Exploration of Kastification and Characterization Based on Borehole Image

Abstract

The characteristics of the karst pore structure not only affect the seepage features of the rock mass in the karst area but also have a noticeable effect on the mechanical behavior in the process of rock mass loading. The exploration of the exhibition karst pore structure plays a crucial role in the development of science, technology, and engineering construction. In order to appropriately unlock the problem of image brightness imbalance caused by probe eccentricity in field image acquisition and to realize the proper in situ identification and precise characterization of the borehole structure, the scrutiny of karst pore recognition and a characterization method based on the borehole image are proposed. First, combined with the imaging characteristics of borehole image construction, an eccentric image acquisition model is constructed, the change law of image illumination intensity is clarified, and a suitable pretreatment method is developed for karst pore structures, which effectively enhances the borehole image quality. Subsequently, the pore structure identification method is established by integrating the gradient operator and the maximum interclass variance method, which could successfully screen and filter out the non-porous region segments and ensure that the identified pore structure features are more accurate and rich. Finally, on the basis of representing the single pore structure, number and area proportion functions are constructed in both the depth and azimuth directions, and the distribution characteristics of the pore structure on the borehole wall are evaluated in various dimensions. The achieved results reveal that the proposed pore structure identification and characterization approach could substantially enhance the work efficiency of the karst pore structure in borehole images and provide a simple, reliable, and effective method for the statistics and application of karst pore data.

1. Introduction

China is one of the most developed karst countries in the world, with the distribution area of soluble rock reaching 3.65 million km². In total, karst development areas account for approximately one-third of the national land area. The problem of karst disasters originated from the engineering construction of karst areas, and the development of land resources, water resources, and mineral resources are becoming increasingly prominent. This issue seriously hinders the economic construction and social development of these areas, influencing the daily life of the people. In general, rock is a complex geological body composed of particles, pores, and cementation. It is of great scientific significance to understand the structural characteristics of the pores in rocks, their mechanical properties, reservoir capacity, and permeability characteristics [1,2,3,4,5]. In the karst strata, the dissolved pores develop, and the pore structures provide crucial channels for the flow of groundwater, intrusion of saline water, and diffusion of pollutants. As a typical porous medium, both the mechanical and osmotic characteristics of the dissolved rock mass are deeply affected by the pore structure [6,7,8]. Pore structure is a vital factor affecting the physical properties of porous materials, including the study of the porous structure. It is not a perfect exploration to evaluate the dissolved rock mass only from a porosity point of view in practical engineering. Pore structure characteristics not only affect the seepage properties of the rock mass but also remarkably influence mechanical behavior in the process of rock mass loading. Therefore, the research of karst pore structure plays a crucial role in the development of science, technology, and engineering construction.

At present, the main data sources of pore structure research chiefly include indoor tests and field logging [9,10,11,12]. In the exploitation of indoor test data analysis, based on the scanning image of the core CT, Wang et al. [13] combined image processing technology and various mathematical analysis methods. Therefore, they measured the average porosity and analyzed the pore distribution. Ju et al. [14] examined the geometric characteristics and distribution characteristics of the rock pore by the sandstone CT scanning test, and the statistical characteristics of the center of mass coordinates, pore distance, number and size, and their probability density functions were presented and discussed. Feng et al. [15] used SEM technology to obtain two-dimensional apparent porosity at different thresholds; introducing the idea of binary integration, we propose a calculation method based on SEM 2D images. Liu et al. [16] developed a set of comprehensive evaluation methods of low permeability reservoirs based on complex rock mass identification established from rock core, casting sheet, cathode luminescence, SEM, and ESC logging. The indoor test method could measure and predict many parameters, but the test results are greatly affected by man and rely on the core since it is difficult to achieve pore structure continuity analysis of the whole well section. Field logging data can conduct a wide range of feature evaluations of rock mass pores, but it is difficult to meet the requirements of rock mass fine structure description as it is often high cost, limiting its wide application [17].

Borehole camera technology is more and more extensively employed in field logging. It enables us to take high-resolution images of the borehole wall and fully record the rock structure information on the borehole wall, such as bedding, cracks, pores, and its depth and orientation information. Additionally, the detailed description of the rock mass structure of the whole well section could also be realized by borehole images. Wang and Wang [18,19] developed a technical method to identify and characterize coral reef holes, and Wang et al. [20] proposed an approach for the accurate identification and quantitative analysis of the rock pore structure for hole wall optical images. Therefore, it is possible to analyze the geological pore structure of the karst region by employing the borehole images obtained by borehole imaging technology. Due to the complexity of geological boreholes in karst regions, including borehole walls’ collapse and borehole tilt, it is easy to cause the image acquisition probe to be in the off-center position during the image acquisition operation in the borehole, and the image is formed with light and dark stripes, hence influencing the identification and characterization of the pore structure. Therefore, in order to effectively unlock the problem of light and dark stripes in borehole images of the karst region, this paper provides a novel technical approach to identify and characterize pore structures in the karst development region.

2. Borehole Image Acquisition Technique

Borehole images can be obtained through borehole optics, acoustics, and electricity. Since optical imaging exhibits the pore structure characteristics of rock walls more directly, the borehole images explored in the present study are mainly optical borehole images. Currently, the optical borehole images collected by borehole camera technology have high accuracy. Borehole camera technology is the use of an optical probe to go deep into the borehole interior and to continuously take photos or video of the hole wall so as to visually present the rock mass structure information. The borehole images analyzed in this paper are taken from the digital panoramic borehole camera system developed by the Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. The system is mainly composed of a panoramic probe, cable, depth encoder, control box, and other components. A schematic representation of the system structure is presented in Figure 1a. The device has a maximum lateral resolution of 0.05 mm and a maximum longitudinal resolution of 0.1 mm.

Digital panoramic borehole camera technology is based on the optical principle of geological borehole structure in situ test technology. Through undisturbed in situ camera recording of the borehole wall, the geological information on the borehole wall is directly collected to avoid the impact of disturbance caused by drilling and coring, which can better reflect the geological structure in the borehole compared to the rock core, and the results obtained are more credible and intuitive. The basic working principle is displayed as follows:

Panoramic impact acquisition technology. An HD camera is utilized to collect the optical images of the rock wall reflected by the cut-head cone mirror in real-time, obtaining the borehole wall 360° image data. Panoramic image data usually includes the ring hole wall image, depth information, and orientation information, as demonstrated in Figure 1b.

Digital image expansion technology. Digital image expansion technology mainly includes continuous frame narrow-band image acquisition, feature detection and data matching, narrow-band image splicing and fusion, image optimization and information annotation, and other steps. It is the use of digital image processing technology to transform the panoramic image into a panoramic one. The panoramic image usually consists of two forms: the hole wall plane expansion map and the virtual core map. The left side of the plan expansion diagram is in the due north direction, the horizontal length is the borehole circumference, and the vertical length is the borehole depth, as illustrated in Figure 1c.

3. Identification of the Karst Pore Structure

3.1. Eccentric Image Acquisition Model

Since the actual geological borehole is usually in a non-absolute vertical state, the actual state of the hole panoramic probe without the added probe centering device is mostly an eccentric acquisition image state, resulting in the collected borehole image being prone to uneven illumination phenomena. The more the probe favors the borehole wall, the stronger the light received at the wall and the clearer the wall image becomes. The farther away from the probe, the less light the wall receives, and the more blurred the image. The schematic representation of the eccentric image is demonstrated in Figure 2. Figure 2a presents a schematic diagram of the relative position of the probe with respect to the borehole. Figure 2b illustrates the expanded image of the corresponding borehole wall. The brighter the color, the stronger the light intensity, the darker the color, and the weaker the light intensity. Position A in Figure 2 represents the closest position to the probe and receives the strongest light intensity, which more visibly presents the pore characteristics on the pore wall at this position. Position C in Figure 2 is the furthest point from the probe and receives the weakest light intensity, making it difficult to present the pore characteristics on the pore wall at this position.

In order to adapt to the actual test state, uneven hole wall illumination caused by probe eccentricity is avoided. This paper aims to establish an image acquisition model based on the eccentric image acquisition model. As illustrated in Figure 3a, the central origin of the probe is coincident with point O, the origin of the rectangular coordinate system. In such a system, the horizontal and vertical directions are set as the x-axis and the y-axis, respectively.

Let us set the radius of the probe, radius of the hole, and coordinates of the center point O’ equal to r, R, and (x₀, y₀), respectively. Then, the circular equation of the circle outside the probe and the wall of the borehole hole could be, respectively provided by:

$$\{\begin{array}{l}{x}^2+y^2=r^2\\ {\left(x-x_0\right)}^2+{\left(y-y_0\right)}^2=R^2\end{array}.$$

(1)

Suppose a ray with an angle of α along the central point O intersects the probe circle at point P₁ and the hole wall circle at point P₂. Using Equation (1), the relations corresponding to point P₁ and point P₂ are stated by:

$$\{\begin{array}{l}{\left(r\cos \alpha \right)}^2+{\left(r\sin \alpha \right)}^2=r^2\\ {\left(\left(r+l\right)\cos \alpha -x_0\right)}^2+{\left(\left(r+l\right)\sin \alpha -y_0\right)}^2=R^2\end{array}.$$

(2)

Among them, parameter l is the shortest distance between the probe and the hole wall, and the light intensity is evaluated by the size of its value. In other words, the smaller the l, the stronger the light, and the larger the l, the weaker the light. To this end, the corresponding valid solution to Equation (2) is sought as follows:

$$\begin{array}{l}l=(\mathrm{x}0*\cos (\mathrm{a})-\mathrm{r}*\sin (\mathrm{a})^2+\mathrm{y}0*\sin (\mathrm{a})+(^2*\cos \left(\mathrm{a}\right)+\\ (\mathrm{R}^2*\cos (\mathrm{a})^2+\mathrm{R}^2*\sin (\mathrm{a})^2*\cos (\mathrm{a})^2-\\ \mathrm{x}0^2*\sin \left(\mathrm{a}\right)^2+2*\mathrm{x}0*\mathrm{y}0*\mathrm{c}\mathrm{o}\mathrm{s}\left(\mathrm{a}\right)*\sin \left(\mathrm{a}\right))^(1/2)\\ -\mathrm{r}*\cos \left(\mathrm{a}\right)^2)/(\cos \left(\mathrm{a}\right)^2+\sin \left(\mathrm{a}\right)^2)\end{array}.$$

(3)

If x₀, y₀, r, and R are constant values, then the relationship between the shortest distance l and the light angle α is expressed by a trigonometric function. Assuming that the position of the borehole center in the coordinate system is (10,10), the eccentric distance of the probe center is $10\sqrt{2}$ mm, the probe diameter is set as 70 mm, and the hole diameter is 110 mm; therefore, one can write: x₀ = 10 mm, y₀ = 10 mm, r = 35 mm, and R = 55 mm, and the variation curve of l in the range of [0,2π] is presented by the red line in Figure 3b. Assuming that the position of the borehole center in the coordinate system is given as (−10,−10), the corresponding eccentric distance would be $10\sqrt{2}$ mm, 70 mm and 110 mm as the probe diameter and hole diameter, respectively; hence, if one can arrive at x₀ = 10 mm, y₀ = 10 mm, r = 35 mm, and R = 55 mm, then the variation curve of l in the interval of [0,2 π] is depicted by the blue line in Figure 3b.

As can be seen from Figure 3b, the eccentric image acquisition model can be utilized to examine the characteristics of variation of the light intensity in the presence of the eccentric state of the probe. The energy intensity of light is evaluated by mastering the shortest distance between the light source and the hole wall, and then the imaging quality of the hole wall image is estimated. The eccentric image acquisition model further reveals that when the probe favors the borehole rock wall, the more intense illumination in the rock wall area is clear and better.

3.2. Bore Image Preprocessing

Due to the actual borehole optical image acquisition process, the probe is prone to be eccentric, and the image formed is usually prone to light and shade features, as presented in Figure 4a. To eliminate this image phenomenon and highlight the karst pore structure features, borehole image preprocessing is required before pore identification. The optical images presented below depict a borehole located in Kunming, Yunnan Province, China, which belongs to the karst development stratum. The borehole depth is 15 m, the diameter is 110 mm, and the borehole fluid is a water-based slurry. In the whole borehole, the karst development of the 5.0–5.5 m section borehole wall is more obvious. Thereby, such a section is considered as the research object for further analysis. Figure 4a demonstrates the optical image of the hole wall from 5.0 to 5.5 m, vertical from top to bottom varies in the range of 5.0–5.5 m, and horizontal from left to right to north-east–south-west to north. As can be seen from Figure 4a, there is an apparent light and shade alternation in the unfolding image of the borehole, which is essentially related to probe bias in the process of image acquisition. The basic principle of preprocessing in the present work is to exploit the eccentric image acquisition model to enhance the hole wall image in various directions (i.e., the enhancement degree of pixel points in various directions is different).

The core of this preprocessing is to determine the azimuth angle associated with the strongest light point, which corresponds to the shortest distance between the light source and the hole wall. RGB color space is one of the most broadly exploited color systems, which includes the changes of red (R), green (G), and blue (B) (i.e., three color channels) and their superposition to acquire a wide variety of colors. The HSV color space is mainly represented by three components: hue (H), saturation (S), and value (V). The V component represents the brightness of the color. The corresponding value range is [0,1], reflecting the maximum value of R, G, and B components of each pixel within the image in the RGB color space. The expression of V is provided by:

$$V=\max (R/255,G/255,B/255).$$

(4)

Specifically, R, G, and B correspond to the gray values of the red, green, and blue channels in the images. Let us evaluate the RGB value of each pixel in Figure 4a according to Equation (4) and present the calculation result for an image with the corresponding brightness image (see Figure 4b). The image with a depth of 0.5 m is divided into 50 equal-height image bands with equal spacing of 10 mm. The highest lightness value V_i, maximum on each image band, is calculated, and location C_i, pertinent to V_i,max, is marked, where C_i represents the C_i-th pixel point on the image band. Sequentially, positions C_i of the highest brightness on the adjacent image belt are connected to form the bright position change curve on the borehole unfolded image, as demonstrated by the red line in Figure 4c.

If the lightness value before the j-th pixel in the i-th image is represented by $V_{i,j}$, the cosine enhancement function in combination with the eccentric image acquisition model could be established to form the preprocessed image. Therefore, the lightness value of the j-th pixel in the i-th image (${\overline{V}}_{i,j}$) is expressed as follows:

$${\overline{V}}_{i,j}=V_{i,j}·\left[1+\lambda ·\left(\cos \left(\pi +\frac{2·\left(j-J_{i,\max }\right)·\pi }{N}\right)+1\right)\right],$$

(5)

where the enhancement coefficient $\lambda$ could be adjusted according to the actual situation, $J_{i,\max }$ represents the location of the lateral pixels associated with V_i,max, and N denotes the total number of lateral pixels in the image band. After the original image is acted upon by the numerical processing of lightness, the HSV color space image is converted into an RGB color space image, indicating that the preprocessing of the image becomes complete. If the enhancement coefficient is set as 0.5, Figure 4a is enhanced, and the formed image is demonstrated in Figure 4d. This image reveals that after enhanced preprocessing, the light and dark stripe phenomenon on the image disappears, and the pore structure on the image is clearer, providing clearer digital image information for pore recognition in the posterior segment.

3.3. Pore Structure Identification

In identifying the karst pore structure, the distinction between the pore structure and the background is achieved. By setting the threshold value, the grayscale value and the threshold value of each pixel on the identified image are compared, and the pixel is divided into the target point or the background based on the comparison result. The grayscale value F(i,j) < T of the pixel point (i,j) on the pore wall image is called the background point, and the pixel point of the grayscale value F(i,j) > T is called the target point, indicating the pore structure on the pore wall. The threshold value on each channel is split as:

$$G(i,j)=\{\begin{array}{l}0,\hspace{0.17em}\hspace{0.17em}F(i,j)\hspace{0.17em}<\hspace{0.17em}T\\ 1,\hspace{0.17em}\hspace{0.17em}F(i,j)\hspace{0.17em}\ge \hspace{0.17em}T\end{array},$$

(6)

where G(i,j) represents the threshold-processed image, pixels labeled 0 are associated with the background, pixels labeled 1 are pertinent to the target point, and T denotes the set threshold. In the identification of karst pore structures, the key is to determine an appropriate threshold to effectively distinguish the target point and the background. The maximum inter-class variance methodology is one of the more commonly exploited approaches in threshold distinction. The maximum inter-class variance method is simple in principle and also fast in processing speed, but it cannot be appropriately adapted to the actual images. There are some differences in the gray values of the pore structure in the pore wall image and those of the background area, and the gray values of the adjacent pixels at the boundary edge of the pore substantially vary. Therefore, the gradient can be employed to represent the discontinuity at the pore edge, realizing the sharpening of the pore area. For this purpose, the gradient is defined as:

$$\nabla F=grad(F)=\left[\begin{array}{l}{G}_x\\ G_y\end{array}\right],$$

(7)

where $G_x$ and $G_y$ denote the approximate first-order partial derivatives. The magnitude of the expression in Equation (7) is evaluated as follows:

$$\left|\nabla FF(x,y)\right|=\sqrt{G_x{}^2+G_y{}^2}.$$

(8)

The edge points of the image are initially determined by the traditional Canny operator, and then the Sobel convolution template P, as presented in Equation (7), is utilized based on the x-direction and y-direction. The grayscale plots of the images are convolved to obtain a gradient G_x in the x-direction. The same story holds true for the gradient term of G_y in the y-direction. Hence, let us define:

$$P_x=\left[\begin{array}{l}-1\hspace{0.17em}\hspace{0.17em}0\hspace{0.17em}\hspace{0.17em}1\\ -2\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}0\hspace{0.17em}\hspace{0.17em}2\\ -1\hspace{0.17em}\hspace{0.17em}0\hspace{0.17em}\hspace{0.17em}1\end{array}\right]P_y=\left[\begin{array}{l}\hspace{0.17em}1\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}2\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}1\\ \hspace{0.17em}\hspace{0.17em}0\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}0\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}0\\ -1\hspace{0.17em}\hspace{0.17em}-2-1\end{array}\right].$$

(9)

The azimuth of each pixel is further obtained by Equation (8), where atan2(G_x,G_y) indicates the four-quadrant anyway tangent function. Let us define the γ function in the following form:

$$\gamma (x,y)=\frac{a\tan 2(G_x,G_y)\ast 180}{\pi }.$$

(10)

Let us divide the azimuth angle $\gamma (x,y)$ by the D₁–D₈ (i.e., the eight-direction intervals, as demonstrated in Figure 5a). The threshold value T could also be evaluated via the maximum interclass variance method. For each edge point Q(x,y), L points are obtained along the interval direction of the azimuth reverse extension line. Further, the edge is suppressed as Q(x,y) satisfies the following relation:

$$255T\ge \{\begin{array}{l}\max \{Q(x,y+1),\dots ,Q(x,y+L)\},\gamma \in D_1\\ \max \{Q(x-1,y+1),\dots ,Q(x-L,y+L)\},\gamma \in D_2\\ \max \{Q(x-1,y),\dots ,Q(x-L,y)\},\gamma \in D_3\\ \max \{Q(x-1,y-1),\dots ,Q(x-L,y-L)\},\gamma \in D_4\\ \max \{Q(x,y-1),\dots ,Q(x,y-L)\},\gamma \in D_5\\ \max \{Q(x+1,y-1),\dots ,Q(x+L,y-L)\},\gamma \in D_6\\ \max \{Q(x+1,y),\dots ,Q(x+L,y)\},\gamma \in D_7\\ \max \{Q(x+1,y+1),\dots ,Q(x+L,y+L)\},\gamma \in D_8\end{array}.$$

(11)

In Equation (11), 255T denotes the reverse normalization result of the threshold value T, and Equation (10) reveals that when the gray value of all L points in the corresponding interval is less than 255T, it is the distractor edge point. By binarizing the above algorithm, the processed image has been presented in Figure 5b. Since there are still some isolated points in the image, which are regarded as invalid image information, by mixing with the mathematical morphological operation method, the information of the isolated points is eliminated, and the remaining closed areas are regarded as the pore structure. The identified pore structure is demonstrated in Figure 5c.

In order to verify the superiority of identifying the karst pores presented here, the existing results are compared with those of other methods (see Figure 6a–c). Figure 6a is the result of threshold segmentation processing between Figure 4a. Namely, the traditional probe is not considered eccentric image acquisition. As can be seen from the figure, in the strong light area, the pore structure can be effectively identified, and in the weak light area, it is difficult to excellently distinguish the pore structure, and the identification results could only provide some effective information. Figure 6b,c demonstrate the results of preprocessing the images according to the method developed in this paper. By comparing it with Figure 6a, it can be seen that the proposed image preprocessing approach could effectively decline the difficulty of successfully distinguishing between the pores due to probe eccentricity. Figure 6b illustrates the results of the traditional histogram threshold method, and Figure 6c presents the results of combining the gradient operator with the maximum interclass variance approach. A comparison between Figure 6b,c reveals that the traditional histogram segmentation is easy to blur the locally effective information, while the pore structure obtained by the sampling method is more abundant.

4. Characterization and Analysis of the Karst Pore Structure

4.1. Characterization of the Karst Pore Structure

Commonly, karst pores are characterized by a specific closed region in the image. In order to effectively characterize the karst pore structure herein, three representative parameters of pore radius, pore area, and shape factor are chosen as the characterization target. The pore radius (R) is essentially evaluated by counting the pixel points of the largest inscribed circle in the closed area as

$$R=\frac{2N_r·\delta d}{\pi },$$

(12)

where N_r denotes the total number of maximum inscribed circle pixels in the closed area and $\delta d$ is the corresponding size of pixels. The pore area (S) chiefly counts the area represented by the pixel points of the closed area. If the pore area is divided into n × n, the expression of the pore area takes the following form,

$$S=\{\begin{array}{l}\frac{1}{\pi }·\delta d·\delta d·{\displaystyle \sum _{i=1}^n(y_{ij}-y_{ij}^{\prime }+1)\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{Macro}\mathrm{size}}\\ \frac{1}{2}·\delta d·\delta d·{\displaystyle \sum _{i=1}^n(y_{ij}-y_{ij}^{\prime }+1)\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{Non}\text{-}\mathrm{macro}\mathrm{dimensions}}\end{array},$$

(13)

in which y_ij denotes the ordinate of the leftmost square point in each line, and y_ij’ represents the ordinate of the rightmost square point in each line. In addition, the shape factor (G) is mainly exploited to simplify the complex pore structure and reflect the morphological characteristics of pores. This is defined by

$$G=\frac{S}{C},$$

(14)

where C represents the pore perimeter. This factor is essentially calculated by counting the side length represented by the outermost pixel point of the closed area; however, the chain code is an alternative approach to evaluate that.

4.2. Analysis of the Karst Pore Structure

The 38 pore structures in the image are characterized as described above, and the obtained results are demonstrated in Figure 7. Figure 7a–c presents the pore radius, pore area, and shape factor, respectively. As can be seen from Figure 7, the corresponding values of the radius, area, and shape factor vary between various pore structures. By calculating the pore radius, pore area, and pore shape factor, the scale and morphological characteristics of the pore structure could be reasonably characterized.

After completing the characterization of the pore structure, the corresponding statistical analyses of the regional pore structure are performed from different angles. In the statistical analysis of the karst pore structure, the quantitative statistical analyses of pores and area statistics are mainly included. The number of pores in the karst hole (h) is recorded as n(h), and the pore area in the karst hole (h) is recorded as S(h). In the depth direction, the number–ratio function N_v(z) and the area–scale function S_v(z) of the pore are established through the following definitions:

$$N_V(z)=\frac{{\displaystyle \sum _{i=z}^{z+\Delta h}n(i)}}{{\displaystyle \sum _{i=h_1}^{h_2}n(i)}},S_V(z)=\frac{{\displaystyle \sum _{i=z}^{z+\Delta h}S(i)}}{{\displaystyle \sum _{i=h_1}^{h_2}S(i)}},$$

(15)

where z is the statistical region depth number, h₁ and h₂ denote the minimum and maximum values of the statistical region depth, and Δh represents the length of the statistical region z. Equation (15) indicates the projection of the pore number ratio and the area ratio in the depth direction. The proportion of the pore area in the 5.0–5.5 m depth direction is demonstrated in Figure 8a. It can be seen from Figure 8 that at a borehole depth of 5.085 m, the nearby pore structure is moderately small, revealing that the pore structure at a borehole depth of 5.085 m is chiefly manifested as cracks, which is more consistent with the actual situation.

In the circumferential direction, the number ratio function N_c(z) and the area ratio function S_c(z) of the pore could be established as follows:

$$N_C(\alpha )=\frac{{\displaystyle \sum _{i=\alpha }^{\alpha +\Delta \theta }n(i)}}{{\displaystyle \sum _{i=0}^{2\pi }n(i)}},S_C(\alpha )=\frac{{\displaystyle \sum _{i=\alpha }^{\alpha +\Delta \theta }S(i)}}{{\displaystyle \sum _{i=0}^{2\pi }S(i)}},$$

(16)

in which angle $\alpha$ corresponds to the borehole image of the statistical area, and Δθ is the unit angle of the statistical area. Equation (16) indicates the projection of the pore number ratio and the area ratio in the circumferential direction. The proportion of the pore area in the depth interval of 5.0–5.5 m through the circumferential direction is presented in Figure 8b. The results for the borehole orientation 53° indicate that the corresponding pore structure is densely distributed, which is more consistent with the actual situation.

Statistical analysis of borehole images at borehole depths 5.0–5.5 m is performed based on Equations (14) and (15). In the depth direction, the borehole depth is divided into five sections, i.e., the statistical unit depth is set as 0.1 m, and the corresponding quantity proportion and area proportion distribution are presented in Figure 9a. As can be seen from Figure 9a, in terms of quantity, pore structure in the depth range of 5.3–5.4 m and the number of pore structures in at depth intervals of 5.0–5.1 m and 5.4–5.5 m are almost equal to zero. This means that the center of the pore structure is not distributed in these two regions, and the pore structure is chiefly distributed in the depth range of 5.1–5.4 m. In terms of area, the pore structure has the largest area proportion at a depth interval of 5.3–5.4 m, and no pore structure is detectable in the depth range of 5.4–5.5 m, meaning that the pore structure is not distributed in this region. Through a comprehensive analysis of quantity and area distribution, it can be seen that the pore structure in the borehole at a depth interval of 5.0–5.5 m is essentially distributed between the depth values of 5.1 m and 5.4 m. In the circumferential direction, the borehole circumference is divided into 12 areas, namely the statistical unit of 30°, corresponding to quantity proportion and area proportion distribution, as shown in Figure 9b. In terms of quantity, this figure shows that the number of pore structures is the largest proportion in the interval of 30–60°, and the largest number of pore structures in the ranges of 300–330° is almost zero, namely, the center of the pore structure is not distributed in this region. In terms of area, pore structures are larger in the ranges of 30–60°, 90–120°, and 120–150° and are smaller at intervals of 300–330° and 330–360°. By comprehensively analyzing the number and the area distribution, we can see that the pore structure distribution of the borehole in the angle range of 30–210° is relatively dense.

5. Conclusions

The proposed eccentric image acquisition model and borehole image preprocessing approach could effectively enhance borehole image quality. Bored–expanded images are commonly subjected to probe eccentricity, and image illumination intensity varies based on a triangular function. By establishing an eccentric image acquisition model and constructing the cosine enhancement function, the influence of uneven illumination could be reduced.

The identification methodology effectively screens and filters out the non-pore region by combining the inter-class variance method, which makes it harder to blur local effective information and enables us to obtain pore structure features that are more abundant.

On the basis of representing the single pore structure, the number ratio function, the area ratio function in the depth direction, and the orientation direction are appropriately constructed, which could successfully reflect the distribution characteristics of the pore structure on the borehole wall.

The proposed pore structure identification and characterization approach can greatly improve the efficiency of the identification and analysis of karst pore structures in borehole images and provide a simple, reliable, and effective approach for the statistics and application of karst pore data.