*2.3. Correction for the Depth Shifting Between Wireline-Logged Depth and Core Depth*

The depth of the wireline-logged data are usually measured depending on the length of the wireline used during the logging operation while the recorded depths of core data are based on the length of the drill string. Therefore, it is common to have some mismatch between core and log data. The main reasons for this discrepancy between the two depths are drill pipe stretch, cable stretch, tidal changes, incomplete core recovery, and core expansion [35]. Hence, this difference should be accounted while correlating log data with core measurements. To identify this shift, density-log data are plotted

in the same plot with density-data obtained from the core obtained from the same interval [36]. Then, both data are correlated by taking the shift-correction value into account using Equation (3).

$$Log\_{depth} = Cor\_{depth} \pm Slift\_{depth} \tag{3}$$

#### *2.4. Inputs*/*Output Relative Importance*

The accuracy of prediction using artificial intelligence (AI) techniques depends on the selected input parameters and their effect on the predicted output. The relative importance of these input parameters with respect to the output can be indicated in terms of the correlation coefficient (*R*) between them. The correlation coefficient (*R*) is bounded between −1 and 1. When *R* equals one, it indicates that the two selected variables are strongly and directly dependent on each other, while for *R* equals −1, it indicates that they are inversely dependent on each other. When *R* equals to zero, a linear relationship between these variables does not exist [37]. The mathematical formula used to calculate *R* is given in Appendix A. Studying the relative importance of the input parameters (*RHOB*, Δ*tcomp* and Δ*tshear*) with the output (*PRstatic*) resulted in reasonable *R* values of 0.32, −0.57, −0.21 between *PRstatic* and the inputs *RHOB*, Δ*tcomp*, and Δ*tshear* respectively, as shown in Figure 2.

**Figure 2.** Relative importance between the input parameters and the output, the static Poisson's ratio (*PRstatic*).

#### *2.5. The Proposed Prediction Approach*

Both artificial neural network (ANN) and self-adaptive differential evolution (SADE) algorithm are implemented in this study to predict *PRstatic.*

#### 2.5.1. Artificial Neural Network (ANN)

Artificial intelligence (AI) and machine learning have become very effective tools for handling complex engineering problems with high accuracy. Many studies have been reported for utilizing AI tools in rock characterization [38–44]. Among these tools, ANN is considered one of the most effective and applicable AI techniques, especially in the petroleum industry [45]. Based on the literature, there are many applications of ANN in the field of formation evaluation, such as mechanical property prediction of carbonate rocks [5,21], and reservoir characterization [19,46]. ANN can characterize a system under analysis without the need for any physical phenomenon [47]. There is a significant similarity between the performance of biological neural networks and ANN in processing the input

signals to get output responses [48]. The ANN elementary units are called neurons. The minimum number of layers composing the ANN architecture is three; namely input layer, hidden layer, and output layer. These layers are linked using transfer functions and trained using appropriate algorithms representing the nature of the problem [47]. The connections between the neurons are associated with weights and biases [49]. The output layer is commonly assigned to the activation function "pure linear", while there are many available options for the transfer functions assigned to input/hidden layers, such as the log-sigmoidal and tan-sigmoidal types [50]. The backpropagation feedforward neural network is recommended as an effective tool in preference to multilayer perceptron (MLP) [15,51]. The number of neurons should be optimized as a large number of neurons may cause over-fitting and negatively affect the prediction process, while using few neurons may yield under-fitting [52].
