## 1 Introduction
Validation of these relationships is crucial to ensure their reliability in seismic hazard assessment--assessing the probability of earthquakes and induced shaking and their potential impact on building infrastructure, or for interpreting near-surface structures, as well as mapping seismic activity in volcanic areas and assessing the stability of faults in oil fields [5; 14; 15; 16; 17]. On the laboratory scale, with regard to seismoacoustic emissions, the recognition of shear and tension signals can be found in [18]. These results can be generalised to issues of mining seismology given that many rock mass tremors are characterised by a shear mechanism, but there are also phenomena in which the explosives component dominates. In seismology, isotropic models such as the preliminary reference earth model (PREM) developed by [PERSON] and [PERSON] [19] are used to describe the earth's seismic velocity properties. These models consider parameters such as P and S velocities, density and attenuation as functions of depth. Isotropic models are important because they provide a complete reference for calculating synthetic seismograms without additional assumptions [20; 21; 22; 23; 24]. Anisotropic models are important for understanding the behavior of seismic waves in different geological structures. Anisotropy refers to the directional variation of physical properties. In seismology, anisotropy can affect the propagation of seismic waves in the Earth's crust. Considering anisotropy in seismology is important for the accurate interpretation of seismic data and improving seismic imaging techniques. This can provide more precise insights into geological structures and the properties of rock formations, as these models can accurately predict the behavior of anisotropic rocks by more accurately predicting the behavior of geomaterials such as rocks and sediments [25; 26; 27; 28; 29]. The models which take into account the directionality of ground vibration attenuation proposed in global seismology, e.g., ref. [5], are often characterized by a relatively large number of parameters. This requires having measurement results from many surface monitoring stations. In the case of observation networks installed by mining plants, as a rule, data on registered ground vibrations is determined by a relatively small number of measuring apparatuses. For this reason, it is necessary to use simpler regression models. With the above assumption in mind, this paper proposes a new method for predicting the distribution of ground vibration accelerations (PGAs) induced by mining activities, taking into account the directionality of vibration attenuation. The results of its application to the description of the field of ground vibration acceleration were compared with the results obtained from the isotropic model [5], which is often used in Poland, and the anisotropic model [9] previously developed by the authors. In this study, the authors analyzed and evaluated the accuracy of predicting the distribution of PGAs induced by mining activities, taking into account three models, including two (No. 2 and No. 3) that take into account the directional nature of vibration attenuation:  
1. The Joyner-Boor, hereafter referred to as the classical model, which assumes isotropic vibration attenuation, the distribution of isolines of predicted ground vibration velocities and accelerations taking the shape of circles;
2. The elliptical model, accounting for anisotropy of vibration attenuation and elliptical isolines [9];
3. The rotational model, accounting for the anisotropy of vibration attenuation without assuming the shape of the isolines of vibration intensity parameters. In our calculations, the variation of the vibration amplification factor was omitted in order to clearly illustrate the effects of anisotropy of vibration attenuation. When considering registrations for a single station, this procedure is justified.