*4.1. CMP Gather of Real Data Application*

A marine CMP gather after normal movement correction was applied to further examine the effectiveness of the SPRT*Lq*<sup>1</sup> − *Lq*<sup>2</sup> method. We chose the time window of 3.2 s–4.8 s in the field data to process because there exists a large number of multiple reflections, as shown in Figure 8a. The reason is that this part of the data has more developed multiple waves, and the effect of suppression can be clearly seen in the final result. There are 400 sampling points in the time direction and 92 offset traces. The sampling interval is 4 ms. In addition, those multiple reflections cover the primary data and affect the imaging effect of the primary reflections.

Figure 8 is the multiple attenuation results. Figure 8b,c show the multiple attenuation results of the LSPRT and SPRT*L*1, and there are still some residual multiple reflections, as indicated by the rectangle. The information of the primaries is masked, and it makes the seismic events discontinuous. Shown in Figure 8d is the multiple attenuation result obtained by SPRT*Lq*<sup>1</sup> − *Lq*2, and there are no obvious residual multiples. Because of the sparsity of SPRT*Lq*<sup>1</sup> − *Lq*2, the multiples are suppressed effectively at both near and far offsets. The primaries are highlighted, and the black arrows indicate that the continuity of the seismic events are improved. In addition, we can obviously see that the CMP gather is clear and clean.

In order to further compare the advantages of the proposed algorithm with respect to the LSPRT and SPRT*L*1, we extracted three single trace amplitudes after multiple attenuation, and they were compared with single-channel amplitudes before suppression. As shown in Figure 9, there is almost no disturbance in the original location of multiples after multiple attenuation by SPRT*Lq*<sup>1</sup> − *Lq*2, and it is obvious at 4.4 s–4.6 s, and the red rectangle marks the difference in this location. The amplitude of the primary reflection is intact and not attenuated, as at 3.4 s and 3.6 s. The proposed method is effective in suppressing multiples and achieves a better performance.

**Figure 8.** Multiple attenuation result: (**a**) CMP gather of marine real data; (**b**) by LSPRT method; (**c**) by SPRT*L*<sup>1</sup> method; (**d**) by SPRT*Lq*<sup>1</sup> − *Lq*<sup>2</sup> method. The black arrows indicate the continuity of the seismic events are improved in the Figure 8d.

**Figure 9.** Comparison of single trace amplitude after multiple attenuation by three algorithms. The red rectangle indicate that the amplitude of multiple decays more significantly in the proposed method.
