## 5 Quantitative Seismic Characterization Based on the RPM-FCNN Framework
Three sets of RPM-FCNN frameworks have been established to describe the relationship between three seismic elastic parameters (\(Vp\), \(Vs\), density) and seven reservoir physical parameters. The first group takes \(Vp\), \(Vs\), and density as input elements and computes the organic matter mixture aspect ratio \(\alpha_{k}\) and organic matter porosity \(\Phi_{k}\) as output results. The second group uses \(Vp\), \(Vs\), and density as input elements and computes the anisotropy parameters \(\varepsilon\) and \(\gamma\) as output results. The third group takes \(Vp\), \(Vs\), and density as input elements and computes the clay content _Vclay_, kerogen content _Vkerogen_, and total porosity \(\Phi\) as output results. The PyTorch deep-learning framework and MATLAB were used for this training. Normalization was applied during the training process. The optimizer used was Adam (adaptive moment estimation) with a learning rate of 0.001. Adam is a gradient-based optimization algorithm designed to progressively adjust learning rates over time. It amalgamates the principles of momentum and RMSProp (root mean square propagation) by adaptively tuning the learning rates for each parameter through the exponential moving average of past gradients. In terms of utilizing Adam, the PyTorch deep-learning library is equipped with the Adam optimization algorithm. Parameters for the optimizer can be directly set using torch.optim.Adam in Pythonch 1.11.0 documentation. The activation function used in deep learning is the ReLU activation function. The framework structure consists of one input layer, two hidden layers, and one output layer. The first and second groups of input layers each include 3 neurons, the first hidden layer has 128 neurons, the second hidden layer has 64 neurons, and the output layer has 2 neurons. The third group's input layer includes 3 neurons, the first hidden layer has 128 neurons, the second hidden layer has 64 neurons, and the output layer has 3 neurons. All three sets of data were iterated 100 times, and as the number of iterations increased, the error decreased, as shown in Figure 13. The error for all three sets was less than \(10^{-2}\). With the expected error achieved, the trained RPM-FCNN framework can be used for the regional prediction of reservoir physical parameters. The trained RPM-FCNN framework can be applied for quantitative seismic characterization of the elastic parameters in the pre-stack seismic inversion data in the study area. The spatial distribution of reservoir properties in the shale gas reservoir is obtained. The pre-stack seismic inversion data in the target layer of the study area are the input data shown in Figure 14, including \(Vp\), \(Vs\), and density. The results obtained by the RPM-FCNN framework are depicted in Figure 15 and include predictions of the organic matter mixture aspect ratio \(\alpha_{k}\), organic matter porosity \(\Phi_{k}\), and seismic anisotropy parameters \(\varepsilon\) and \(\gamma\), and total porosity \(\Phi\), clay content _Vclay_, and kerogen content _Vkerogen_. Figure 14: Pre-stack seismic inversion data of the shale gas reservoir in target interval: (**a**) Longitudinal wave velocity \(Vp\); (**b**) Shear wave velocity \(Vs\); (**c**) Density \(\rho\). Figure 13: The convergence curves of three groups: (**a**) The convergence curves of \(\alpha_{k}\) and \(\Phi_{k}\); (**b**) The convergence curves of \(\varepsilon\) and \(\gamma\); (**c**) The convergence curves of _Vclay_, _Vkerogen_, and \(\Phi\). Figure 15a shows the predicted spatial distribution of the organic matter mixture aspect ratio \(\alpha_{k}\), which reflects the shape of the organic matter mixture. We use the negative logarithm of the organic matter mixture aspect ratio to describe the shape.