# Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain
## 4 Discussion
### The Computational Efficiency of the ES-SRT and GMD  
A processing method should not only consider the quality of its processing results but also the calculation time and efficiency. We analyze the computational efficiency of the EH-SRT and GMD-R here. Taking the synthetic data in Section 3.2 as an example, we record the computation time of performing the LSRT and EH-SRT to the data and the time of GMD-R decomposition on these two Radon models. Table 1 shows the statistical time.  
Figure 19: (**a**) and (**b**) are the two decomposed modes using GMD-R in Radon space, (**c**) and (**d**) are the recovered events corresponding to (**a**) and (**b**).  
Figure 18: (**a**–**d**) denotes the four decomposed modes in the Radon space; (**e**–**h**) denotes the four recovered events corresponding to (**a**–**d**).  
Table 1 shows that the proposed EH-SRT is a little slower than the LSRT because there are several iterations required in the procedure. However, the method can obtain a higher sparsity Radon model, which can be used not only for GMD-R decomposition but also helpful for the filter method for multiple elimination. Therefore, we consider this increased computational effort acceptable [40; 41]. Then, we perform GMD-R to the Radon model of LSRT and EH-SRT, respectively, and the decomposition on the EH-SRT model exhibits a shorter computation time. This is because the increasing sparsity of the Radon model makes the modes in GMD-R easier to reach convergence during the iteration process, and hence accelerate the computation. Therefore, we suggest performing sparse RT first to obtain the Radon model with high sparsity, which not only can achieve better separation of primaries and multiples but can also improve the computational efficiency of GMD-R.  
Another important point to note is that both the GMD-based method and the filtering method are implemented in the Radon domain. The RT is the kernel of the proposed method for multiple suppression. However, the RT depends on the quality of the original seismic data. When the trace interval of the input data is large, the Radon model tends to have aliasing issues, and the sparsity is low. Although the sparse Radon transform proposed in this paper can improve its sparsity, it is difficult to solve the aliasing problem, which affects the processing results of this method [25]. In addition, the reason why the RT can be used for multiple removals is that multiples and primaries have a certain separability in the Radon domain due to their differences in curvature. Short-period multiples do not have obvious moveout differences with primaries due to their short propagation paths, so it is difficult to suppress them with the Radon-based multiple suppression method. In the field data test in Section 3.3, we do not suppress free-surface multiples in advance, and the GMD-based method has limited ability to suppress them. Therefore, there are several remaining free-surface multiples in the stack profile at 2.4 s. In the industry, it is customary to employ techniques such as SRME and MWD [42; 43; 44] as an initial step to suppress free-surface multiples, and then the remaining long-period multiples are suppressed using the Radon-based methods. Multiple elimination cannot be completely solved by one method, and a combination of methods is needed to achieve better suppression results. The method proposed in this paper aims to simplify the processing flow by reducing the parameter setting and complementing other methods for better elimination of multiples.