Geophysical logging plays a very important role in reservoir evaluation. In the actual production process, some logging data are often missing due to well wall collapse and instrument failure. Therefore, this paper proposes a logging reconstruction method based on improved sand cat swarm optimization (ISCSO) and a temporal convolutional network (TCN) and bidirectional gated recurrent unit network with attention mechanism (BiGRU-AM). The ISCSO-TCN-BiGRU-AM can process both past and future states efficiently, thereby extracting valuable deterioration information from logging data. Firstly, the sand cat swarm optimization (SCSO) improved by the variable spiral strategy and sparrow warning mechanism is introduced. Secondly, the ISCSO’s performance is evaluated using the CEC–2022 functions and the Wilcoxon test, and the findings demonstrate that the ISCSO outperforms the rival algorithms. Finally, the logging reconstruction method based on the ISCSO-TCN-BiGRU-AM is obtained. The results are compared with the competing models, including the back propagation neural network (BPNN), GRU, and BiGRU-AM. The results show that the ISCSO-TCN-BiGRU-AM has the best performance, which verifies its high accuracy and feasibility for the missing logging reconstruction.