## 1 Introduction  
The instability of energy prices and the difficult geopolitical situation in central Europe are forcing the development of solutions to balance the energy market. Despite the fact that in recent decades many mining plants have been closed down, which is related to the process of restructuring the industry's enterprises and the country's energy transition, hard coal in Poland is still its main energy resource. The process of intensification of mining, which is part of the restructuring and urgency of mining companies, is accompanied by serious difficulties related to, among other things, the need to protect the surface from the possible effects of increased mining. The need to reach deeper and deeper coal seams, and the concentration of mining fronts in a relatively small area, often generate seismic phenomena that can be dangerous to surface infrastructure facilities and cause concern for the populations living in areas affected by these phenomena. Ground vibrations, which are induced by technological processes in mines where blasting is used to extract rock, are also a significant problem [1]. Despite the fact that entrepreneurs conducting mining works under conditions of rockburst hazards are obliged to conduct studies in the field of engineering geophysics, including measurement, interpretation and evaluation of the impact of tremors on surface facilities, for technical reasons it is difficult to monitor vibrations at all points affected by mining activities [2]. For this reason, mine geophysics stations are expanding their seismological networks, which, on the one hand, makes it possible to more precisely determine the distribution of vibrations on the surface, but on the other hand, significantly increases the company's operating costs, associated mainly with the need to maintain the measurement apparatus. Therefore, it becomes expedient to look for solutions that provide greater accuracy in predicting the distribution of ground vibration parameters and do not generate higher costs associated with the maintenance of additional measurement apparatuses. In seismology, attenuation relations that do not take into account the directionality of vibrations are generally used. Many examples of different forms of these dependencies can be found in the literature [3; 4; 5; 6]. For mining problems in Poland, the model proposed in [4] is usually used. Frequently, after the occurrence of vibrations generated by rock mass tremors, large differences in the magnitude of observed accelerations and velocities of vibrations at points located at similar epicentral distances are observed. This phenomenon cannot always be explained by changes in the value of the vibrations' amplification coefficient. Similar observations are found in global seismology [7]. This may be evidence of the directional nature of the attenuation of ground vibrations caused by tremors. Some interesting conclusions taking into account the directionality of ground vibration attenuation can be found in the following works [7; 8; 9]. Relations describing the directionality of elastic wave attenuation are successfully used for probabilistic seismic hazard assessment (PSHA) [10; 11]. The above-mentioned relationships make it possible to estimate the decrease in ground shaking intensity with distance from the earthquake source [12]. By providing information on how the amplitude of seismic waves decreases with distance, they can be used to estimate parameters such as equivalent peak acceleration (EPA) in specific areas, peak ground velocity (PGV) and peak ground acceleration (PGA). By accounting for uncertainties associated with various parameters such as ground acceleration velocity and distance from the measurement site to the tremor source, these relationships provide more accurate estimates of the mean and variance of ground attenuation [13].