# Shear Sonic Prediction Based on DELM Optimized by Improved Sparrow Search Algorithm
###### Abstract  
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.  
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relationship between the target curve and other logging curves, but this method has the problem of insufficient expression of equation [3].  
In geophysical exploration, the application of the observation data (such as seismic, logging, and magnetic) to identify the reservoir prediction and hydrocarbon is a process of establishing complex nonlinear relationships [3]. The machine learning approach has obvious advantages in solving these kinds of nonlinear problems. The ELM belongs to the single hidden layer feedforward neural network, which has the characteristics of a simple structure and fast learning speed [4]. By referring to the idea of deep learning, the DELM extends the ELM to a multi-layer structure, which can more effectively mine the essential characteristics of data and has a higher feature learning ability [5]. However, the initial input weights of DELM are stochastic, and the training accuracy and time are easily affected by randomness [6]. Therefore, a variety of intelligent optimization algorithms can be used for optimizing DELM [7; 8; 9; 10; 11; 12; 13; 14].  
It has been demonstrated that the SSA provides an outstanding search performance [15]. Due to the decrease of population variation in the middle and later iterations, the SSA occasionally suffers from drawbacks, such as slow convergence speed, poor solution accuracy, and ease of falling into regional optimal solutions [16]. The ISSA with the firefly search disturbance algorithm [17; 18; 19], aimed at the defects of the SSA, was introduced to improve the optimization ability of the SSA. Moreover, the ISSA-DELM model is applied to the logging data from a block of the Ordos Basin in China. It can be found that the ISSA-DELM has better prediction performance, and can estimate DTS more precisely than the ordinary models (ELM and DELM) and the hybrid models (GA-DELM, PSO-DELM, and SSA-DELM), which provides a promised method for DTS estimation. The remainder of this paper is organized as follows. Section 2 presents the principle and modeling of ISSA-DELM. Section 3 presents the flow of DTS prediction based on the ISSA-DELM. Section 4 presents the practical application and result analysis by using the logging data from the Ordos Basin in China. Finally, the paper is concluded in Section 5.