A Case Study Comparing Methods for Coal Thickness Identification in Complex Geological Conditions

Abstract

This study compares the effectiveness of different methods for coal thickness identification, aiming to identify the most accurate approach and provide a reference for intelligent coalmine development. Focused on the No. 2 coal seam in a mining area in Shanxi, China, the analysis employs well log-constrained impedance inversion and seismic multi-attribute techniques. The results show that the back propagation (BP) neural network model, as part of the seismic multi-attribute approach, delivers prediction accuracy comparable to the well log-constrained inversion method. Specifically, after applying proper static corrections, a four-layer BP neural network was constructed using four optimized sensitive attributes as the input layer, achieving an error range of 0.11% to 1.36%, compared to 0.03% to 6.59% for the logging-based method. The BP neural network demonstrated strong applicability in complex geological environments. Empirical analysis further validated the BP neural network’s geological reliability and practicality in systematic coal thickness determination.

1. Introduction

The accurate identification of coal thickness is crucial for intelligent mining and economic efficiency in coalmines. Issues, such as coal seam absence, stripping, bifurcation, and merging, can severely impact coal production. If the actual coal seam thickness is reduced by 10% to 20% compared to the designed thickness, coal output can decrease by 35% to 40%. Intelligent coal mining is a development trend in the industry, with accurate coal seam thickness determination being a critical prerequisite for automated mining. Intelligent mining is a process that continuously integrates, extracts, and transforms geological data [1,2]. In the construction of intelligent mining information entities, coal seam information falls under the category of entity attribute information. Three-dimensional seismic data hold a significant position in geological exploration data, containing rich geological information. Seismic attributes encompass the geometrical, kinematic, dynamic, and statistical features of waveforms in seismic data [3]. Thus, technologies for extracting, storing, visualizing, analyzing, verifying, and evaluating seismic attributes are crucial for constructing entity attributes and accurately describing target coal seam information, meeting the diverse requirements of intelligent coal mining [4,5,6].

As a target body in seismic exploration, coal seams have relatively small thicknesses and belong to the category of thin layers. Compared to the main wavelength λ of the coal seam reflection (approximately 45 m), the thickness is less than λ/4, making direct interpretation of the target coal seam difficult. Widess (1973) proposed the relationship between thin layer thickness and its reflection amplitude in an infinitely homogeneous medium, surpassing purely geometrical methods to determine the limits of thin layer thickness [7]. Subsequently, Voogd and Koefoed defined thin layers using the quasi-linear relationship between composite reflection wave amplitude and thickness [8]. For different reflection coefficients, the sinusoidal response amplitude of wedge bodies is approximately linear with d/λ. For a given reflection coefficient, thin layers are defined as those where the error between the true amplitude curve and the linear approximation is less than 10%. Currently, coal thickness determination in production typically uses borehole interpolation methods; however, due to the limited density and number of boreholes [9], the results have significant errors and cannot effectively guide operations. Although underground channel wave exploration has high accuracy for coal thickness, its application is limited by time and data volume; therefore, it plays a corrective role in intelligent mining processes [10,11].

To solve the problem of the quantitative interpretation of coal thickness, many scholars have explored and studied seismic attributes [12,13]. Seismic attribute methods can effectively reflect the characteristics of thin layers in seismic information, establishing a physical relationship between thin layers and seismic attributes, providing a new approach for quantitative determination of coal thickness. Some researchers believe that coal seam thickness is related to the ratio between the integral of the amplitude spectrum of coal seam reflection waves and the first moment of the seismic wavelet amplitude spectrum [14]. To demonstrate the correlation between amplitude attributes and coal thickness, a wedge-shaped coal seam model was established for verification [15]. However, single seismic attribute methods use only one type of seismic attribute parameter, leading to significant random errors and limited calculation accuracy [16]. Neural network algorithms and multiple regression models can provide effective predictions by simulating the input feature set (such as seismic waveforms) and the expected output values (such as phase types, arrival times, etc.) [17,18]. For coal thickness determination, training and processing the multi-attribute features of incomplete seismic data samples with unique generalization capabilities can reduce interpretational ambiguity and improve interpretation efficiency and accuracy. Analysis shows a close relationship between coal seam thickness and seismic amplitude and frequency attributes. Training and processing the multi-attribute features of incomplete seismic data can enhance interpretation accuracy and efficiency, yielding good results in the inversion of seismic wave attribute parameters to coal thickness [19,20].

On the other hand, the method of predicting coal thickness using well log-constrained impedance inversion improves prediction accuracy [21]. High-resolution stratigraphic impedance data can provide a good geological description of thin layers. By fully acquiring high-frequency information and retaining low-frequency components, the bandwidth limitations of seismic data can be compensated for. The low- and high-frequency information is obtained from well log data, while the structural features and mid-frequency range depend on seismic data.

Seismic inversion inherently carries a degree of uncertainty. However, by conducting comparative studies of different methods using the same seismic exploration data, this uncertainty can be significantly reduced. A comparative analysis of two methods for coal thickness identification under complex geological conditions revealed that the BP neural network is not only effective in standard geological environments but also highly adaptable to more complex settings. This adaptability enhances the reliability of inversion results, allowing for more accurate quantitative interpretations of coal thickness. These improvements boost both the precision and reliability of geological interpretations and resource estimations. The integration of seismic multi-attribute methods with well log-constrained impedance inversion technology proves highly effective for predicting coal thickness. Moreover, by leveraging simulation technology for improved situational awareness and conducting hypothetical scenario analysis for proactive risk assessment [22], the efficiency and safety of mining operations are enhanced. These advancements provide a robust technical foundation for the intelligent development of coalmines, marking a significant step forward in mining innovation.

2. Geological Test

2.1. Seismic Geological Setting

The research area of the 24 Mining District in Shanxi, China is characterized by low- to mid-mountain erosion and structural terrain. The mining field is located on the eastern foothills of the Luyashan Range, in the northern section of the Lüliang Mountains, with the Fen River to its east. The overall topography of the mining field is higher in the northwest and lower in the southeast. The highest point in the area has an elevation of 1715.079 m, while the lowest point is at 1402.472 m, resulting in a maximum relative height difference of 312.607 m. The surface layer mainly consists of exposed bedrock and Quaternary loess coverage, with localized colluvial deposits. Typical landforms of the exploration area are shown in Figure 1.

Structurally, the area is characterized by the Ningjing syncline, which trends northeast. Most of the field lies on the northwest limb of this syncline, where the strata are relatively gentle, with small dips. The coal seam dip angles within the exploration area range from 2° to 4°, dipping towards the southeast. Fault structures are not well-developed in the mining field. Some parts of the area are covered by Quaternary loess, while bedrock outcrops can be found in the western region. The coal-bearing strata belong to the Middle Jurassic Datong formation, primarily comprising the No. 2 and No. 3 coal seams. The main stratigraphy in the area, from oldest to youngest, includes the Triassic, Jurassic, and Quaternary formations. The Jurassic No. 2 coal seam is the primary mineable coal seam in this area, with an average thickness of 3.28 m. The coal seam thickness ranges from 0.12 to 6.84 m, with an average of 3.02 m, classifying it as a medium-thick coal seam. The overall mineable index for the entire field is 84%, with a coal thickness variation coefficient of 52%. Within the mineable range, the coal thickness varies from 0.73 to 6.84 m, with an average of 3.79 m and a variation coefficient of 23%.

In this region, the roof and floor of the coal seam are mainly composed of sandstone and siltstone, creating differences in wave impedance, and producing a set of continuous reflection waves (T₂ waves), which are the primary target waves for seismic exploration. The No. 3 coal seam, located near the No. 2 coal seam, also exhibits significant wave impedance differences with the surrounding rock, resulting in another set of continuously traceable reflection waves (T₃ waves). The T₂ waves have some influence on the T₃ waves, making the T₃ waves a set of composite waves, as shown in Figure 2.

Overall, the mid-deep seismic geological conditions in the research area are favorable. Figure 2 shows a typical single-shot record and seismic time section of this area. While the near-surface and shallow seismic geological conditions are complex, the deep seismic geological conditions are relatively favorable.

For areas with complex mountainous erosion structures characterized by rugged terrain, numerous ravines, and significant lateral variation in surface layers, various excitation and reception combination techniques were employed. In shallow loess-covered areas (with a thickness of less than or equal to 4 m), shallow boreholes reaching 1–2 m into the bedrock were used. In medium-thick loess areas (with a thickness greater than 4 m but generally not exceeding 10 m), single boreholes were drilled into the bedrock surface. In bedrock-exposed areas, single boreholes were drilled to a depth of 3 m; in weathered bedrock areas, the depth was set to 4 m. The excitation was carried out with three geophones connected in series in a clustered pattern; an observation system was arranged to ensure uniform distribution of stacking directions and source–receiver distances.

2.2. Design Observation System

The design parameters were as follows: a 10-line, 8-source midpoint excitation fan-shaped observation system; each receiving line had 100 channels; the distance between receiving lines was 40 m; the receiving channel interval was 10 m; the lateral source interval was 20 m; the longitudinal source interval was 100 m; the CDP grid was 5 m by 10 m; and the coverage was 20-fold (4 times laterally, 5 times longitudinally), with an aspect ratio of 0.5 (Figure 3). In the study area, 21 source fans were deployed, covering an exploration area of 4.50 square kilometers, with a full coverage area of 4.87 square kilometers. A total of 2741 physical points were surveyed, with 2669 physical points for fan-line deployment and 72 points for testing at 4 sites.

2.3. Static Correction

Given the complex surface topography of the study area, effective field static correction is a critical step in the subsequent processing and interpretation of seismic data for coal thickness. Static correction eliminates time shifts in reflection waves caused by changes in excitation and reception conditions, primarily due to variations in topography and near-surface velocity structures. Static correction involves two main tasks: calculating the static correction values and applying the correction [23].

We adopted the Green Mountain first-break refraction static correction method and used a specialized module to separate long- and short-wavelength correction values. The Fathom method decomposes refraction information into the delay times at shot and geophone points and the velocity of the refracting layer. In the velocity analysis algorithm, the reciprocal velocity analysis (RVA) method was chosen and the near-surface model was gradually analyzed and interpreted [24]. The delay time analysis algorithm performs three iterations on the shot and geophone points, first using median estimates and then refining them with mean estimates, as shown in Figure 4.

In the subsequent work after the static correction, dip–moveout (DMO) stacking was performed in conjunction with multiple automatic residual static corrections (short-wavelength). Considering the characteristics of the Fathom method, the following key calculation methods and parameters were used for field static correction: the reference elevation for static correction was set at 1550 m; and the replacement velocity was set at 3500 m/s to account for variations in geophone elevation and source well depth.

3. Methods

3.1. Seismic Wave Impedance Inversion Based on Well Log Constraints

Seismic wave impedance inversion is a technique used to infer the wave impedance characteristics of strata (or rock layers) by utilizing seismic data [25]. This method links seismic reflection profiles with lithology and physical property profiles, enabling a comparison between seismic data and drilling data [26,27]. The technical process primarily includes the following steps: Initial Model Setup: Set an initial wave impedance model of the strata and perform seismic forward modeling to generate synthetic seismic records. Comparison and Adjustment: Compare the synthetic records with actual seismic data to adjust the main parameters of the geological model. Perform forward modeling again to obtain new synthetic records. Iteration: Continuously compare the new synthetic records with the actual seismic records, iteratively modifying the geological model until the synthetic seismic data best match the actual seismic records. The geological model obtained when the error is minimized is considered the result of the wave impedance model inversion, as shown in Figure 5.

Given a seismic record, as follows:

$$S(t)=R(t)\times W(t)+N(t)$$

(1)

$S(t)$ is the seismic record, R(t) is the reflection coefficient of the interfaces, W(t) is the seismic wavelet, and N(t) is noise. The goal of seismic inversion is to obtain the reflection coefficient series R(t), which only reflects the changes in subsurface interfaces. Through the reflection coefficient series, the relationship between the velocity and density of each reflection layer is established, allowing for the prediction of the distribution of subsurface media.

Assume the initial seismic wavelet is W₁(t), and the initial reflectivity series is R₁(t). The formula for the synthetically generated record y₁(t) is as follows:

$$y_1(t)=R_1(t)\times W_1(t)+N_1(t)$$

(2)

The cross-correlation between x(t) and y₁(t) is given by the following correlation coefficient R_xy:

$$R_{xy}(s)={\displaystyle \frac{1}{n}}{\displaystyle \sum _{t=1}^{n}x(t)y_1(t+s)}$$

(3)

By adjusting y₁(t) to maximize Rxy, the initial seismic wavelet W₁(t) and the initial reflectivity series R₁(t) are modified. Once R_xy reaches a satisfactory value, an initial model is established using density, velocity, and reflectivity through Kriging interpolation to generate the initial impedance data volume. This process is a forward modeling procedure that involves adjusting the well logs, initial reflectivity, and initial wavelet.

Based on the initial model, all interpolated impedances are subjected to a limited number of adjustments within a certain range to find an optimal stratigraphic model. This model minimizes the error energy between the synthetic seismic data generated from it and the actual observed data, achieving the minimum value of the objective function (Equation (4)). The result is the final inversion profile, where e₁(t) represents the degree of match between the model and the seismic record. This process is an inversion procedure that modifies the impedance of the initial model [28], as follows:

$$e_1(t)=x(t)-y_1(t)$$

(4)

Processing Well Log Data: Well log data, particularly acoustic and density logs, are crucial for constructing the initial model and geological interpretation [29,30]. However, acoustic logs often face interference from borehole conditions, such as borehole collapse and mud invasion, potentially leading to errors that require correction. Additionally, the time-domain thickness of converted acoustic log curves may exhibit inaccuracies. To mitigate such velocity errors, a common approach is to accurately determine the correspondence between the main wave group in the synthetic record and the nearby seismic trace. Subsequently, the well log data are adjusted through compression or stretching to match the time thickness of the seismic record, enhancing the similarity between the synthetic record and the nearby seismic trace. This method helps to establish an accurate time–depth conversion relationship and accurately depicts the reflection positions of lithological interfaces on seismic profiles.

Seismic Wavelet Extraction and Synthetic Records: Synthetic seismic records are generated by convolving the wavelet with the model’s reflection coefficients [31]. The termination condition for synthetic seismic data is the minimization of errors with actual seismic data. Both well and seismic data are used to extract the wavelet and its corresponding amplitude and phase spectra. This wavelet is then used to establish a matching relationship between the well logs and seismic data. If the match is unsatisfactory, the wavelet is extracted again to further improve it until a satisfactory match is achieved.

Constructing a Reasonable Initial Wave Impedance Model: Building the wave impedance model involves a complex interactive process that combines seismic interface information with well log wave impedance. In seismology, accurately interpreting the primary wave impedance interface should best reflect the stratigraphic sequence interfaces of sedimentary structures. In well-logging, this means assigning appropriate wave impedance information to the strata between wave impedance interfaces [32].

3.2. Seismic Multi-Attribute Method

The seismic multi-attribute method for predicting coal thickness primarily involves two aspects: first, researching and selecting optimal seismic attributes related to coal seams; and second, characterizing the complex mapping relationship between coal thickness and various influencing seismic attributes to establish a coal thickness prediction model.

3.2.1. Attribute System Optimization

Seismic attributes refer to the geometrical, kinematic, dynamic, or statistical characteristics of seismic waves derived from pre-stack or post-stack seismic data through mathematical transformations [33]. The characteristics of seismic signals are directly influenced by the physical properties and variations of rock layers. Seismic information reflecting anomalies related to coal thickness mainly includes amplitude attributes, frequency attributes, velocity attributes, absorption attenuation information, and other attributes related to coal thickness [34]. Since many attribute anomalies have certain ambiguities, it is crucial to extract sensitive parameters of seismic attributes that are related to coal thickness [35]. By selecting the most sensitive seismic attributes or combinations of attributes with the fewest numbers, the prediction accuracy of seismic attributes can be improved. This selection is integrated with geological data for comprehensive analysis and judgment, facilitating the prediction of target coal seam thickness.

By calculating correlation coefficients and cross-correlation, the accuracy of seismic attribute extraction for coal thickness is ensured. This process optimizes the combination and selection of attributes to minimize prediction errors with multi-parameter, selected, effective attribute combinations.

(1) Seismic Layer Attribute Extraction and Normalization

Extracting seismic layer (interlayer or along-layer) attributes provides information on the lateral variation of various attributes along the target layer interface. For the No. 2 coal seam, 20 types of seismic attributes (including amplitude attributes, trajectory attributes, and frequency (energy) spectrum statistical attributes) were extracted along the layer (with an extraction window length of 20 ms). The extracted attributes were then normalized using the following formula:

$$y_{(i)}=(x_{(i)}-x_{\min })/(x_{\max }-x_{\min })$$

(5)

where x_(i) is the value at the ith point before normalization, y_(i) is the value at the ith point after normalization, and x_min and x_max are the minimum and maximum values for normalization, respectively.

(2) Attribute Optimization

Attribute optimization is mainly divided into the following two steps: first, correlation analysis to preliminarily screen for attributes sensitive to coal thickness changes; second, cross-correlation analysis to independently screen the initially selected parameters and eliminate redundant attributes with strong correlations [36], as follows:

$$R_{xy}={\displaystyle \frac{{\displaystyle \sum (X_i-\overline{X})(Y_i-\overline{Y})}}{\sqrt{{\displaystyle \sum {(X_i-\overline{X})}^2{(Y_i-\overline{Y})}^2}}}}$$

(6)

The correlation coefficient between X and Y, denoted as R_xy, is calculated as follows: $\overline{X}$ and $\overline{Y}$ represent the ith observations of variables X and Y, respectively. X_i and Y_i are the mean values of X and Y. The value of the correlation coefficient ranges between −1 and 1, where 1 indicates a perfect positive correlation, −1 indicates a perfect negative correlation, and 0 indicates no linear correlation. The expression for cross-correlation is similar to that of the correlation coefficient, but with different parameter values.

(3) Optimal Attribute Combination

Stepwise regression is used for system attribute selection to screen for the best attribute combination that minimizes prediction errors [37]. Assuming that the optimal combination of M attributes is known, the optimal combination of M + 1 attributes includes the previous M attributes. The steps are as follows:

a. Perform an exhaustive search to identify the optimal attribute, attribute 1; b. Incrementally add the next best attribute to the system, targeting the smallest prediction error to determine attribute 2; c. Combine the attributes according to their correlation and iteratively seek the optimal combination, determining attribute 3, and so on.

(4) Effectiveness Analysis

The average effective error and average theoretical prediction error are calculated for different numbers of attribute combinations to select the most suitable effective attribute count.

The formula for the mean effective error is as follows:

$$E_V^2={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{e}_{vi}^2}$$

(7)

In Equation (7), E_v represents the mean effective error across all wells, e_vi is the effective error for the ith well, and N is the total number of wells analyzed.

3.2.2. BP Neural Network Prediction Model

A BP (Backpropagation) neural network consists of an input layer, an output layer, and one or more hidden layers [38], as shown in Figure 6. During implementation, initial data normalization is performed to control the scale of each feature within the same range. Then, the network model and structure are established. Next, training samples are selected as needed, and the network is trained by incorporating the input and expected output data. Through forward propagation and backpropagation processes, weight and threshold adjustments are made, and output errors are calculated until the learning error requirements are met, achieving function approximation [39]. After training, the model is evaluated using actual data to make the final result determination.

The thickness of coal seams exhibits a linear relationship with certain seismic reflection wave attributes within a defined range. However, the correlation between seismic reflection wave attributes and coal seam thickness typically demonstrates non-linear characteristics. BP neural networks can adjust parameters via error feedback, thereby ensuring the network’s capacity for non-linear mapping.

4. Results and Discussion

4.1. Impedance Inversion Result

By adjusting the wavelet length, the seismic wavelet was optimized to have stable waveform characteristics, with energy concentrated in the main lobe, minimal energy in the side lobes that decay rapidly, a broad frequency band, and high dominant frequency. These characteristics best met the requirements for modeling. The wavelet length was adjusted to 100 ms, with a constant-phase wavelet and side-lobe length of 25 ms, within a time window of 200–500 ms for extraction. Figure 7 shows the initially extracted wavelet and its spectrum, while Figure 8 presents the final modified wavelet and spectrum.

By employing the least squares method for the analysis, impedance was determined. The calculation of reflection coefficients was based on the linear relationship between density and velocity, allowing for the estimation of impedance values. By selecting an appropriate seismic wavelet (Figure 9), a synthetic seismic record was generated, which was then used for horizon calibration, Typical seismic profiles were then transformed and compared with drilling and well-logging data, as depicted in Figure 8.

The precision of seismic stratigraphic interpretation directly influences the lateral resolution of the initial model, while seismic sampling rate is the primary factor affecting vertical resolution. Utilizing high-frequency information from well-logging enables detailed description of geological thin layers, often requiring densification of seismic data sampling. To meet the high vertical resolution requirements for reservoir identification, the seismic data sampling rate is increased to 0.5 to 1 ms. In constrained inversion, ensuring minimal error between observed seismic data and synthetic records calculated by the model involves employing a hard constraint approach, which bounds the final impedance values within a specified range of variability. The wave impedance values at borehole LB12 (see Figure 10) indicated that the wave impedance of the coal seam was relatively low compared to the wave impedance of the roof and floor. The inversion profile accurately identified the boundaries of the coal seam; the results at the borehole location aligned perfectly with the well log data. In this parameter testing, a hard constraint of 25% resulted in relatively small overall errors. Throughout this process, the average block size was chosen to match the sampling interval (1 ms).

4.2. Seismic Multi-Attribute Prediction Result

4.2.1. Attribute Optimization Result

Normalization: Seismic layer attributes were extracted and normalized for the No. 2 coal seam target layer. Eleven seismic attributes were selected with absolute correlation coefficients exceeding 0.6, as detailed in

Table 1. Correlation coefficients between coal thickness and seismic attributes.

Seismic Attribute	Correlation Coefficient	Seismic Attribute	Correlation Coefficient
	2# Coal Seam		2# Coal Seam
Root Mean Square Amplitude	0.708	Decile Frequency (2)	0.636
Maximum Energy Level	0.74	Decile Frequency (3)	0.595
Instantaneous Frequency	−0.622	Decile Frequency (7)	0.307
Maximum Amplitude	0.743	Dominant Frequency	0.399
Average Energy Level	0.681	High Cross-section	−0.63
Bandwidth Deviation Ratio	−0.607	Low Cross-Section	0.311
Arc Length	0.768	Total Energy	0.657
Bandwidth Ratio (4)	−0.465	Asymmetry	−0.131
Bandwidth Ratio (5)	0.269	Area above Half Peak	−0.346
Bandwidth Ratio (9)	0.706	Slope above Half Peak	0.56

.

Attribute Optimization: Following correlation coefficient calculations among seismic attributes and their correlations with coal thickness, a refined selection process was undertaken. Attributes demonstrating significant correlations were retained or merged, while those showing high mutual independence, but substantial correlation, were excluded. This process identified seven independent and sensitive attributes crucial for constructing a robust decision model.

Table 2. Cross-correlation coefficients of selected attributes for the No. 2 coal seam.

R	a	b	c	d	e	f	g	h	i	j	k
a	1	0.9955	−0.8003	0.9949	0.9974	−0.8443	0.8661	0.2221	0.1029	−0.6572	0.9329
b	0.9955	1	−0.8023	0.9997	0.9882	−0.8418	0.8928	0.2871	0.1766	−0.6501	0.9407
c	−0.8003	−0.8022	1	−0.8056	0.7693	0.9752	−0.4967	−0.3558	0.2117	0.8204	−0.5618
d	0.9949	0.9998	−0.8056	1	0.9876	−0.8479	0.8927	0.2923	0.1828	−0.6519	0.9401
e	0.9974	0.9883	−0.7694	0.9875	1	−0.8228	0.8636	0.1668	0.0495	−0.6243	0.9397
f	−0.8443	−0.8418	0.9752	−0.8479	−0.8228	1	−0.5611	0.2853	0.1544	0.7664	−0.6451
g	0.8662	0.8928	−0.4967	0.8927	0.8636	0.5611	1	0.3978	0.3551	−0.4121	0.9652
h	0.2221	0.2871	−0.3559	0.2924	0.1668	−0.2853	0.3977	1	0.9811	−0.5609	0.2035
i	0.1209	0.1767	−0.2117	0.1829	0.0495	−0.1544	0.3551	0.9811	1	−0.3954	0.1372
j	−0.6572	−0.6502	0.8204	−0.6519	−0.6244	0.7664	−0.4121	−0.5609	−0.3954	1	−0.4362
k	0.9330	0.9407	−0.5618	0.9401	0.9397	−0.6451	0.9652	0.2035	0.1373	−0.4362	1

(a) Root mean square amplitude; (b) maximum energy level; (c) instantaneous frequency; (d) maximum amplitude; (e) average energy level; (f) bandwidth deviation ratio; (g) arc length; (h) bandwidth ratio 9; (i) decile frequency 2; (j) high cross-section; and (k) total energy.

illustrates the outcomes of mutual correlation computations, highlighting attributes such as arc length, decile frequency, maximum amplitude, maximum energy level, high cross-section, and total energy.

Optimal Attribute Combination: Utilizing results from mutual correlation assessments, an exhaustive search approach was employed to determine the optimal attribute combination. The methodology involved sequentially selecting the most relevant attribute from the set of seven identified attributes: (a) beginning with attribute 1; (b) assessing combinations with the remaining six attributes to minimize prediction errors, identifying attribute 2 with minimal error; and (c) continuing to evaluate combinations with attributes 1 and 2 to identify the top three combinations with the smallest prediction errors, thereby establishing attribute 3. Stepwise regression further refined subsequent attribute combinations.

Effectiveness Analysis: Effectiveness analysis methods can determine the most suitable number of attributes based on actual conditions, thereby improving the accuracy and reliability of the model, and avoiding overfitting phenomena.

For the No. 2 coal seam, the optimal combination of attributes includes length, percentile frequency (2), maximum amplitude, and total energy as shown in Figure 10.

In Figure 11, the horizontal axis represents the number of seismic attributes, while the vertical axis represents the average error. It can be observed that when the number of attributes increases to five, the actual error significantly rises. Therefore, it is concluded that additional attributes beyond the fourth attribute may lead to overfitting. Hence, the optimal number of attributes was determined to be four.

4.2.2. BP Neural Network Prediction Result

Utilizing the BP neural network from machine learning for nonlinear problem determination, we trained the model using revealed point coal thickness data and validated it against predictions from nearby working face boreholes. This approach achieved function approximation from input to output and integrated multiple seismic attributes, revealing complex relationships with coal thickness.

In selecting other network parameters, the transfer function from the input layer to the hidden layers was chosen as the logsig function, known for its good differential properties and belonging to the sigmoid function family. This choice ensures neurons produce outputs even with weak sample attribute values and prevent overflow with large values. The transfer function from the hidden layers to the output layer was purelin, a linear transfer function that retains and scales values from any previous range for comparison with predicted sample values.

Specific parameters included: the initial learning rate set to 0.01; the target function error reduced to 0.01; and the momentum factor set to 0.9 to effectively enhance learning efficiency, reduce errors and prevent the network from converging to local minima.

The actual observation data from the No. 2 coal seam in the 24 Mining Area of the Lu’an coalmine were filtered to select nine borehole seismic attributes as learning samples for network training. To ensure robustness with a moderate model complexity, we constructed an initial BP artificial neural network model with four layers. Four selected seismic attributes were chosen as input layer nodes, followed by two hidden layers with three and two nodes, respectively. The output layer predicted coal thickness. Training with samples established from arc length, percentile frequency (2), maximum amplitude, and total energy resulted in learned connection weights W₁ between the input and first hidden layer; W₂ between the first and the second hidden layer; and W₃ between the second hidden layer and output layers. The first hidden layer contained three nodes, while the second had two nodes.

$$W_1=\left[\begin{array}{cccc}5.252644441& -4.233421812& 3.957612198& -3.207962213\\ 3.36081903& -1.123996543& 4.813339729& -0.89108932\\ 9.408939889& 2.654392006& 3.112900161& -14.91667746\end{array}\right]$$

(8)

$$W_2=\left[\begin{array}{cccc}4.533082705& 2.492960496& 0.877679381& -3.252873526\\ 1.470133801& -3.082943086& 12.57992379& -1.66106168\end{array}\right]$$

(9)

$$W_3=\left[\begin{array}{ccc}8.026619943& 7.672284883& 8.12632643\end{array}\right]$$

(10)

4.3. Discussion

In this study, the BP neural network served as the model for the coal thickness outcome prediction (Figure 12), which aligned closely with the actual results. The coal thickness at drill hole locations is represented in red. From the thickness variation trend map of the No. 2 coal seam, it can be observed that the thickness of the No. 2 coal seam ranges from 0.12 m to 6.84 m. The thinnest section is located in the northwest corner within the erosion zone, while the thickest section is found near the boundary in the southwest corner. The thin layers are distributed in an irregular banded pattern.

Based on the practical application of impedance inversion methods, the results demonstrate that the BP neural network inversion model based on seismic multi-attributes achieves relatively high accuracy with small errors, As shown in Figure 13, where the x-axis represents revealed drill holes and the y-axis represents relative errors, the comparison reveals the following observations: the impedance inversion shows relative errors ranging from 0.03% to 6.59%; LB12 is the well location constrained by logging inversion; and LB12 had the smallest relative error. The BP neural network model exhibited relative errors ranging from 0.11% to 1.36%. The BP neural network demonstrated optimal performance with the smallest fluctuation range and maximum relative error performance. The residual analysis of the BP neural network prediction shows a minimum value of −0.05425, a maximum value of 0.03865, and a standard deviation of 0.02714. In comparison, the residual analysis of the well log impedance inversion had a minimum value of −1.0334, a maximum value of 0.17914, and a standard deviation of 0.08415.

To better assess the stability of coal thickness predictions, this study analyzed the error comparisons under different attribute combinations using the BP neural network model as follows:

• Replacing one of the top four optimal attributes with the fifth-ranked attribute, high cross-section, as shown in Figure 14;
• Replacing two of the top four optimal attributes with the fifth and sixth-ranked attributes, high cross-section and maximum energy level, as shown in Figure 15.

In Figure 14 and Figure 15, the x-axis labels “B” represent the original system’s optimized attribute combinations, while other letters denote alternative combinations. “IQR” represents the interquartile range, a commonly used statistical measure to assess data variability. The IQR is the difference between the third quartile (upper quartile) and the first quartile (lower quartile). A range of 1.5 times the IQR is often used to identify outliers. Comparing the relative errors in Figure 13 and Figure 14 revealed the following:

Replacing one attribute led to a significant increase in the maximum relative error in coal thickness prediction, from <10% to <18%; replacing two attributes resulted in an even larger increase in the maximum relative error, exceeding 20%; this increase indicates increased data variability and the potential for outlier errors.

Thus, the optimized combination of attributes significantly influences the final prediction error. It determines the magnitude of prediction errors effectively.

The premise of accurate coal seam thickness prediction is the availability of high-quality data imaging. For this region, the key challenge lies in addressing the significant topographic variation of nearly 300 m. In this paper, we accurately determined the refraction statics correction values for the Green Mountain first-break refraction static correction method, successfully separating the long-wavelength and short-wavelength components. By effectively resolving the severe jumps between neighboring channels using the short-wavelength component, we then calculated the residual statics correction values, as shown in Figure 16 and Figure 17. This approach significantly enhanced the quality of seismic data and laid a solid foundation for the application of two distinct methods.

5. Conclusions

The judicious selection of inversion methods and attribute combinations is essential for enhancing the accuracy of coal seam thickness determination systems. While combining log-constrained impedance inversion offers complementary advantages, its effectiveness is influenced by several factors, including, as follows: geological characteristics; the quantity and distribution of drilling wells; seismic data resolution; and the signal-to-noise ratio. In this context, the seismic multi-attribute method shows greater adaptability, particularly when addressing complex geological conditions. The BP neural network, by adjusting parameters through error feedback, demonstrates robust capabilities in non-linear mapping. Constructing BP neural network models to determine coal thickness through optimized combinations of seismic attributes helps to reduce the ambiguity in seismic interpretation, thereby improving the precision of the results. The accuracy of the applied methods is dependent on the quality and resolution of the available seismic and well-logging data, which could limit their effectiveness in areas where data are sparse or of low quality. Continued research in three-dimensional geological statistics and multi-attribute fusion will pave the way for intelligent, automated mining processes and open new avenues for understanding complex geological environments.