**3. Analysis of Numerical Experiments**

This section focuses on analyzing the physical characteristics of the point spread function. Figure 1 shows the global point spread function for the 2D Marmousi model. We can find the variations of observation illumination, wave propagation, and limited wavelet frequency-band at different positions. The propagation effect is mainly reflected in amplitude performance. Compared to the PSFs in the shallow model, those in the deep show much worse focusing with increasing attenuation radius. Since the RTM and PSF results are computed under the same observation system, the deconvolution can remove the influence of limited illumination angles in RTM results. Moreover, the seismic wavelets should match the one in RTM as they may have a great influence on point spread functions with respect to phase, amplitude, and attenuation radius.

**Figure 1.** The global point spread function in the 2D Marmousi model.

Figure 2 displays the inverted images using different point spread functions (red and blue circles in Figure 1). Even with the same wavelet, the images using the PSFs show significant variations in the space. The PSF at grid (26, 1) has wider illumination angles and better focusing than the one at grid (26, 11), and thus it can more accurately reflect the illumination characteristics of shallow structures in the model. As a consequence, the above PSF allows for better descriptions of the shallow structures but provides inaccuracy in the deep model. In contrast, due to limited illumination angle and wavefield propagation effect, the image obtained by the PSF at grid (26, 11) is much closer to an RTM result.

**Figure 2.** Results from LSM in imaging domain by using single point spread function. (**a**) the point spread function at grid (26, 1), the shallow details are similar as reflectivity model; (**b**) the point spread function at grid (26, 11), the image is much closer to RTM result.
