# Accelerating High-Resolution Seismic Imaging by Using Deep Learning
## 2 Methods
### End-to-End Learning with Small Patches  
In most applications pertaining to computer vision science, the image is treated as a whole feature input [40; 41; 42; 43; 44; 45]. Consequently, images with different sizes need to be resized or cropped to a fixed size before being fed into the network. Seismic profile mapping involves more features and characteristics than those for computer image processing, for instance, the features corresponding to semantic segmentation and object detection and classification. Furthermore, mapping the conventional PSTM result to a high-resolution migration image requires the subtle modification of the frequency of the network, which is not spatial/area sensitive. In addition, the use of small-size inputs can make the convergence of the network easier in the training stage and more efficient in the prediction stage. In this study, a relatively small patch size of \(64\times 128\) was selected. The dimension 64 was the number of common depth points (CDPs), and the time-depth dimension corresponded to 128 imaging points. The patches are illustrated in Figure 6. It can be noted that diverse patches with different patterns exist: some patches consist of low-frequency components, whereas the others are compounds of high-frequency components. In addition, the dip angle of the structures varies from patch to patch. In the subsequent sections, we describe the generation of the patches from the imaging result and the data pre-processing, specifically for DL. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer** & **Output Shape** & **Connected to** \\ \hline concatenate-3 & (32,64,256) & conv2d-4 \\  & & conv2d-17 \\ conv2d-18 & (32,64,128) & concatenate-3 \\ conv2d-19 & (32,64,128) & conv2d-18 \\ up-sampling2d-4 & (64,128,128) & conv2d-19 \\ conv2d-20 & (64,128,64) & up-sampling2d-4 \\ concatenate-4 & (64,128,128) & conv2d-2 \\ conv2d-21 & (64,128,64) & concatenate-4 \\ conv2d-22 & (64,128,64) & conv2d-21 \\ conv2d-23 & (64,128,1) & conv2d-22 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 6: Input patches for training the network. Instead of the full image, small patches are used as the network input. Small images require small networks, which involve fewer parameters to tune and can easily converge in training. Furthermore, small networks have a higher generalization capacity. In addition, small patches cover various features, such as frequency appearance and dip angles. Finally, a large number of training samples can be easily generated using small patches, which is critical for DL applications. After the prerequisite processing (e.g., de-noising, static correction for land data, consistent de-convolution, de-multiples for marine data, velocity analysis) of the field seismic data, the 3D migration data volume can be obtained by using the conventional PSTM method. High-resolution imaging using the QPSTM method can be performed for a given imaging line to control the learning procedure. In the actual situation, 20 lines from the work area were considered as the proposal lines. Thereafter, we divided the image result of the proposal lines (including the results of the conventional PSTM and QPSTM) into patches. Specifically, we sampled the patches from the imaging result using a sliding window. In general, the first patch sample was obtained at the left-top (the minimum CDP and minimum time-depth position) of one imaging profile. Next, we moved the window to the right with a fixed step of 32-CDP. After the first row was scanned, we moved the time-depth by a step with 64 time sampling points. After repeating the sampling procedure, the conventional PSTM imaging patches and the corresponding high-resolution imaging patches were obtained. Varying the actual amplitude range from patch to patch was not suitable for training the network; therefore, we scaled the range to \([-1,1]\) by performing amplitude normalization using Equation (2):  
\[s(x,t)=\left\{ \begin{array}{cc}f(x,t)/max&f(x,t)\geq 0\\ -f(x,t)/min&f(x,t)<0.\end{array} \right.