*2.1. Data Description*

The data used for developing the proposed ANN model comprises both core data and wire-lined log data, which are described in the following subsections.

#### 2.1.1. Wire-Lined Log Data Analysis

The selected log dataset represents sandstone rocks for the same sections from which the core samples were also retrieved for experimental measurements. The log dataset included *RHOB*, Δ*tcomp*, and Δ*tshear* measurements. Based on the statistical analysis, the obtained data were found to represent a wide range of sandstone rocks, which is highly recommended for boosting the accuracy of the ANN models. The ranges of the obtained log data are: *RHOB* from 2.24 to 2.98 g/cm3, Δ*tcomp* from 44.34 to 80.49 μs/ft, and Δ*tshear* from 73.19 to 145.6 μs/ft. Table 1 lists different statistical parameters for describing the core and well log data used for building the artificial intelligence (AI) models.

**Table 1.** Statistical parameters of the obtained core data and well-log data. *RHOB*: formation bulk density; Δ*tcomp* : P-wave transit time; Δ*tshear* : S-wave transit time.


#### 2.1.2. Core Data Generation

After retrieving core samples representing sandstone sections from the drilled wells, static mechanical properties of the core samples were experimentally determined. These properties (*ES* and *PRstatic*) were determined using triaxial compressional tests. Triaxial tests were performed under room temperature and an increasing applied confining pressure from 500 to 1500 psi. The triaxial compression test was conducted according to the recommended practice of the American Society of Testing and Materials (ASTM D 2664-86, ASTM D 3148-93) [31]. Figure 1 shows a stress–strain curve for a retrieved sandstone sample using the triaxial compression test. The values of *ES* and *PRstatic* were determined by drawing a tangent straight-line at 50% of the maximum stress value (y-axis) and calculating the slope of this straight line. The slope of the straight-line tangent of the axial stress-strain curve (on the right section) is used to determine *ES* and the slope of the straight-line tangent of the radial stress-strain curve (on the left section) is used to determine *PRstatic*.

**Figure 1.** A typical axial and radial stress–strain curve obtained from the triaxial test of a sandstone sample.

### *2.2. Quality Check and Data Filtration*

The higher the quality of the training data is, the better the accuracy of AI models [32]. This can be accomplished using technical and statistical approaches. First, any unrealistic values such as negative values and zero values were filtered from the data using MATLAB. Then the quality of the obtained data using the values of P-wave and S-wave velocities was checked by calculating *PRdynaimc* values using Equation (1). The values of P-wave and S-wave velocities are the reciprocals of Δ*tcomp* and Δ*tshear*, respectively. For typical rocks Poisson's ratio has positive values; thereafter, any data points yielding negative values of *PRdynaimc* should be removed [30,32]. Subsequently, any outlier values which significantly deviated from the normal trend were removed. The outliers were removed using a box and whisker plot, in which top whisker represents the upper limit of the data and the bottom whisker represents the lower limit of the data. Any value beyond these limits was considered an outlier and removed [33]. These limits are determined by dividing the data into four equal divisions (quartiles) using the minimum, maximum, mean, and median parameters [34] obtained from the results of statistical analysis of the data listed in Table 1.
