A novel directional-oriented method for predicting shear wave velocity through empirical rock physics relationship using geostatistics analysis

This study attempts to design a novel direction–oriented approach for estimating shear wave velocity (V(S)) through geostatistical methods (GM) using density employing geophysical log data. The research area involves three hydrocarbon wells drilled in carbonate reservoirs that are comprised of oil and water. Firstly, V(S) was estimated using the four selected empirical rock physics relationships (ERR) in well A (target well), and then all results were evaluated by ten statistical benchmarks. All results show that the best ERR is Greenberg and Castagna, with R(2) = 0.8104 and Correlation = 0.90, while Gardner's equation obtained the poorest results with R(2) = 0.6766 and correlation = 0.82. Next, Gardner's method was improved through GM by employing Ordinary Kriging (OKr) in two directions in well A, and then Cross-Validation and Jack-knife methods (JKm and CVm, respectively) were used to assess OKr's performance and efficiency. Initially, CVm and JKm were employed to estimate Vs using the available density and its relationship with shear wave velocity, where the performance of CVm was better with R(2) = 0.8865 and correlation = 0.94. In this step, some points from the original V(S) were used to train the data. Finally, Vs was estimated through JKm and using the relationship between the shear wave velocity of two wells near the target well, including wells B and C; however, in this step, the original shear wave velocity of the target well was completely ignored. Reading the results, JKm could show excellent performance with R(2) = 0.8503 and Corr = 0.922. In contrast to previous studies that used only Correlation and R-squared (R(2)), this study further provides accurate results by employing a wide range of statistical benchmarks to investigate all results. In contrast to traditional empirical rock physics relationships, the developed direction-oriented technique demonstrated improved predicted accuracy and robustness in the investigated carbonate field. This work demonstrates that GM can effectively estimate Vs and has a significant potential to enhance V(S) estimation using density.