The mechanical and petrophysical behavior of organic-rich carbonates (ORC) is affected significantly by burial diagenesis and the thermal maturation of their organic matter. Therefore, establishing Rock Physics (RP) relations and appropriate models can be valuable in delineating the spatial distribution of key rock properties such as the total organic carbon (TOC), porosity, water saturation, and thermal maturity in the petroleum system. These key rock properties are of most importance to evaluate during hydrocarbon exploration and production operations when establishing a detailed subsurface model is critical. High-resolution reservoir models are typically based on the inversion of seismic data to calculate the seismic layer properties such as P- and S-wave impedances (or velocities), density, Poisson's ratio, Vp/Vs ratio, etc. If velocity anisotropy data are also available, then another layer of data can be used as input for the subsurface model leading to a better understanding of the geological section. The challenge is to establish reliable geostatistical relations between these seismic layer measurements and petrophysical/geomechanical properties using well logs and laboratory measurements. In this study, we developed RP models to predict the organic richness (TOC of 1-15 wt%), porosity (7-35 %), water saturation, and thermal maturity (Tmax of 420-435°C) of the organic-rich carbonate sections using well logs and laboratory core measurements derived from the Ness 5 well drilled in the Golan Basin (950-1350 m). The RP models are based primarily on the modified lower Hashin-Shtrikman bounds (MLHS) and Gassmann's fluid substitution equations. These organic-rich carbonate sections are unique in their relatively low burial diagenetic stage characterized by a wide range of porosity which decreases with depth, and thermal maturation which increases with depth (from immature up to the oil window). As confirmation of the method, the levels of organic content and maturity were confirmed using Rock-Eval pyrolysis data. Following the RP analysis, horizontal (HTI) and vertical (VTI) S-wave velocity anisotropy were analyzed using cross-dipole shear well logs (based on Stoneley waves response). It was found that anisotropy, in addition to the RP analysis, can assist in delineating the organic-rich sections, microfractures, and changes in gas saturation due to thermal maturation. Specifically, increasing thermal maturation enhances VTI and azimuthal HTI S-wave velocity anisotropies, in the ductile and brittle sections, respectively. The observed relationships are quite robust based on the high-quality laboratory and log data. However, our conclusions may be limited to the early stages of maturation and burial diagenesis, as at higher maturation and diagenesis the changes in physical properties can vary significantly.