## 1 Introduction  
In oil/gas exploration, geophysical logging is an effective way of analyzing and describing the subsurface conditions by using physical measurements. The primary measuring items are the electrochemical, acoustic, radioactive, and other geophysical features of the rock formation. In reservoir evaluation, the lithology, physical property, and oil-gas bearing properties of the reservoir can be comprehensively evaluated by using the results of logging data analysis and interpretation. It is essential to merge the various logs and seismic data in order to efficiently develop a reservoir model and decrease the fuzziness of geological interpretation. However, when the logging instrument is faulty, the borehole wall is damaged and collapses occur, which will lead to the loss of logging curves in the working area [1].  
It is of great significance to use the logging curves of known intervals to supplement the missing logging curves for subsequent reservoir prediction. Therefore, numerous studies have been carried out in an effort to identify the non-linear correlations between various well logs. According to the investigation, the most frequently used approaches include the empirical model [2; 3], the multi-variable linear regression model [4; 5] and the traditional machine learning model [6; 7]. The empirical model can result in the major deviations because of the strong nonlinear relationship between the reservoir characteristics and missing well logs. The multi-variable linear regression model has the disadvantage of inadequate equation expression. The traditional machine learning model has issues with over-fitting or being trapped in local optimums, as well as the need for sufficient and compact training sample sets [8; 9; 10]. Therefore, a missing well logs prediction model with excellent computation speed, prediction accuracy and generalization ability is urgently needed.  
The extreme learning machine (ELM) is a single hidden layer feedforward neural network with the characteristics of a simple structure and fast learning speed. However, the input weights and the threshold of the hidden layer of the ELM are randomly set, and the appropriate number of the hidden layer is difficult to determine. The kernel extreme learning machine (KELM) uses kernel mapping instead of random mapping, which greatly reduces the complexity of the network and means that the model has better prediction and generalization ability. However, the KELM usually adopts a single kernel function in the application process, which is difficult to adapt to samples with multiple data characteristics [11].  
The hybrid kernel extreme learning machine (HKELM) is built by weighing multiple kernel functions to enhance the regression accuracy, which can solve the problem that it is difficult for the KELM with a single kernel function is to obtain the characteristics of a multidimensional sample. However, the parameters of the HKELM model are stochastic, and the training accuracy and time are easily affected by randomness. Therefore, it is necessary to use the optimization algorithm to optimize the hyper-parameters of the HKELM model [12; 13; 14; 15; 16]. It has been established that the Bayes optimization algorithm offers exceptional search performance [17]. In this study, a hybrid kernel extreme learning machine, optimized by a Bayesian optimization algorithm (BO-HKELM), is proposed to predict the missing well logs. Furthermore, the BO-HKELM model is applied to two wells (Well A1 and Well A2) in a block of the Ordos Basin in China. It can be found that the BO-HKELM model has higher precision compared to the other models proposed in this research.