## 2 Methodology
### Process Flow for RTM-Based Calculation to Output SOGs  
The RTM calculation is high in intensity, requiring parallel computing. With the development of computer technology, especially the emergence of GPUs, the RTM calculation can be improved significantly by accelerating the RTM finite difference with multiple kernels, substantially raising the computing efficiency of RTM, thus promoting its calculative application in industries. In the RTM calculation using a GPU, to break through the bandwidth bottleneck between the central processing unit (CPU) and the GPU, random boundary processing conditions [19] are used to calculate the wavefield propagation of shots twice to exchange computation for storage, which saves time consumed for data transmission. The RTM calculation process on the GPU is as follows: the shot wavefield is forward-propagated to the boundary where it is randomized and reversed; the receiver wavefield is propagated backward; both are imaged at the same time; the shot-by-shot migration is completed to obtain the entire imaging profile.  
Figure 3: RTM SOGs calculated with attribute migration: (**a**) gathers at about CMP 150, and (**b**) gathers at about CMP 350.  
The shot-domain RTM migration outputs the zero shot-receiver distance profile, namely, the stacked profile, and in this study, the strategy of attribute migration was used to output SOGs from the RTM calculation. According to the aforesaid theory on attribute migration, it was necessary to calculate the values of offset at imaging points using the ratio of the results from the migration of the modulated and original shot data, thus sorting to obtain the migrated SOGs. Compared with the stacked profile RTM calculation process, the two kinds of migration results are the same, except for the input receiver data, and other imaging elements are the same. Therefore, only the RTM calculation process needs to be modified in order to be used in a calculation to output the offset gathers; thus, the calculation process is now as follows: the shot wavefield is forward-propagated to the boundary where it is randomized and then backward-propagated; the wavefields of both the receivers and the modulated receivers are backward-propagated, respectively; one shot wavefield and two receiver wavefields are coherently imaged at the same time, outputting results from two kinds of single-shot migration; the ratio of the two wavefields is used to obtain the offset attribute, thus sorting to generate SOGs. The above calculation and sorting are completed shot by shot and obtain the final results of the imaged SOGs.  
Figure 5 shows the process for the RTM-based calculation to output SOGs. Obviously, if the imaging part of the modulated wavefields is removed, it is a common RTM. Since the forward and reverse propagations of the shot wavefield are unchanged, only the modulated wavefield is added to the forward propagation of the receivers, so the total calculation is only increased by about one-third. In the next section, we will introduce how to improve these wave propagation kernels on GPUs.  
Figure 4: Imaging profiles and gathers at the velocity increased (**a**) and the enlarged display of partial gathers (**b**) decreased by 5% (**c**), and (**d**) enlarged display of partial gathers (**d**).