity coefficient is obtained to obtain the stationarity coefficient of the entire image. The calculation results of the stationarity coefficient of different training images are shown in the following table.

[0056] serial number Stability TI21 0.3098 TI15 0.3116 TI19 0.313 TI26 0.3152 TI20 0.3243 TI13 0.3305 TI8 0.333 TI22 0.3368 TI25 0.3379 TI9 0.3385 TI18 0.3399 TI12 0.3412 TI17 0.3413 TI3 0.3419 TI23 0.3506 TI24 0.353 TI6 0.3531 TI16 0.3537 TI5 0.3582 TI1 0.3591 TI10 0.3592 TI4 0.3602 TI7 0.3605 TI11 0.3636

[0057] 7) According to the stationary coefficients of all anchor points, the average value is calculated to obtain the stationary coefficient of the image; the stationary coefficients of multiple sets of training images are calculated and sorted, such as Figure 4 As shown on the right, the stability of the training images increases from top to bottom and from left to right, and the stability coefficients are sorted from small to large, as shown in Figure 5 As shown in the figure, the stability coefficient histogram of each training image is shown. According to the statistical chart, the critical value of stable image and non-stationary image can be divided. When the stability coefficient is about 0.35, it is at the critical value between stable and non-stationary images. It can be seen from the figure that when the training image is less than 0.35, it is in a non-stationary state, and when it is greater than 0.35, the training image is in a stable state.

[0058] 8) The same steps for 2D images apply to 3D images, with the addition of the vertical axis (z-axis). Stationarity calculations are performed on five sets of 2D training images and three sets of 3D training images. The stationarity coefficients corresponding to each training image are obtained and ranked. Stationarity calculations are performed on the predicted training images, and the stationarity of the image can be determined based on the critical value of the stationarity coefficient.

[0059] like Figure 7As shown, the critical values ​​of the stationary coefficient for stationary and non-stationary images are obtained, respectively. The left figure shows the critical value determination for the 2D stationary coefficient. The arrows indicate the range of the 2D stationary coefficient, increasing from left to right. 0.35 and 0.3687 are the critical values ​​for non-stationary and stationary, respectively. The left side of the 0.35 critical value indicates a non-stationary state, where the image exhibits significant inhomogeneity and fluctuation. The right side represents a stationary state, where the image structure tends to be consistent with minimal variation, demonstrating a high degree of uniformity. The rightmost point, 0.3687, represents the critical state for highly stationary images, where the image displays a completely random and uniform distribution with almost no discernible structure. The image stationary coefficient does not increase further to the right as the arrow moves to the right. The right figure shows the critical value determination for the 3D stationary coefficient, similar to the 2D image. The arrows indicate the range of the 3D stationary coefficient, increasing from left to right. 0.365 and 0.382 represent the critical values ​​for non-stationary and stationary, respectively. The left side of the 0.365 critical value indicates a non-stationary state, while the right side represents a stationary state. The rightmost point, 0.3687, represents the critical state for highly stationary images, where the image stationary coefficient does not increase further to the right as the arrow moves to the right.

[0060] The stationarity of geological features such as braided river deltas and lake sedimentary environments gradually shifts to nonstationarity with increasing spatial distance. Therefore, the present invention determines stationarity by statistically calculating the distance between identical variogram values ​​in space. Specifically, if the spatial distribution is uniform, the larger the distance, the higher the stationarity; conversely, the stronger the nonstationarity. To achieve this objective, the present invention employs the following technical solution: The variogram is used to quantify the variability between different spatial anchor points and other regions of a training image, generating an anchor point distance model. The anchor point distance model is then used to calculate the stationarity coefficient for each anchor point. Finally, the stationarity coefficients of all distance models are statistically combined to form a quantitative indicator of the stationarity of the training image. Traditional geological modeling methods, when assessing the stationarity and local anisotropy of training images, are often limited by simplified statistical models and assumed stationarity. This results in insufficient applicability and accuracy for models dealing with non-uniform geological phenomena, thus impacting the accuracy of geological modeling. The present invention introduces a variogram-based quantitative evaluation method for training image stationarity, systematically analyzing the spatial variability within the training image, effectively overcoming these limitations.

[0061] In order to better understand the present invention, the following are explanations of relevant terms:

[0062] 1. Grid cell (C): A rectangular cubic unit with a specified length (ISize), width (JSize), and height (KSize) along the X, Y, and Z directions. The grid cell stores specific values ​​representing its properties.

[0063] 2. Grid (G): A three-dimensional structure composed of a number of grid cells C. Its dimensions in the X, Y, and Z directions are I × J × K, and it is essentially a three-dimensional matrix. G(i, j, k) represents the grid cell with index i in the X direction, j in the Y direction, and k in the Z direction.

[0064] 3. Training image (TI): prior geological concept model, using grid G TI As a data carrier, it is a digital model that can describe the actual reservoir structure, geometry and distribution pattern.

[0065] 4. Simulation realization (R): refers to the simulation model results, which uses the grid G R As a data carrier, it is a digital model that can describe the actual reservoir structure, geometry and distribution pattern.

[0066] 5. Variation function parameter (γ): that is, the radius of the regional window, with anchor point A as the center, and spatial correlation analysis is used to find the unit body that can represent the actual reservoir structure.

[0067] 6. Pattern similarity parameter (H r ): The template radius r of the image defines the range of surrounding pixels considered when processing each point in the image, which uses the grid G Pat As a data carrier.

[0068] 7. Anchor point (A): A point selected on the training image to determine the spatial correlation between a point in the training image and another anchor point.

[0069] 8. Anchor database (PatA): refers to a dataset containing information about specific pixels (anchor points A) to support various image analysis tasks. On the training image, the values ​​of the pixels in the training image are traversed according to the variogram parameters.

[0070] 9. Non-anchor point database (PatNA): All non-Null points except anchor points, that is, points containing pixel values, and a database consisting of all non-anchor points NA.

[0071] 10. Distance normal distribution (Dnd): refers to the normal distribution of the maximum and minimum values ​​of the distance between the anchor point A and the NA non-anchor point in the image.

[0072] 11. Stationary quantification index (Kt): The average point-to-point distance (Dr) is calculated using Euclidean distance to identify non-stationary features in the image area.

[0073] 12. Anisotropic Similarity Model (ASmodel): A mathematical model that evaluates different directional characteristics in an image, measuring the similarity or difference between image regions based on the directional dependence between pixels.

[0074] The above embodiments are not limitations of the present invention, and the present invention is not limited to the above examples. Any changes, modifications, additions or substitutions made by technicians in this technical field within the scope of the technical solution of the present invention also fall within the scope of protection of the present invention.

Claims

1. A quantitative evaluation method for the stationarity of a training image based on a variogram, characterized by: The following steps are involved: Step S1: Define the window size of each anchor point of the training image through spatial autocorrelation analysis; Step S2: Find the non-anchor point on the training image and calculate the experimental variation function values ​​at four directions of 0°, 45°, 90°, and 135° between the anchor point and the non-anchor point; Step S3: Using the Euclidean distance formula, calculate the distances between the anchor point and the non-anchor point at the grid points with the same value in each direction space, and calculate the average distance. Step S4: Calculate the average distance between the anchor point and all non-anchor points on the training image, find the maximum and minimum distances of the corresponding anchor points, and divide the normal distribution graph of the distance into equal proportion segments according to the maximum and minimum distances; Step S5: For the segmented distance model, the stationary coefficient of the non-anchor point position is obtained by calculating the cumulative sum and average of the distances of each segment point to the non-anchor point, and the anisotropic similarity model of the anchor point position is plotted; Step S6: Repeat the operations from step S2 to step S5 until all anchor point positions in the training image are calculated; Step S7: averaging the stationary coefficients of all anchor point feature maps to obtain the stationary coefficient of the image; Step S8: The stationarity calculation of the three-dimensional training image only requires adding the vertical z-axis to the operation of the two-dimensional training image, and judging whether the image is in a stationary state according to the stationarity coefficient.

2. The method for quantitatively evaluating the stationarity of training images based on variogram according to claim 1, wherein: In step S2, non-anchor points are found on the training image, and experimental variogram values ​​in four directions of anchor points and non-anchor points are calculated respectively. The formula for calculating the variogram value is: ， ， in, is the mean value of the experimental variogram, is the distance between two points, yes The pixel value at is a given distance The number of pixel pairs on is non-Null value, Distance Experimental variogram values ​​calculated along the 0°, 45°, 90°, and 135° directions.

3. The method for quantitatively evaluating the stationarity of training images based on variogram according to claim 1, wherein: In step S4, according to the normal distribution of the training image , divide the image into For the paragraph Segment k=1,2,...,n-1, corresponding segmentation points The calculation formula is: ， in, Represents a normal distribution at point The cumulative distribution function value at It is The value of the segment point, is the error function, which is used to describe the variability of the random variable and is defined as: , z is the parameter of the error function, is the mean of the normal distribution, is the standard deviation of the normal distribution.

4. The method for quantitatively evaluating the stationarity of training images based on variogram according to claim 1, wherein: In step S5, the stationary coefficient of the training image is calculated, and the calculation formula of the stationary coefficient is: ， in, represents the image stability coefficient, is the total number of anchor points in the image, is the index of the anchor point, where The value range is from 1 to That is, traverse all anchor points, Indicates The number of segmentation points associated with each anchor point, is the index of the segment point, used to represent the first Anchor point segmentation points, where The value range is from 1 to , that is, traverse all segment points of a certain anchor point, For the Anchor point and its The distance between segment points.

5. The method for quantitatively evaluating the stationarity of training images based on variogram according to claim 1, wherein: In step S8, stationary coefficients are calculated for multiple groups of two-dimensional training images and three-dimensional training images. Based on the stationary coefficients, critical values ​​for stationary and non-stationary conditions are determined for the two-dimensional training images and the three-dimensional training images. Based on the critical values, it is determined whether the image is in a stationary state.

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