Computational Cost

To compare the computational cost of frequency-selection LSRTM to conventional shot-domain RTM, there are two factors that must be considered. The first one is the difference in the size of computation grid. For shot-domain RTM, the computation grid only need to be long enough to cover the shot and all the receivers, but for migration of a supergather, the computation grid has to be of the full model size. In this example, this factor is $\frac{8}{2}=4$ . The second factor is the simulation time difference. As shown in the single frequency modeling test, to obtain a spike frequency spectrum and avoid crosstalk between different shots, the simulation time is doubled for frequency-selection LSRTM. In this example of Marmousi2 model, LSRTM image is obtained after 80 iterations. Assuming each iteration cost twice that of a single RTM operation, the computational cost of Figure 3.9(c) is $\frac{80*2*2*4}{400}=3.2$ times that of conventional RTM (Figure 3.8(a)). If the LSRTM is computed without phase-encoding technique, its computational cost would be 160 times that of conventional RTM, assuming 80 iterations are still needed.