Fractal Analysis of Volcanic Rock Image Based on Difference Box-Counting Dimension and Gray-Level Co-Occurrence Matrix: A Case Study in the Liaohe Basin, China

Abstract

Volcanic rocks, as a widely distributed rock type on the earth, are mostly buried deep within basins, and their internal structures possess characteristics by irregularity and self-similarity. In the study of volcanic rocks, accurately identifying the lithology of volcanic rocks is significant for reservoir description and reservoir evaluation. The accuracy of lithology identification can improve the success rate of petroleum exploration and development as well as the safety of engineering construction. In this study, we took the electron microscope images of four types of volcanic rocks in the Liaohe Basin as the research objects and comprehensively used the differential box-counting dimension (DBC) and the gray-level co-occurrence matrix (GLCM) to identify the lithology of volcanic rocks. Obtain the images of volcanic rocks in the research area and conduct preprocessing so that the images can meet the requirements of calculations. Firstly, calculate the different box-counting dimension. Divide the grayscale image into boxes of different scales and determine the differential box-counting dimension based on the variation of grayscale values within each box. The differential box-counting dimension of basalt ranges from 1.7 to 1.75, that of trachyte ranges from 1.82 to 1.87, that of gabbro ranges from 1.76 to 1.79, and that of diabase ranges from 1.78 to 1.82. Then, the gray-level co-occurrence matrix is utilized to extract four image texture features of volcanic rock images, namely contrast, energy, entropy, and variance. The recognition of four types of volcanic rock images is achieved by combining the different box-counting dimension and the gray-level co-occurrence matrix. This method has been experimentally verified by volcanic rock image samples. It has a relatively high accuracy in identifying the lithology of volcanic rocks and can effectively distinguish four different types of volcanic rocks. Compared with single-feature recognition methods, this approach significantly improves recognition accuracy, offers reliable technical support and a data basis for volcanic rock-related geological analyses, and drives the further development of volcanic rock research.

1. Introduction

1.1. The Theoretical Basis of Volcanic Rock Lithology Identification

Against the background of the increasing demand for oil and gas resources and the growing difficulty in oil and gas exploration, identifying the lithology of volcanic rocks constitutes an important part in the reservoir evaluation of volcanic rock formations and oil and gas exploration [1,2,3,4].

The formation of volcanic rocks is a complex geological process involving the eruption, cooling, and solidification of high-temperature magma and the subsequent geological transformation. During this process, differences in physical properties, such as mineral composition, degree of crystallization, grain size, and arrangement, directly determine the lithological characteristics of volcanic rocks.

During the formation of volcanic rocks, the crystallization and aggregation of minerals exhibit complex self-organizing phenomena, endowing them with fractal structures at different scales. For example, during volcanic eruptions, the rapid or slow cooling of magma leads to different degrees of mineral crystallization, thereby forming fractal structures with different degrees of complexity. As a quantitative index, the fractal dimension can effectively reflect the complexity of this structure and provides an important basis for distinguishing different lithologies [5,6].

Regarding texture features, parameters extracted from the Gray-Level Co-Occurrence Matrix (GLCM), such as contrast, correlation, energy, and entropy, are closely related to the arrangement and distribution of minerals inside the rock. The size, shape of mineral grains, and the spatial relationships among them determine the texture features of the image.

1.2. Comparison of Advantages Between Traditional Methods and Fractal Dimension

In recent years, with the renewal and development of logging equipment, logging data have become more abundant. As a result, a variety of logging lithology interpretation methods based on logging response characteristics have emerged, ranging from cross-plot interpretation methods to multivariate statistical analysis methods, and then to machine learning algorithms that have emerged with the application of big data, gradually improving the timeliness of logging lithology interpretation [7,8,9,10].

Compared with the various logging lithology interpretation methods developed in recent years based on logging response characteristics, using the fractal dimension of volcanic rock core images to identify volcanic rock lithology has unique advantages [11,12,13].

From the perspective of cost, the renewal and maintenance costs of logging equipment are high, while the cost of obtaining core images is relatively low, which makes our method more feasible in research and application scenarios with limited resources. In terms of intuitiveness, methods based on logging data require complex data processing and analysis, while the fractal dimension analysis of core images can more intuitively reflect lithological characteristics, facilitating rapid understanding and judgment by researchers. In addition, under some complex geological conditions, logging data are easily interfered with, leading to deviations in interpretation results. However, the fractal dimension identification of volcanic rock core images is relatively less sensitive to geological conditions and has stronger stability.

1.3. Fractal Geometry

In view of the complexity and irregularity of volcanic rocks, traditional Euclidean geometric theories are unable to accurately describe these objects [14]. Therefore, the introduction of fractal characteristics serves as a new approach to the study of volcanic rocks. Fractal dimension (FD) is an important parameter for describing fractal characteristics, which can reflect the surface roughness and structural irregularity of fractal objects [15,16,17]. Generally speaking, a larger fractal dimension value represents a more complex structure. Research is conducted by calculating the fractal dimension of well logging curves and the distribution of volcanic lithology in the formation, and the corresponding lithological profile is established. The larger the fractal dimension of the well logging curve is, the more complex the internal structure and composition of the corresponding volcanic rocks will be [18,19].

With the continuous development of digitalization, the application of digital image processing technology in the geological field has opened up new avenues and infused new vitality into the identification of volcanic rock lithology. In two-dimensional images, the pore structure is studied by calculating the fractal dimension of the grayscale CT images of rocks [20]. The fractal dimension of the rock pore structure increases with the increase in the porosity ratio. Even with the same porosity, the fractal dimensions may vary. In the three-dimensional CT images of sandstone reservoir rocks, their fractal dimensions, porosity, and sphericity are estimated to analyze the microstructure differences among sandstone reservoir rocks with different permeabilities [21].

1.4. Gray Release Co-Occurrence Matrix

In the 1970s, Haralick proposed the gray-level co-occurrence matrix (GLCM), which was used to describe and analyze the texture features of image [22,23]. Image texture features are one of the important features used to identify the objects or regions of interest in an image, which describe the surface characteristics of the image or a certain region of the image. Due to the fact that different rock structures possess distinct image texture characteristics, the classification of rocks can be achieved by utilizing image texture features [24]. The gray-level co-occurrence matrix was applied to the analysis of computed tomography images of different rock types. The results demonstrated that each rock type had a unique GLCM, based on which the rocks could be classified [25,26,27].

1.5. DBC-GLCM

The method proposed in this paper, which comprehensively utilizes the Differential Box-counting Dimension (DBC) and the Gray-Level Co-occurrence Matrix (GLCM), has unique advantages.

The DBC method can effectively capture the complexity and self-similarity characteristics of rock textures by calculating the fractal dimension of volcanic rock images. Due to the differences in the microstructures of volcanic rocks with different lithologies, these differences will be reflected in the fractal dimension, thus providing a quantitative basis for lithology identification. Compared with traditional methods, the DBC method does not rely on the collection of a large number of rock samples, and it can rapidly process a large amount of image data, improving the identification efficiency.

The GLCM method starts from the spatial dependence of image gray levels and extracts texture features such as energy, contrast, and entropy. These features can reflect information such as the arrangement of internal mineral particles and the distribution uniformity of volcanic rocks. They are of great significance for differentiating lithologies with similar appearances but different microstructures.

Combining the DBC and GLCM methods gives rise to a comprehensive lithology identification system. This system can not only fully leverage the advantages of the two methods and describe the lithological characteristics of volcanic rocks from multiple dimensions, but it can also improve the accuracy and stability of lithology identification. Compared with traditional methods, this DBC-GLCM-based approach can better address the challenges of volcanic rock lithology identification under complex geological conditions, providing more reliable technical support for petroleum exploration and engineering construction.

2. Samples and Methods

2.1. Geological Background and Samples

The Liaohe Basin is located in the plain area of central and southern Liaoning Province, China, and it is part of the Bohai Bay Basin, with a total area of approximately 25,500 square kilometers [28,29]. Among them, the eastern sag of the Liaohe Basin is the research area of this paper [30,31]. The research area is shown in Figure 1 [32]. The eastern sag of the Liaohe Basin is a NE-trending half-graben sag. A large number of volcanic rocks have developed in the strata. These volcanic rocks have not only completely recorded the process of Paleogene volcanism in this area but also constitute the most important oil and gas reservoirs in this area. Conducting comprehensive, in-depth, and systematic research on it holds significant importance for understanding the Paleogene tectonic evolution and dynamic processes in the Liaohe and Bohai Bay basins, as well as for practical hydrocarbon exploration and application. Obtain 2000 typical volcanic rock samples in the eastern sag area of the Liaohe Basin. In this paper, taking the microscopic images of four types of volcanic rock cores, namely basalt, trachyte, gabbro, and diabase, as the research objects, combined with the lithofacies characteristics of Cenozoic intermediate–basic volcanic rocks in the Liaohe Basin, the lithology of these four types of volcanic rocks was identified by using DBC and GLCM.

2.2. Experimental Data Preprocessing

2.2.1. Image Gray Release

A color image contains multiple color channels (such as the three RGB channels). When processing it, the data volume is relatively large and complex, and gray scaling can reduce the computational difficulty. When R = G = B, the color represents a grayscale color, where the value of R = G = B is called the grayscale value. Therefore, each pixel in a grayscale image only requires one byte to store the grayscale value (also known as the intensity value or brightness value), and the grayscale range is from 0 to 255. Commonly used gray scaling methods include the maximum-value method, the average-value method, and the weighted-average method, as shown in Figure 2. To ensure the consistency of the analysis, all original images adopt a common resolution with a pixel size of 519 × 392. In Matlab, the resolution of an image can be adjusted using the imresize function.

In practical applications, the weighted-average method is widely recognized. It can generally meet the gray scaling requirements in most cases. The grayscale image obtained through this method is visually closer to the human eye’s perception of a color image. It can preserve the details and contrast of the image well, facilitating subsequent processing and analysis based on the grayscale image [33].

Grayscale Scaling Range: Scaling the grayscale image and altering its grayscale range can affect the image’s contrast and detail representation. If the grayscale scaling range is too large, some subtle texture features in the image may be overmagnified. As a result, during the calculation of the fractal dimension, these details, which might not be dominant originally, can have a significant impact on the result, making the calculated fractal dimension unstable or inaccurate. Conversely, if the grayscale scaling range is too small, the image contrast decreases, and some important texture features may be weakened. This will also affect the accuracy of the fractal dimension calculation and prevent it from truly reflecting the fractal characteristics of the volcanic rock image.

2.2.2. Filtering Processing

Before analyzing an image, one of the most crucial steps is to remove unwanted noisy pixels from the image. This task is referred to as filtering or denoising. Image filtering is classified into linear filtering and non-linear filtering. Commonly used filtering methods include mean filtering, median filtering, Gaussian filtering, etc. In this study, a Gaussian filter with a kernel size of 5 × 5 and a mean squared deviation of 1.5 was first applied to reduce Gaussian noise. Subsequently, a median filter with a kernel size of 3 × 3 was used to remove salt-and-pepper noise. The following are the results of the filtering process applied to the microscopic images of basalt [34,35].

(1)

Gaussian filtering: It belongs to linear smoothing filtering. The principle is to perform a weighted average on the image. The value of each pixel is obtained by a weighted average of its own value and those of other pixels in the neighborhood. Figure 3 shows the result of Gaussian filtering.

(2)

Median filtering: It is a type of non-linear filtering. Its principle is to replace the grayscale value of a pixel with the median value of the grayscale values in the neighborhood of that pixel. The advantage of this method is that the obtained pixel values are mostly real values, and isolated noise points can be easily removed. Figure 4 shows the result of median filtering.

2.2.3. Binarization

Convert the obtained image into grayscale, with the brightness range from 0 to 255. During the binarization process, the size of each pixel in the image is compared with the threshold value. If the grayscale value of a pixel is greater than or equal to the threshold T, the grayscale value of this pixel is set to a fixed value (usually 255, representing white); if the grayscale value of a pixel is less than the threshold T, the grayscale value of this pixel is set to another fixed value (usually 0, representing black). In this way, a grayscale image can be converted into a binary image with only two colors, black and white.

The threshold can be determined using global and local thresholding methods. However, different thresholding methods will have a certain impact on the results. When extremely high or low thresholds are used during the binarization process, the generated binary image may lose some important texture information, resulting in inaccurate fractal dimension values. Global thresholding methods, such as the Otsu method, also known as the maximum between-class variance method, is an adaptive threshold-selection approach. The core idea of this method is to analyze the grayscale histogram of the image to find an optimal threshold that maximizes the between-class variance between the foreground and the background. In the calculation of the fractal dimension of volcanic rock images, the Otsu method can binarize the images reasonably according to the grayscale distribution characteristics of the images themselves, effectively avoiding the subjectivity of artificially setting thresholds. Generally speaking, in the calculation of the fractal dimension, the binary image obtained by this method can effectively reflect the macroscopic outline and main structural features of volcanic rocks. The calculated fractal dimension is relatively stable and highly accurate and can be used for the preliminary classification and feature extraction of volcanic rock images. Local thresholding methods calculate a unique local threshold using the brightness of detected pixels in the neighborhood around a pixel (i.e., the window). This local approach can effectively identify the local features of pixels in images with varying backgrounds, including illumination or background noise. However, it requires more computational effort. For complex volcanic rock images, due to its inability to adapt to the local variations of the image, the binarization effect may be poor, which in turn can lead to significant deviations in the calculated results of the fractal dimension [36,37,38].

In this study, we used the Otsu method to determine the threshold. Through Matlab calculation, the threshold of Figure 5a was obtained as 92. If the grayscale value of a pixel is greater than or equal to the threshold of 92, the grayscale value of this pixel is set to 255 (i.e., white); if the grayscale value of a pixel is less than the threshold of 92, the grayscale value of this pixel is set to 0 (i.e., black). A binary image with only two colors, black and white, was obtained as shown in the Figure 5c.

2.3. Methods

2.3.1. DBC

Its main idea is as follows as shown in Figure 6: An image with a pixel size of $M\times M$ is regarded as a three-dimensional (3-D) spatial surface, where $\left(x,y\right)$ represent the positions of pixels on the two-dimensional spatial plane of the image and $\left(z\right)$ represents the gray level of pixels. The $\left(x,y\right)$ plane is divided into non-overlapping grids of size $s\times s$. The proportion of each block is $r=s/M$, where ${\displaystyle \frac{M}{2}}\ge s>1$ and $s$ are integers. In this case, a non-square grid introduces 0 to form a complete grid with a size of $s\times s$ pixels. There is a column of $s\times s\times h$ on each grid, where $h$ represents the height of each box. $n_r$ is the total number of boxes required to fill each grid at a ratio r, and the subscript r indicates the result obtained using the ratio r. If the total number of gray levels is $G$, then $G/h=M/s$, $h=sG/M$. Let the minimum and maximum gray levels in the $\left(i,j\right)$th block fall into the $k$th and $l$th bins, respectively. Then

$$n_r\left(i,j\right)=l-k+1$$

(1)

For example, when $s=h=3$, assign numbers 1, 2, 3…, and the minimum and maximum gray levels of the image in the grid fall into box numbers 3 and 1, respectively. Then the number of boxes covering this block is calculated as follows:

$n_r=3-1+1=3$, as shown in Figure 7 [39].

$N_r$ is the number of boxes required to fill the entire image at a proportion $r$.

$$N_r={\displaystyle \sum _{i,j}{n}_r}\left(i,j\right)$$

(2)

Perform the least squares linear fitting estimation on the slope of the curve within the range of $\log \left(N_r\right)$-$\log \left(1/r\right)$ to obtain the FD, namely the fractal dimension [39].

$$FD=\underset{r\to 0}{\lim }{\displaystyle \frac{\log \left(N_r\right)}{\log \left(1/r\right)}}$$

(3)

2.3.2. GLCM

As shown in Figure 8. Firstly, grayscale processing is carried out on the volcanic rock images. Then, the GLCM can be defined as the probability of the occurrence of two pixels with gray values of i and j, whose adjacent distance is d and directions are θ (0°, 45°, 90°, 135°) within the image domain N_x × N_y.

$$P\left(\left.i,j\right|d,\theta \right)=\#\left\{\left(x_1,y_1\right),\left(x_2,y_2\right)\in N_x\times \left.N_y\right|f\left(x_1,y_1\right)=i,f\left(x_2,y_2\right)=j\right\}$$

(4)

In the formula, #(x) represents the number of elements in set x that satisfy certain conditions. d is the distance between (x₁,y₁) and (x₂,y₂), and θ is the included angle between the coordinates of (x₁,y₁) and (x₂,y₂), as shown in Figure 9.

The GLCM can extract texture features in four directions (0°, 45°, 90°, 135°). Here, contrast, energy, entropy, variance, and mean sum are listed, and their formulas are as follows [40,41,42]:

• Contrast $W_1$: Contrast is manifested by the difference in brightness of pixel points in image textures. It is related to the gray values and positions of pixels and reflects the amplitude of local grayscale changes in an image.

  $$W_1={{\displaystyle \sum {\displaystyle \sum p\left(i,j\right)\left(i-j\right)}}}^2$$

  (5)
• Energy $W_2$: Energy, also known as angular second moment, is the sum of the squares of all elements in the gray-level co-occurrence matrix. It can reflect the uniformity of the gray distribution and the coarseness or fineness of the texture in an image.

  $$W_2={{\displaystyle \sum {\displaystyle \sum p\left(i,j\right)}}}^2$$

  (6)
• Entropy $W_3$: Entropy represents the amount of information in an image and can characterize the complexity of textures. It reflects the randomness or complexity of textures in an image. The greater the entropy value is, the more complex the texture will be.

  $$W_3=-{\displaystyle \sum {\displaystyle \sum p\left(x,j\right){\log }_{10}p\left(i,j\right)}}$$

  (7)
• Sum of variances $W_4$: Among them, m is the mean value of p.

  $$W_4=-{\displaystyle \sum {\displaystyle \sum {\left(i-m\right)}^{2}p\left(i,j\right)}}$$

  (8)
• Sum of averages $W_5$: The mean value sum is a measure of the average gray value of the pixel points within the image area, reflecting the brightness and darkness of the image and is applicable to grayscale images.

  $$P_X\left(k\right)={\displaystyle \sum {\displaystyle \sum p\left(i,j\right),k=2,3\cdots }}$$

  $$W_5={\displaystyle \sum k\times P_X\left(k\right)}$$

  (9)

3. Results

The dataset is divided into a training set, a test set, and a validation set. The training set accounts for 70%, the test set makes up 15%, and the remaining 15% is used for validation. This stratification is based on the distribution of different lithologies in the dataset to ensure that each subset contains a representative proportion of each rock type.

In this paper, the different box-counting dimension and gray-level co-occurrence matrix are utilized to comprehensively discriminate the lithology of volcanic rocks. The process of this discrimination method is illustrated in Figure 10 [43,44].

3.1. DBC Experiment Results

The fractional box-counting dimension of volcanic rocks was calculated using the Fraclab toolbox in Matlab. Nine points were selected within each box, and a least squares linear fitting was performed. The results are shown in Figure 11. The linear equation $y=kx+b$ was obtained, and the absolute value of the slope k of this straight line is the fractional box dimension; that is, |k| = FD.

• As can be seen from Figure 12, the difference box-counting dimension of volcanic rocks in this area ranges from 1.6 to 1.9. The surface texture of volcanic rocks is relatively complex, and its difference box-counting dimension is between 1 and 2 (the difference box-counting dimension of a straight line is 1, and that of a planar figure is 2).
• The difference box-counting dimensions of trachyte, diabase, and gabbro are all larger than that of basalt, indicating that the surface structures of trachyte, diabase, and gabbro are more complex than that of basalt. As can be seen from the obtained data, the differential box-counting dimension can, to a certain extent, distinguish basalt and trachyte from the other two types of volcanic rocks. When the fractal dimension ranges of diabase and gabbro overlap (1.76–1.84), the FD-GLCM method is comprehensively utilized to distinguish the lithologies of these three types of volcanic rocks.

3.2. GLCM Experiment Results

In this study, diabase and gabbro samples were selected as the test objects. The gray-level co-occurrence matrices were calculated when d = 1, 2, 3, and 4, respectively. For the distances (d = 1 to d = 4), we chose these values because they can capture texture information at different scales. A smaller distance (d = 1) focuses on the local texture details, while larger distances (up to d = 4) can reveal more global and coarser-scale texture features. Analyze the influence of different values of d on the texture parameter values. To neglect the impact of directional differences and make the characteristic parameter values independent of image rotation, the characteristic parameter values calculated here are taken as the average of the values in four directions: 0°, 45°, 90°, 135°. Generally, contrast, energy (angular second moment), entropy, and variance are used as texture feature parameters. Although the sum of means is not a traditional texture feature parameter, it reflects the overall grayscale characteristics of an image and can serve as an indicator of color shade and intensity. It holds significant importance for enhancing texture expression and classification. In

Table 1. Analysis of gabbro samples.

d	W1	W2 (1 × 10−4)	W3	W4	W5
d = 1	18,575.288	4.115	13.231	123.162	3406.308
d = 2	18,550.121	3.279	13.615	123.061	3406.229
d = 3	18,526.246	3.006	13.759	122.965	3405.892
d = 4	18,505.105	2.821	13.847	122.871	3405.526

and

Table 2. Analysis of diabase samples.

d	W1	W2 (1 × 10−4)	W3	W4	W5
d = 1	32,059.146	2.461	13.657	169.219	3423.735
d = 2	32,035.065	1.892	13.962	169.144	3425.269
d = 3	32,014.594	1.787	14.057	169.078	3427.228
d = 4	31,994.295	1.702	14.119	169.013	3428.788

, W₁, W₂, W₃, W₄, and W₅ represent contrast, energy, entropy, variance, and mean value, respectively.

As can be seen from Table 1 and Table 2, when the distance between pixel pairs d varies from 1 to 4, the values of W₁, W₂, W₃, W₄, and W₅ are all affected to a certain extent. W₃ shows an upward trend as the value of d increases; while W₁, W₂, and W₄ exhibit a downward trend with the increase in d. Corresponding to the change in d value in the texture characteristics of volcanic rocks, it can be indicated that when d is within the range of 3–5, it represents the periodic change in the volcanic rock texture corresponding to the co-occurrence matrix. Therefore, it is considered that when d = 4, the calculated texture feature parameter values have better representativeness for the texture.

For gabbro and diabase images, when d = 4, their gray-level co-occurrence matrices are calculated and shown in

Table 3. Gray-level co-occurrence matrix of gabbro images.

Sample	W1	W2 (1 × 10−4)	W3	W4	W5
1	18,597.376	4.959	13.092	3406.319	123.252
2	21,326.265	5.118	12.873	2851.409	135.922
3	18,911.328	1.212	13.948	2696.592	127.337
4	18,453.301	1.553	13.612	2978.959	124.396
5	17,703.911	6.291	12.773	4230.387	116.075
6	13,253.303	1.706	13.778	3667.949	97.905
7	23,534.587	4.499	12.618	2156.852	146.211
8	27,924.793	9.424	11.761	1865.669	161.428
9	18,904.292	6.849	12.361	4359.485	120.601
10	25,812.256	4.467	12.925	2061.523	154.114

and

Table 4. Gray-level co-occurrence matrix of diabase images.

Sample	W1	W2 (1 × 10−4)	W3	W4	W5
1	32,045.486	2.865	13.627	3424.492	169.1774
2	29,986.944	0.827	14.209	2795.745	164.898
3	20,582.479	0.949	13.836	2206.793	135.557
4	19,231.518	1.119	13.601	1848.355	131.845
5	26,672.479	1.586	14.188	4477.683	148.979
6	25,713.986	3.138	13.634	2599.351	152.035
7	22,705.355	1.158	13.653	2586.818	141.8398
8	20,343.634	1.849	13.509	1571.144	137.013
9	19,205.051	6.55	12.634	1972.271	131.274
10	22,749.615	5.87	12.083	5925.378	132.083

, respectively.

The contrast W₁ mainly reflects the degree of local grayscale differences in the image. Although there are certain differences in mineral grain size between gabbro and diabase, the manifestation of this grain-size difference in the image grayscale contrast is not sufficient to form distinct features that can accurately distinguish the two. The energy W₂ is vulnerable to interference from factors such as local noise in the image and small-scale mineral impurities. In actual rock images, these local interfering factors may cause fluctuations in the energy values, thus affecting its reliability as a means to distinguish between gabbro and diabase. Entropy W₃ has unique advantages in differentiating between gabbro and diabase. It can better capture the differences between the two types of rocks from the perspectives of texture complexity and randomness. Entropy is sensitive to the uniformity of the grayscale distribution in an image. The differences in the size, shape, and distribution uniformity of mineral grains in gabbro and diabase lead to variations in the grayscale distribution of the images, thus resulting in different entropy values. For example, the texture formed by the interweaving of mineral grains in diabase may result in a relatively non-uniform grayscale distribution, leading to a larger entropy value. In contrast, the equigranular texture of gabbro may make the grayscale distribution more uniform, with a relatively smaller entropy value. This threshold is obtained through calculation and comparison. By comparing the magnitude relationship between the entropy value and the threshold, these two types of rocks can be distinguished to a certain extent.

Evidently, for the images of gabbro and diabase, the lithology of volcanic rocks can be discriminated through a comprehensive analysis of the W₃ value. By integrating two different sets of experimental data from the differential box-counting dimension and the gray-level co-occurrence matrix, basalt, trachyte, diabase, and gabbro can be distinguished.

4. Discussion

4.1. Model Evaluation

In this study, accuracy, precision, recall, and F₁-score were used as evaluation indicators to conduct a comparative analysis of the results of the random forest model and FD-GLCM. The results are shown in

Table 5. Comparison of lithology identification results between the random forest model and FD-GLCM method.

Lithology	Random Forest Model			FD-GLCM
	Precision/1	Recall/1	F1	Precision/1	Recall/1	F1
Basalt	0.81	0.91	0.85	0.91	0.92	0.915
Trachyte	0.87	0.92	0.894	0.88	0.90	0.89
Gabbro	0.82	0.67	0.738	0.67	0.67	0.67
Diabase	0.76	0.67	0.712	0.87	0.78	0.823
Accuracy/1	0.88			0.86

.

As can be seen from the table, the recognition effects of random forest and FD-GLCM on gabbro and diabase are not very good. The three evaluation indicators, namely precision, recall, and F₁-score, are not high, resulting in a relatively large number of misjudgments for this type of lithology. Firstly, the fractal dimension values and the texture features derived from GLCM of a small number of diabase samples are extremely close to those of gabbro. This similarity makes it difficult for our classification method to accurately distinguish between them. In addition, during the sampling and imaging processes, some samples may be affected by local rock heterogeneity or small-scale impurities, which also leads to misjudgments. However, both methods have relatively good identification results for basalt and trachyte. Overall, the identification accuracy of the random forest model is approximately 88%, and that of the FD-GLCM (Feature-Distribution Gray-Level Co-occurrence Matrix, if this is what it stands for; replace it with the accurate full name if otherwise) is approximately 86%.

4.2. Analysis of Application Effect

Take Well H24 in the study area as an example, and compare the prediction results with the lithologic section. In the well section with a depth ranging from 2870 to 2980 m, as shown in Figure 13, the lithological profile of the volcanic rock is basalt and diabase. The interval from 2942 to 2951 m is diabase. The random forest method misclassified diabase as gabbro at 2946 m and 2929 m. The FD-GLCM method misidentified diabase as gabbro at 2942 m and 2945 m. Both of the above-mentioned methods wrongly judged diabase as gabbro. Overall, except for individual thin layers, the prediction results are basically consistent with the lithologic section, indicating a relatively good prediction effect.

In lithology identification, there is an overlapping range in the differential box-counting dimensions of gabbro and diabase. Therefore, the gray-level co-occurrence matrix (GLCM) is further utilized to discriminate the lithology. Due to the fact that the texture features derived from GLCM of some gabbro and diabase are highly similar, misjudgments between gabbro and diabase are likely to occur.

4.3. Computational Complexity of DBC and GLCM Methods

The time complexity of the DBC method is proportional to the image size and the number of scales taken into account, where the main computational cost stems from grid partitioning and grayscale change analysis. The spatial complexity is primarily determined by the image size.

The time complexity of the GLCM method is related to the image size, the number of gray levels, and the number of distances and angles considered and is significantly influenced by the number of gray levels. The spatial complexity is mainly determined by the number of gray levels (for storing the GLCM matrix) but is also related to the image size. In practical applications, it is necessary to select an appropriate method or optimize the algorithm according to the specific image data and computing resources so as to improve the computational efficiency and reduce resource consumption.

4.4. Limitation

Regarding the sensitivity to image resolution, we acknowledge that when the image resolution is low, detailed information in the image will be lost. There will be spatial blurring between pixels, making it impossible to accurately calculate the differential box-counting dimension and affecting the construction of the gray-level co-occurrence matrix. When the image resolution is high, some unnecessary noise will be introduced. This noise can interfere with the calculation of the differential box-counting dimension. The calculation of the gray-level co-occurrence matrix (GLCM) increases significantly, and at high resolutions, the GLCM matrix becomes extremely large. The DBC and GLCM methods have certain limitations when dealing with high-resolution images. In practical applications, appropriate adjustments and optimizations are required according to specific circumstances to ensure the effectiveness and accuracy of these methods.

4.5. Practical Application and Scalability

In practical geological exploration, our method can be integrated into the existing logging and core analysis workflows. For instance, during logging operations, our method can be used to process the acquired images in real time to identify the lithology of volcanic rocks. Subsequently, this information can be utilized to guide subsequent exploration and production decisions, such as determining the location of potential oil-bearing reservoirs. For the discovered oil and gas reservoirs, using this method to conduct a detailed analysis of the lithology of the surrounding volcanic rocks helps to describe the reservoir characteristics more comprehensively. This provides a scientific basis for formulating reservoir exploitation plans and improving the oil and gas recovery rate.

Regarding scalability, we analyzed the computational complexity of our method. Although the current implementation incurs a certain computational cost, we have proposed several strategies for handling larger datasets. For instance, we can utilize parallel computing techniques to accelerate the processing of a large number of images. Additionally, we can adopt distributed computing techniques, distributing data-processing tasks to multiple computing nodes for parallel processing to improve computational efficiency and reduce the overall computing time. For example, by using distributed computing frameworks such as Apache Spark, it is possible to rapidly process large-scale image data and compute features such as the Gray-Level Co-occurrence Matrix (GLCM).

5. Conclusions

(1)

The images of volcanic rocks indicate that the microscopic structures of volcanic rocks are fractal structures with self-similarity, the complexity of which can be described by the magnitude of the fractal dimension. The value of the differential box-counting dimension of volcanic rocks is in direct proportion to the complexity of the rock surface. For rocks with more complex surface textures, the calculated values of the differential box-counting dimension will be larger.

(2)

The differential box-counting dimension of basalt ranges from 1.7 to 1.75, that of trachyte ranges from 1.82 to 1.87, that of gabbro ranges from 1.76 to 1.79, and that of diabase ranges from 1.78 to 1.82. The application of the differential box-counting dimension can distinguish basalt from the other three types of volcanic rocks.

(3)

Since the differential box-counting dimensions of trachyte, diabase, and gabbro overlap to some extent, we further comprehensively utilize the differential box-counting dimension and the gray-level co-occurrence matrix method to distinguish the lithology of volcanic rocks. In terms of the W₃ value, it is gabbro when W₃ > 14 and diabase when W₃ < 14. Compared with the method of identifying volcanic rocks based on a single feature, the method that combines the differential box-counting dimension and the gray-level co-occurrence matrix is more accurate in identifying the lithology of volcanic rocks.