Sonic well logs provide a cost-effective and efficient non-destructive tool for continuous dynamic evaluation of reservoir formations. In the exploration and production of oil and gas reservoirs, these sonic logs contain crucial information about the formation. However, shear sonic logs are not acquired in all oil and gas exploration wells. More so, many offset wells are not run with the most recent sonic logging tools capable of measuring both shear and compressional sonic transit times due to the relatively high costs of running such equipment. And in wells where they are deployed, they are run only over limited intervals of the formation. Such wells lack continuous shear wave transit time measurements along the formation. In this study, an exponential Gaussian process model is presented. The model accurately predicts the shear wave transit times in the formations which lack reliable shear wave transit time measurements. The proposed model is developed using an array of well logs, namely depth, density, porosity, gamma ray, and compressional transit time. A Monte Carlo simulation is used to quantify the proposed model uncertainty. The shear sonic transit time predictions are used to estimate some formation deformation properties, namely Youngs modulus and Poissons ratio of a reservoir formation. The results suggest that shear transit time can be represented and predicted by Gaussian-based process model with RMSE,
R2, and MSE of 11.147, 0.99, and 124.6, respectively. The proposed model provides a reliable and cost-effective tool for oil and gas dynamic formation evaluation. The findings from this study can help for better understanding of shear transit times in formations which do not have multipole sonic logs or where data have been corrupted while logging in the Niger Delta.