Identification and Application of Wave Field Characteristics of Channel Waves in Extra-Thick Coal Seams

Abstract

Channel wave seismic activity often occurs with thin and medium-thick coal seams being the main target layer. To address the problem of channel wave applicability detection in extremely thick coal seams, the propagation and identification characteristics of channel waves remain the focus of research. Therefore, this paper takes the in-seam wave exploration of a 27 m extremely thick coal seam as an example and uses the staggered mesh finite difference method to construct a three-dimensional medium model for numerical simulation. An analysis of the physical parameters of coal and rock, along with the dispersion characteristics of channel waves in extra-thick coal seams, is utilized, through the Zoeppritz equation and the total reflection propagation method, to calculate the imaging. We found the following: (1) The dispersion areas and weak dispersion areas along the detection direction are extremely thick coal seams. (2) There are apparent channel waves in extra-thick coal seams, with a waveform similar to body waves; the length of the wave train is shorter than that of the conventional channel wave, and the arrival time can be estimated accurately. The amplitude of the apparent channel wave is affected by the degree of dispersion, with lower attenuation and higher resolution. The characteristic of total reflection in extremely thick coal seams is that the incident angle is equal to the critical angle, and the dispersion characteristics are weak. (3) The channel waves with weak dispersion characteristics in extra-thick coal seams are mainly Love-type waves.

1. Introduction

Deposited in an environment under a unique set of geological coal-forming conditions, extra-thick coal seams have become a prominent focus of mining Mesozoic coal accumulations in Northwest China [1]. Specifically, extra-thick coal seams play a crucial role in raising the productivity and efficiency of coal mining. Among the many methods for exploring coal seams and detecting discontinuities, channel wave seismic spectroscopy has unique advantages [2,3] and has thus become a trending research topic in recent years. Channel waves are defined as guided waves that are excited within coal seams, with manifest dispersion characteristics [4,5] that reduce the resolution of identifying structures. However, because of its superb detection ability and slower rate of energy decay [6,7,8], this technique is an invaluable tool for mine exploration.

To date, most of the research on channel waves has been limited to thin and moderately thick coal seams [9,10,11]. Theoretically, channel wave seismic data are suitable only for the above coal seams, but the variation in coal thickness is an important factor affecting the dispersion of Love-type channel waves [12,13,14]. According to the theoretical dispersion curve, the main frequency decreases with increasing coal thickness, and at the same frequency, the channel wave velocity decreases with increasing coal seam thickness [15,16,17]. For extra-thick coal seams, the foremost step is to discuss the adaptability of channel waves for detection [18,19,20]. However, there are relatively few studies on the adaptation of channel waves under these special geological conditions. Currently, most coal seam exploration methods rely on surface-based three-dimensional seismic surveys and drilling. While both of these methods can investigate the geological structures within a working face, they are limited by their detection range and spatial resolution, which constrains their interpretation accuracy. Additionally, these methods are highly affected by surface environmental conditions, making it difficult to perform effective stratigraphic calibration in areas with low exploration coverage. This can lead to the omission of small structures during inversion. Seismic surface wave methods, particularly channel waves, effectively address this limitation. However, for extremely thick coal seams, the excitation and reception of channel waves cannot be arranged according to the conventional methods used for medium and thin coal seams. Instead, the observation system must be arranged according to the actual mining conditions. Similarly, under the conditions of extremely thick coal seams, the dispersion characteristics and propagation paths of channel waves are the central issues addressed in this study.

To study the propagation characteristics of seismic wavefields and their identifying features in extra-thick coal seams, numerical simulation methods are used for their characterization. At present, the main numerical simulation methods include the numerical equation method [21,22], the integral equation method [23,24,25], and the ray-tracing method [26]. This paper adopts the staggered-grid finite-difference numerical equation method because the staggered grid division is unrestricted by the geometric distributions of media and boundaries [27]. In addition, it is easy to add prior information, and the model has a high discretization resolution and low computational cost. The finite-difference seismic simulation method is based on a regular grid in a Cartesian coordinate system. When simulating complex geological structures and the intricate interfaces of geological bodies, curved boundaries inevitably arise. These curved boundaries can introduce artificial diffraction waves, which are not physically accurate. To mitigate these artificial diffractions, finer grids must be employed. However, this not only results in increased storage requirements and computational load but, more importantly, it can also lead to significant accumulation of errors.

In this paper, by constructing a three-dimensional model with isotropic media and taking the actual coal thickness as a constraint, a high-order staggered-grid finite difference method is applied to the forward modeling of a channel wavefield within an extra-thick coal seam. We discovered an area in the extra-thick coal seam within which channel waves exhibit weak dispersion and total reflection characteristics as the propagation and identifying channel waves. Then, when the incident angle is equal to the critical angle, the velocity is equal to the shear wave velocity of the coal seam, which is calculated by Snell’s law and the Zoeppritz equations, and the velocity represents the “normal model” of the first part of the channel wave. Finally, the weak dispersion characteristics of channel waves are utilized to calculate and image the result with an error of only 5 m, which is of practical significance for the high-resolution identification of extra-thick coal seams.

2. Numerical Simulation

To explain the propagation and identifying characteristics of channel waves in extra-thick coal seams, a three-component wavefield is numerically simulated in a 3D model composed of horizontally layered isotropic media using perfectly matched layers (PMLs) to absorb boundary reflections [22,28]. Figure 1 illustrates the schematic of the 3D staggered-grid method. To handle the different physical quantities (such as velocity and stress) and their coupling relationships in the wave equation efficiently, the staggered-grid method is utilized to enhance the convergence velocity and local accuracy of numerical simulations effectively.

The explicit finite-difference numerical solution uses an approximation for the time derivatives, so it must meet stability conditions to ensure that the forward simulation proceeds smoothly. To ensure forward stability, the time step $\mathsf{\Delta }t$ must satisfy Equation (1):

$$\mathsf{\Delta }t\le {\displaystyle \frac{\mathsf{\Delta }h}{\sqrt{3}{V}_{P\max }}}{\left|{\displaystyle \sum _{i=1}^N{a}_i}\right|}^{-1},$$

(1)

where $\mathsf{\Delta }t$ represents the time step, $\mathsf{\Delta }h$ is the spatial step size, $a_i$ is the Courant number, and $V_{P\max }$ is the maximum P-wave velocity in the model parameters.

To ensure stability and avoid grid dispersion phenomena, both the spatial step size and the time step must adhere to certain constraints. The maximum spatial discretization step size is determined by the minimum velocity in the model parameters, while the maximum time step is determined by the maximum velocity in the model.

2.1. Extra-Thick Coal Seam Model

The dimensions (x*y*z) of the 3D model are 300 × 500 × 75 m, where the corresponding grid spacing (dx, dy, and dz) are all 1 m. To balance high-resolution imaging and computational accuracy in finite-difference simulations, the main frequency of the source (which excites a P-wave) is 150 Hz, and the sampling rate is dt = 0.01 ms. A schematic of the three-layer coal seam model is shown in Figure 2a. In the z-direction, the roof layer is at depths of 0–25 m, the middle layer is the coal seam at 25–50 m, and the floor layer is at 50–75 m. Running along with the bottom interface of the middle layer and separated by a distance of 250 m, the dimensions of each roadway are 4 × 500 × 4 m. The receiver line is on roadway 1 (x-direction is 276–280 m; y-direction is 0–500 m; z-direction is 46–50 m). For a comparison of the homogeneous coal seam with a heterogeneous feature, a collapsed column with a design radius R of 25 m is placed in the middle of another (otherwise identical) model, as shown in Figure 2b. The source coordinates are 26, 250, and 49 m, and the sampling time is 350 ms. The parameters of the isotropic media (and collapse column) within the model are shown in

Table 1. Parameters of the model strata and collapse column.

Layer	Thickness/Radius R/(m)	P/(m·s−1)	S/(m·s−1)	ρ/(kg·m−3)
Roof	25	4200	2300	2650
Coal seam	25	2200	1400	1450
Floor	25	4200	2300	2650
Collapse column	25	3600	2000	2200

. Considering that typical coal-bearing strata are characterized by a layered structure, the coal seam and its roof and floor can be approximately regarded as horizontally stratified, isotropic media. The values in Table 1 fall within the reasonable range of the physical properties for coal and rock and have been adjusted based on the velocity measurements detected at the actual working face.

2.2. Wavefield Characteristics Analysis

In the three-layer isotropic coal seam model, after the source is excited, three-dimensional snapshots of the x, y, and z wavefield components at different times in the x–z plane at y = 250 m are displayed in (Figure 3, Figure 4 and Figure 5). Figure 3 shows snapshots of the x wavefield component in the model at 20, 40, 60, and 80 ms. Compared with the P- and S-waves propagating through the surrounding rock, the channel waves have relatively longer wavelengths, lower velocities, and higher energy. From these snapshots of the wavefield, for the dispersion region at 20 ms, at the initial stage of source excitation, the P-waves, S-waves, and converted waves are superimposed on each other, and multiple groups of these waves interfere constructively (as shown in Figure 3a). The phase interference is weakened. As the propagation distance increases, the wave front of critically refracted waves is indicated by lines perpendicular to the interfaces. Over time, the total reflection characteristics at the critical angle become increasingly apparent (Figure 3b–d). As the propagation distance increases, the wave group interval between phases changes, and the roof, floor, and coal seam layers display the total reflection feature in the coal seam. The wave group propagation path is clear, the interfaces separating layers at z = 25 m and z = 50 m are distinguishable, and the wavefront of the channel wave experiences total reflection at the critical angle, which serves as an identifying feature for extra-thick coal seams.

Comparing the x, y, and z components, we find that the energy confined to the coal seam of the z component is more than other components. The critical angle total reflection is the most obvious in the weak dispersion region, and the characteristics of other coal seams are different. As seen in the wavefield snapshot at 80 ms, the phases of the x and y components have good sym7metry with the critical angle (Figure 3d and Figure 4a), the propagation characteristics of the z component are consistent with those of the x and y components, and the energy of the z component seems to be concentrated in the coal seam, in which the amplitude is relatively strong, the vertical interference of wave phases is obvious, and the occurrence of total reflection is prominent (Figure 4b).

Next, the wavefield snapshots in the models with and without a collapsed column to be compared (Figure 3d) show that the waves reflect from the collapsed column (Figure 5). This suggests that the formation of a collapse column in a coal seam changes the coal seam waveguide properties and the formation conditions of channel waves.

2.3. Calculating the Critical Angle and Petrophysical Parameters

We can determine from Snell’s quantification in Equation (2) that the incident angle must be greater than or equal to the critical angle for total reflection to occur. There is a weak dispersion region in which the incident angle is equal to the critical angle; thus, total reflection occurs throughout the entire propagation process with a uniform amplitude. Combining the Zoeppritz Equations (3) and (4) with the parameters of the strata in Table 1 can reveal the relationship between the energy distribution of seismic waves on the elastic interface, and the relationship between the reflection coefficient and the incident angle can be calculated:

$${\displaystyle \frac{1}{V_x}}={\displaystyle \frac{\sin {\alpha }_1}{V_{P1}}}={\displaystyle \frac{\sin {\beta }_1}{V_{S1}}}={\displaystyle \frac{\sin {\alpha }_2}{V_{P2}}}={\displaystyle \frac{\sin {\beta }_2}{V_{S2}}},$$

(2)

$$\left[\begin{array}{cccc}-\sin {\alpha }_1& -\cos {\beta }_1& \sin {\alpha }_2& -\cos {\beta }_2\\ \cos {\alpha }_1& -\sin {\beta }_1& \cos {\alpha }_2& \sin {\beta }_2\\ \sin 2{\alpha }_1& {\displaystyle \frac{V_{P1}}{V_{S1}}}\cos 2{\beta }_1& {\displaystyle \frac{{\rho }_2{V}_{S2}^2{V}_{P1}}{{\rho }_1{V}_{S1}^2{V}_{P2}}}\sin 2{\alpha }_2& -{\displaystyle \frac{{\rho }_2{V}_{P1}{V}_{S2}}{{\rho }_1{V}_{S1}^2}}\cos 2{\beta }_2\\ -\cos 2{\beta }_1& {\displaystyle \frac{V_{S1}}{V_{P1}}}\sin 2{\beta }_1& {\displaystyle \frac{{\rho }_2{V}_{P2}}{{\rho }_1{V}_{P1}}}\cos 2{\beta }_2& {\displaystyle \frac{{\rho }_2{V}_{S2}}{{\rho }_1{V}_{p1}}}\sin 2{\beta }_2\end{array}\right]\left[\begin{array}{c}{R}_P\\ R_{SV}\\ T_P\\ T_{SV}\end{array}\right]=\left[\begin{array}{c}\sin a_1\\ \cos a_1\\ \sin 2a_1\\ \cos 2{\beta }_1\end{array}\right],$$

(3)

where the P-wave incident angle and reflection angle are both ${\alpha }_1$; the P-wave refraction angle is ${\beta }_1$; the P-wave transmission angle is ${\alpha }_2$; the P-wave critical refraction angle is ${\beta }_2$; the P-wave velocity in the coal seam is $V_{P1}$; the P-wave velocity in the surrounding rock is $V_{P2}$; the S-wave velocity in the coal seam is $V_{S1}$; the S-wave velocity in the surrounding rock is $V_{S2}$; $T_P$ and $R_P$ are the P-wave transmission coefficient and reflection coefficient, respectively, indicating the amplitude ratios of the transmitted P-wave and the reflected P-wave to the incident P-wave, respectively; and $T_{SV}$ and $R_{SV}$ are the S-wave transmission coefficient and reflection coefficient, respectively, indicating the amplitude ratios of the transmitted S-wave and reflected S-wave to the incident S-wave.

$$\left[\begin{array}{cc}-1& 1\\ V_{s1}\cos \alpha & {\displaystyle \frac{{\rho }_2}{{\rho }_1}}{V}_{S2}\cos \beta \end{array}\right]\left[\begin{array}{c}{R}_{SH}\\ T_{SH}\end{array}\right]=\left[\begin{array}{c}1\\ V_{s1}\cos \alpha \end{array}\right]$$

(4)

In Equation (4), $R_{SH}$ and $T_{SH}$ are the SH-wave reflection and transmission coefficients, respectively; $\alpha$ and $\beta$ are the SH-wave reflection and transmission angles, respectively; ${\rho }_1$ and ${\rho }_2$ are the densities of the coal seam and surrounding rock, respectively; and $V_{S1}$ and $V_{S2}$ are the S-wave velocities of the coal seam and surrounding rock, respectively. Combining Equations (3) and (4), we can obtain the following:

$$R_{SH}={\displaystyle \frac{{\rho }_1{V}_{S1}\cos \alpha -{\rho }_2{V}_{S2}\cos \beta }{{\rho }_1{V}_{S1}\cos \alpha +{\rho }_2{V}_{S2}\cos \beta }}.$$

(5)

The relationships of the P- and S-wave reflection coefficients with the incident angle are shown in Figure 6. When it does not reach the critical angle, most of the reflected energy is released. When the incident SH-wave reaches the critical angle, the energy increases to the maximum and remains constant with an increase in the angle. This corresponds to the leakage mode and normal mode of channel wave propagation in the process of wave field propagation. In contrast, the P-wave energy is also highest when the incident angle is the critical angle of refraction, but the energy weakens as the angle decreases below or increases above the critical angle, causing the intensities of transmission and reflection to decay rapidly.

According to the channel wave propagation mode, we ascertain the time propagation difference between the refracted channel wave and the wave experiencing total reflection (Figure 7). However, under the condition of an extra-thick coal seam, this paper discusses only the case where the incident angle of Love-type waves is equal to the critical angle. According to Snell’s law, the SH-wave first experiences total reflection when the incident angle initially exceeds the critical angle. The corresponding formulae are shown in Equations (6)–(8).

The total reflection of a Love-type channel wave in the coal seam along the entire path is expressed as in Equation (6):

$$L={\displaystyle \frac{d}{\sin \theta }}\mathrm{m},$$

(6)

where d is the direct detection distance, L is the length of the total path for critical angle reflection signals, and $\theta$ is the critical angle.

The critical angle is calculated in Equation (7):

$$\sin \theta ={\displaystyle \frac{V_{S1}}{V_{S2}}}.$$

(7)

When $\theta$ is equal to the critical angle, the phase velocity is equal to V_S2 and the group velocity is equal to V_S1. The time propagation difference between the refracted channel wave and the wave experiencing total reflection is given by Equation (8):

$$\mathsf{\Delta }{t}_1={\displaystyle \frac{d}{V_{s1}}}-{\displaystyle \frac{d}{V_{s2}}}={\displaystyle \frac{d}{V_{s1}}}-{\displaystyle \frac{d\sin \theta }{V_{S1}}}={\displaystyle \frac{\sin \theta (L-d)}{V_{S1}}}.$$

(8)

3. Real Date

3.1. Geology and Design

To examine the existence, propagation, and identifying characteristics of apparent channel waves in extra-thick coal seams, we take the actual exploration of the 61,202 working face of a coal mine in Inner Mongolia as an example. The width of the working face is 240 m, the coal thickness varies from 24.05 to 35.95 m with an average of 27.71 m, and the 6# coal depth ranges from 335 to 380 m with an average of 355 m. The coal is anthracite located in the upper part of the Taiyuan Formation, and the dip angle of the coal seam is 2.5° on average. The top and bottom layers are composed of siltstone, sandy mudstone, and clay. The observation system is arranged as shown in Figure 8. The shots are spaced 10 m apart along the lower roadway in Figure 8 (red five-pointed stars), while the receivers (two-component detectors) are also spaced 10 m apart along the upper roadway (blue arrows). Each source is excited by the detonation of 300 g of dynamite, and the shot and receiver lines are both 850 m long. We use an XY two-component geophone for data acquisition, with the natural frequency of the geophone being 28–2000 Hz, the sampling length being 800 ms, and the sampling rate being 0.25 ms.

3.2. Data Analysis

Shot 1 is taken as an example and is effectively received by 50 two-component receivers. Four groups of waves are evident in the seismic records, as shown in Figure 9 (listed in order from top to bottom). The record shows that after the refracted direct P-wave and S-wave arrive, two waves arrive at different times on the x and y components, indicating that both can carry the complete channel wave information of the extra-thick coal seam, which is a distinctive characteristic, different from thin and moderately thick coal seams.

The first and second waves to arrive are the refracted P- and S-waves, respectively, whose calculated velocities are 4200 m/s and 2300 m/s. The velocity of the third wave group is 1100 m/s, and that of the fourth and last wave group is 900 m/s. The amplitude characteristics of the third wave group on the y component are more obvious than those on the x component, the overall continuity of the third wave group is relatively good, and extra-thick coal seams highlight the total reflection propagation characteristics. The actual data are consistent with the characteristics of the wavefield snapshot in the area of the weak dispersion area. The third wave with the velocity is stable, and the fourth wave group is the channel wave, indicating that both can carry the complete channel wave information of the extra-thick coal seam, which is a distinctive characteristic different from thin and moderately thick coal seams.

The propagation characteristics of channel waves can also be studied by dispersion analysis. We compare the shot seismic record with the dispersion curve of channel waves (Figure 10) and take the x and y components of the 33rd channel of shot 1 as an example. The left panel in Figure 10 shows the single-channel data and an enlarged view of the record, where the vertical axis represents the travel time, and the horizontal axis is the amplitude value. The abscissa of the dispersion curve is the frequency, and the ordinate is the velocity (time scale). The velocity value is stable, and the velocity corresponding to the propagation of the channel wave is consistent with that of the single-shot seismic record.

We find that two wave groups (Figure 10a) appear at 360 ms and 430–480 ms on the time axis, which is similar to the general times when the channel waves appear, and the time–frequency characteristics are consistent with those of the dispersion curve. In the first wave group in the red box, the amplitudes of the x and y components are obvious, and the y component has a stronger amplitude than the x component. The waves characterized by a short duration, a shape similar to a body wave, and weak dispersion characteristics are defined herein as apparent channel waves, and their velocity value is equal to the shear wave velocity of the coal seam.

In the second wave group in the red box, the x component displays many phases, a long duration, and relatively obvious dispersion characteristics, which are in line with the characteristics of channel waves (Figure 10b).

From the characteristics of the dispersion curves, we discover that the corresponding velocities of the first wave group in the red box are stable with increasing propagation distance, and the frequency and energy are constant, all of which are consistent with the characteristics of the weak dispersion region in the wavefield snapshot.

4. Results and Discussion

4.1. Results

The total reflection characteristics of apparent channel waves are analyzed by calculating the critical angle. Taking the y component of the 33rd channel of shot 1 as an example, the wave was recorded at 360 ms at a distance of 400 m. The velocity was calculated as 1100 m/s when the incident angle was equal to the critical angle. The refracted direct S-wave is 2300 m/s, corresponding to a time of 180 ms. According to Equation (8), the time difference between the arrival of the refracted direct S-wave and that of the apparent channel waves is 184 ms. When the incident angle is equal to the critical angle, the propagation of channel waves exhibits total reflection, with a phase velocity of 2300 m/s, which is equal to the refracted direct S-wave.

Next, we employ the apparent channel wave velocity for imaging (Figure 11), in which the pink semicircular area along the upper roadway represents a collapse column. Analyzing the lower roadway reveals a fault or fissure zone that extends into the working face and intersects the lower roadway at a large angle. The error range of the imaging is less than 5 m, and the results are geologically verified.

4.2. Discussion

The propagation characteristics of channel waves in extra-thick coal seams were discovered through wavefield forward modeling and actual data application, which conform to the propagation laws of channel waves. According to Zoeppritz and Snell’s equations, it is determined that the extra-thick coal seam is mainly a Love-type channel wave. We demonstrated suitable detection to extra-thick coal seams, with areas of strong dispersion and weak dispersion along the detection direction of the extra-thick coal seam. When the source is excited, the Love-type channel wavefront propagates as follows, where the incident angles of SH-waves are equal to the critical angle; SH-waves are both totally reflected and critically refracted, which forms an interference system referred to as the “normal mode” range of Love-type channel waves within the extra-thick coal seam; and no energy escapes into either adjacent half-space. Where the angles of the incident SH-waves are less than the critical angle, there is a rapid decrease in energy.

In the estimation of velocity and critical angle, potential sources of error and uncertainty, aside from data quality, data processing, inversion, and factors related to instrument reception, primarily stem from discrepancies between the model assumptions and the actual coal thickness and coal seam velocity. These discrepancies significantly affect phase velocity, leading to deviations from the true values. According to Snell’s Law, the critical angle can be directly calculated using the information from the shear waves in the coal seam and the roof and floor. Numerical simulations show that at the critical angle, the corresponding phase velocity exhibits weak dispersion, while medium-to-thick coal seams demonstrate more pronounced dispersion characteristics. In scenarios where the coal seam thickness varies significantly at the working face, wave analysis may not be the most suitable method, as large variations in coal thickness can lead to fractures in the roof and floor. This irregularity may distort wave propagation, resulting in inaccurate velocity estimations. However, using critical angle estimation can be more effective in helping to plan mining routes with greater precision, enhance safety protocols, and optimize resource extraction.

The main energy of the apparent channel wave propagates in the coal seam, and the characteristics conform to the above definition of a channel wave. Due to the extra-thick coal seam, the seismic event is distinct in the raw recording, the first arrival is identifiable, and the frequency is stable. The apparent channel wave velocity represents the first part of the channel wave in the seam and is consistent with the wavefront velocity, which can be picked up accurately with minor errors. All the conditions provide theoretical support for the accurate exploration of extra-thick coal seams.

5. Conclusions

In this paper, the propagation characteristics of channel waves are theoretically clarified by studying a regional extra-thick coal seam. We reveal that channel waves are suitable for detecting extra-thick coal seams, and propagation is mainly as Love-type channel waves. The numerical simulation results show areas of dispersion and weak dispersion along the detection direction of the extra-thick coal seam. When the incidence angle is equal to the critical angle, the apparent channel wave total reflection is visible in the weak dispersion area. The area in the dispersion is similar to those in relatively thin coal seams. Different wave groups are easy to identify, and the apparent channel wave velocity can be estimated accurately via the arrival time, which plays a key role in the high-resolution imaging of extra-thick coal seams. This study provides a better interpretation of the propagation characteristics of channel waves in coal seams. Based on these characteristics, it is believed that with specialized processing and interpretation methods, valuable information can be obtained in medium-thick coal seams as well. This will be the focus of future research.