## 1 Introduction  
Seismic velocities, including P-wave velocity (V\({}_{\rm P}\)) and S-wave data (V\({}_{\rm S}\)), play a vital role in subsurface studies. For example, geomechanical modeling or rock physical studies requires the V\({}_{\rm S}\) parameter to be estimated as a decisive parameter. Reservoir characterization is one of the most important parts of surveys in oil industry, and research on the V\({}_{\rm S}\) parameter can greatly help to investigate the precise reservoir characterization. Lithofacies and fluids' properties are two significant and useful parameters in hydrocarbon reservoir monitoring. Previous studies have shown that shear wave velocity can help determine such parameters [1; 2; 3; 4]. Besides, the V\({}_{\rm S}\)' porosity relationship can be helpful in assessingthe sorting and volume of cementation, especially for sandstone reservoirs. In surface geophysical investigations, the V\({}_{\text{S}}\) determines the size and geometry of the subsurface structures. Therefore, measuring the V\({}_{\text{S}}\) is essential, and several methods have been introduced to estimate this parameter. Two main methods for measuring V\({}_{\text{S}}\) are reported as direct and indirect methods, each having advantages and drawbacks. The laboratory methods directly measure the shear wave velocity by coring samples [5]. Moreover, a well-logging instrument outlines the Dipole Sonic Imager (DSI) tool, known as one of the most common ways of measuring S-wave velocity. Unfortunately, the V\({}_{\text{S}}\) cannot be measured using coring and well-logging operations, due to a number of problems, as follows: first, in the horizontal and deviation wells and in weak formations (e.g., sandstone formation), obtaining core samples in some of the oil and gas fields is impossible. Secondly, well-logging operating is not applicable in the same situation. Thirdly, these methods are expensive and time-consuming. Lastly, the measurement of shear wave velocity may not be recorded at certain depths, or the recorded sections may include erroneous values. Consequently, this leads to different indirect methods to be presented to address these problems. Verifying the empirical rock physical relationship is one of the indirect approaches and the number of the relevant studies has increased [6; 7; 8; 9; 10; 11; 12]. [PERSON] et al. introduced a shear-wave velocity prediction method that considered the relationship between shear wave velocity and other parameters, such as P-wave velocity (V\({}_{\text{P}}\)) and density in sedimentary rocks [13]. A P-wave is a compressional wave and is one of the two main types of elastic body waves, called seismic waves in seismology. These waves are also primary waves because they are the first waves to be recorded by seismographs and devices. This type of wave is used in subsurface studies to detect the rock, fluid, pressure, and overpressure. [PERSON] et al. employed correlations and artificial intelligence methods to estimate a shear wave velocity from the petrophysical logs in a well drilled in carbonate formation [14]. The relationships provided by these methods were usually specific to the area or formation, and the shear wave velocity could be estimated by localizing their coefficients in some cases. Geostatistical analysis, to which more attention has yet to be paid, can be useful to estimate the V\({}_{\text{S}}\). This method establishes a spatial correlation between the variables, normalizes the database, and modifies the estimation equations [15]. Thanks to immanance advances in science and technology, Artificial Intelligent (AI) techniques have been used to estimate V\({}_{\text{S}}\). Recently, ML methods have become popular and been widely used, because they are inexpensive, fast track, and practical without restrictions concerning the horizontal or deviation position of the wells [16].