## 4 Methodology
### Neural Network and Porosity Prediction  
Neural networks are a type of machine learning algorithm that is inspired by the structure and function of the human brain, which idea is based on the work of [PERSON] and [PERSON] (1943) [24]. They consist of layers of interconnected nodes or neurons that can process and analyze data to identify patterns, make predictions, or perform other tasks. Figure 4: Angle gathers around Well-B. While the concept of neural networks is based on an idealized version of how the brain works, the practical applications of this technology have shown that it can be a highly effective tool for solving real-world problems. By connecting well and seismic data, it is possible to better define the characteristics of the reservoirs. The lateral distribution of porosity is based on the correlation between petrophysical, well, and seismic data [1]. Neural networks are used to define the correlation between input data that are not in a strictly linear relationship [3]. A multilayer neural network, a Deep Forward Neural Network (DFNN) with three hidden layers, was used (Figure 7). Figure 5: \(Vp\) and \(Vs\) logs from several pseudo-wells created to calculate Rock Physics properties changing porosity and reservoir thickness. The reservoir interval is in grey. Figure 6: AVO synthetic gathers generated from the pseudo-wells. Curves in red present \(Vp\) log. Figure 7: Schematic example of DFNN with three hidden layers (modified after [6]). Several published papers attempt to apply neural networks to reservoir property distribution, and research showed that DFNN has better results with petrophysical parameters [4; 25; 26; 27]. Deep neural networks (DFNN) are a type of artificial neural network (ANN) that consists of multiple layers of interconnected artificial neurons organized in a forward propagation manner. DFNNs are often used for various tasks, such as classification, regression, and pattern recognition. DFNN consists of an input layer, multiple hidden layers, and an output layer. Each layer consists of multiple artificial neurons, also known as nodes or units. The connections between neurons are weighted, and the weights determine the strength and significance of the information transmitted between neurons. The forward propagation process of a DFNN involves passing the input data through the network, layer by layer, until the output layer is reached. Each neuron in a layer receives input from the previous layer and applies a mathematical transformation to produce an output. The output of each neuron is then passed as input to neurons in the next layer until a final output is generated. A chronological and systematic overview of the development of deep neural networks is presented by [PERSON] et al. (2019) [PERSON] et al. (2019). Deep neural networks with many layers and parameters increase the risk of overfitting, characterized by small training and large validation errors. Overfitting can be reduced by increasing the amount of training data using synthetic data [20]. Pseudo-wells were used for neural network training as well as created synthetic AVO gathers, which were used as additional volume. DFNN was created with three hidden layers. Log prediction is validated using 30% of overall wells (Figure 8). In the final step of synthetic AVO gathers, synthetic impedance is replaced with real seismic angle stacks and impedance inversion results. Well-A is not used in this process and represents the control blind well. For the purpose of objective comparison of results, we trained the same NN but only with input from two wells and seismic inversion results from actual data. Prior to the implementation of reservoir properties into the reservoir model, lithology discrimination was performed using an unsupervised neural network. Unsupervised neural networks employ a technique that automatically classifies input data into a specific number of classes, which are determined by the user. The network searches for patterns  
Figure 8: DFNN validation cross-plot, which compares actual and predicted total porosity.