# Accelerating High-Resolution Seismic Imaging by Using Deep Learning
## 2 Methods
### Network Architecture  
To leverage the information within the high-resolution imaging results and enhance the efficiency of the QPSTM, we proposed a CNN network architecture, inspired by Deep Labv3 [34; 35] and U-Net [36]. The network was used to map the conventional PSTM results to the high-resolution imaging results. The network has two parts, namely, the encoder and decoder. As shown in Figure 5, the encoder compresses the large-size input, that is, the PSTM migration image, into smaller ones. Additionally, the low-level layer has fewer features than the high-level layers. In other words, in the encoding process, the data dimension becomes _smaller_ and _deeper_, and the information is transformed from the space domain to the feature domain. The transformations from layer to layer rely on the convolution neutral layer [4; 9; 37; 38] and rectified linear unit (ReLU) activation function [9]. Conversely, in the decoding procedure, illustrated on the right side of Figure 5, the information from the deeper feature map is transformed to the image space by using a transposed-convolution layer [38; 39]. The final output layer uses a \(1\times 1\) convolutional layer, which represents the high-resolution result patches. This layer is followed by a tanh activation function, for which the actual expected result is \([-1,+1]\). To overcome the spatial-resolution loss, a skip connection is applied between the encoder and decoder directly [36]. The details of each layer are presented in Table 1. Using such an encoder/decoder framework, we can transform the data from one style to another. In particular, the transformation is not a simple pixel-to-pixel mapping but a feature-to-feature mapping in a high-dimension domain. Figure 4: QPSTM image. After compensating the energy loss and correcting the phase distortion, the resolution of the image is improved. The fault planes can be clearly seen. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer** & **Output Shape** & **Connected to** \\ \hline input-1 & (64,128,1) & \\ conv2d-1 & (64,128,64) & input-1 \\ conv2d-2 & (64,128,64) & conv2d-1 \\ max-pooling2d-1 & (32,64,64) & conv2d-2 \\ conv2d-3 & (32,64,128) & max-pooling2d-1 \\ conv2d-4 & (32,64,128) & conv2d-3 \\ max-pooling2d-2 & (16,32,128) & conv2d-4 \\ conv2d-5 & (16,32,256) & max-pooling2d-2 \\ conv2d-6 & (16,32,256) & conv2d-5 \\ max-pooling2d-3 & (8,16,256) & conv2d-6 \\ conv2d-7 & (8,16,512) & max-pooling2d-3 \\ conv2d-8 & (8,16,512) & conv2d-7 \\ dropout-1 & (8,16,512) & conv2d-8 \\ max-pooling2d-4 & (4,8,512) & dropout-1 \\ conv2d-9 & (4,8,1024) & max-pooling2d-4 \\ conv2d-10 & (4,8,1024) & conv2d-9 \\ dropout-2 & (4,8,1024) & conv2d-10 \\ up-sampling2d-1 & (8,16,1024) & dropout-2 \\ conv2d-11 & (8,16,512) & up-sampling2d-1 \\ concatenate-1 & (8,16,1024) & dropout-1 \\ conv2d-11 & conv2d-12 & conv2d-11 \\ conv2d-12 & (8,16,512) & concatenate-1 \\ conv2d-13 & (8,16,512) & conv2d-12 \\ up-sampling2d-2 & (16,32,512) & conv2d-13 \\ conv2d-14 & (16,32,256) & up-sampling2d-2 \\ concatenate-2 & (16,32,512) & conv2d-6 \\ conv2d-15 & (16,32,256) & conv2d-14 \\ conv2d-16 & (16,32,256) & conv2d-15 \\ up-sampling2d-3 & (32,64,256) & conv2d-16 \\ conv2d-17 & (32,64,128) & p-sampling2d-3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of each layer. Figure 5: Schematic of the network structure. The network structure consists of 23 conventional layers. The input layer involves the patches of the PSTM migration images, and the output layer involves the corresponding high-resolution versions of the image (obtained using the QPSTM). The network is not entirely symmetric. In the encoding and decoding phases, the layers’ size is transformed from \(64\times 128\times 1\) to \(4\times 8\times 1024\) and from \(4\times 8\times 1024\) to \(64\times 128\times 1\), respectively. The activation function of the encoder and decoder layers is the ReLU. The activation function of the layer before the output is _tanh_ because the co-domain of the ReLU is \([0,+\infty]\), and the actual expected result is \([-1,+1]\).