Geologic cores are rock samples that are extracted from deep under the ground during the well drilling process. They are used for petroleum reservoirs' performance characterization. Traditionally, physical studies of cores are carried out by the means of manual time-consuming experiments. With the development of deep learning, scientists actively started working on developing machine-learning-based approaches to identify physical properties without any manual experiments. Several previous works used machine learning to determine the porosity and permeability of the rocks, but either method was inaccurate or computationally expensive. We are proposing to use self-supervised pretraining of the very small CNN-transformer-based model to predict the physical properties of the rocks with high accuracy in a time-efficient manner. We show that this technique prevents overfitting even for extremely small datasets. Github: https://github.com/Shahbozjon/porosity-and-permeability-prediction