Geophysical logging is an essential measurement tool in the oil/gas exploration and development field. In practice, predicting missing well logs is an effective way to reduce the exploration expenses. Because of the complexity and heterogeneity of the reservoir, there must be strong nonlinear correlations between the well logs. To improve the accuracy and stability of the missing well logs prediction, a method based on a Bayesian optimized hybrid kernel extreme learning machine (BO-HKELM) algorithm is proposed. Firstly, the LightGBM algorithm is applied to screen out important features related to the missing well logs and reduce the input dimension of the prediction model. Secondly, the hybrid kernel extreme learning machine (HKELM) algorithm is applied to construct the missing well logs prediction model, and the hyperparameters $(C_0,C_1,d,\sigma ,C)$ of the model are optimized by the Bayesian algorithm. Finally, the BO-HKELM model is applied to the prediction of the missing well logs in a block of the Ordos Basin in China. The results show that the RMSE, MAE, and R-square predicted by the BO-HKELM model are 0.0767, 0.0613, and 0.9029, respectively. It can be found that the BO-HKELM model has better regression accuracy and generalization ability, and can estimate missing logs more accurately than the traditional machine learning methods, which provides a promised method for missing well logs estimation.

In the geophysical exploration field, the sonic log (DT) and shear sonic log (DTS) are frequently used as quick and affordable procedures for reservoir evaluation. Due to the high acquisition costs, DTS is only accessible in a few wells within an oil/gas field. Numerous attempts have been made to establish a precise relationship between DTS and other petrophysical data. In this study, a method based on the deep extreme learning machine optimized by the improved sparrow search algorithm (ISSA-DELM) is proposed to improve the accuracy and stability of the DTS prediction. Firstly, the deep extreme learning machine (DELM) model is constructed by combining the extreme learning machine and the autoencoder algorithm. Secondly, aimed at the defects of the sparrow search algorithm (SSA), an improved sparrow search algorithm (ISSA) with the firefly search disturbance is proposed by merging the iterative strategy of the firefly algorithm and applied to optimize the initial input weights of the DELM. Finally, the ISSA-DELM is applied to the prediction of the DTS in a block of the Ordos Basin in China. The quantitative prediction results show that the RMSE, MAE, and R-square predicted by the ISSA-DELM model are 6.1255, 4.1369, and 0.9916, respectively. The comprehensive performance is better than the ELM, the DELM, and the DELM optimized by the optimization algorithms, such as the genetic algorithm (GA), the particle swarm optimization (PSO), and the SSA. Therefore, it can be concluded that the method provides an effective method for missing DTS estimation.