## 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.