## 3 Methodology
### Synthetic Dataset Library  
The second part of this study involves establishing a rock physics-based synthetic dataset library, utilizing a systematic workflow introduced by [PERSON] et al. [24]. This library is a collection of pseudo-wells and seismic data that simulate the actual subsurface situation. We considered sand and shale as the two dominant facies in the study area. Then, using the available in-situ well information, we examined the range and distributions of several reservoir properties for each predefined facies, such as porosity, water saturation, and clay volume. Next, we applied the Monte Carlo simulation technique to perturbthe reservoir properties within allowable predefined petrophysical limits to account for reasonable geological differences in the subsurface, which is also to better explain the geological possibilities in the actual reservoir condition. Since there is an explicit connection between the attributes of the reservoirs, we also included a spatial sequential Gaussian simulation [25] to correlate sample points within and among the various properties to prevent an unreasonable geological sequence. The spatial correlation is a vital concept in geostatistics that measures the relationship of property at two different points within the same reservoir. The coefficient can be plotted as a function of the distance between two points to obtain the data's vertical correlation function, \(\rho(\mathrm{h})\). From here, we can generate an experimental variogram model by using the formulation as given:  
\[\gamma(\mathrm{h})=\sigma^{2}\left[1-\rho(\mathrm{h})\right] \tag{6}\]  
where \(\sigma^{2}\) is the variance of the entire dataset. The distance in which the correlation function approaches zero is called correlation length, where this length would be one of the key parameters needed for simulation. Typically, experimental variograms are noisy due to limited data issues and errors in measurement. This study used a spherical analytical variogram model to regulate the experimental variogram function. Once the variogram is ready, the next step is to form a 1D spatial symmetrical covariance matrix, \(C\), given as:  
\[C= \begin{bmatrix}\gamma(0)&\cdots&\gamma(d_{max})\\ \vdots&\ddots&\vdots\\ \gamma(d_{max})&\cdots&\gamma(0)\end{bmatrix}  \tag{7}\]  
Next, we computed the Cholesky decomposition, R, of the matrix as:  
\[R=\mathrm{chol}(C) \tag{8}\]  
Later, we used the Cholesky decomposition matrix as the input to compute the vertical random correlated vector by multiplying the matrix with a random uncorrelated vector, \(\mathrm{u}\), as part of the process to simulate the random residual spatial reservoir properties variation. At the same time, we also need to determine the background trend of reservoir properties. A small number of actual wells were chosen and utilized as references to extract low-frequency information and produce such trends. The reference wells should have acceptable log data quality, good coverage of the investigation intervals, and good seismic calibration. Subsequently, we combined each reservoir property's background trend and residual spatial variation to produce the absolute version of synthetic reservoir logs. Once the pseudo reservoir logs are ready, the next step was to exploit them as input to approximate pseudo elastic properties logs, including density, P-wave, and S-wave velocity, by adopting the generalized RPT from the first part of the methodology. Eventually, this will create a pseudo-well with a complete set of petrophysical and geophysical logs. Then, the populated elastic properties were applied to compute the angle-dependent reflectivity at incident angles from 0\({}^{\circ}\) up to 50\({}^{\circ}\) with angle stepping for every 1\({}^{\circ}\), based on full [PERSON] (1919) formulation [26], and convolve with frequencies dependent source wavelets to transform into synthetic seismic gathers. The same procedure was repeated in up to 1000 cases to produce a comprehensive set of pseudo-wells and seismic gathers with proper labeling.