Seismic data have the advantage of wide aerial distribution and deep extent unlike well data that are restricted to the borehole’s location, measuring intervals, and depth. In addition, seismic data are responsible for the structural and stratigraphic features, whereas well logs delineate a much smaller scale of petrophysical properties. Both the methods are beneficial for extending the small-scale petrophysical parameters to large-scale seismic volumes. In seismic data, seismic traces are mainly band limited, whereas the source of the seismic data does not offer the entire band of frequencies required for the desired resolution to be comparable to the well data. Therefore, it is a big challenge to compare well data with a resolution that is several orders greater than the seismic data. The integration of petrophysical parameters and seismic traces helps to predict the lateral distribution of petrophysical properties. However, the traditional prediction methods have their limitations. Therefore, this study used seismic and well logs to predict the shale volume using the proposed model with an artificial neural network. The proposed hybrid model consists of a conventional random vector functional link (RVFL) network and the transient search optimization (TSO) algorithm and is named TSO–RVFL; this model predicts the shale volume of the wells. TSO–RVFL is compared with the standalone RVFL and other two hybrid models. The results of this study validated the successful performance of the artificial neural network for calculating and predicting petrophysical parameters, such as the shale volume. TSO–RVFL outperformed the three other models on different statistical measures