3D SEG/EAGE salt model

The quasi-linear multisource LSRTM algorithm is tested on data generated from the 3D SEG/EAGE salt model. This model contains 676 grid points along the $X$ and $Y$ directions, and 201 grid points along the $Z$ direction, with a 20 m grid interval. There are 400 shots evenly distributed on the surface with a 640 m interval along the $X$ and $Y$ directions. A 5 Hz peak frequency Ricker wavelet is used as the source wavelet. Figure 2.12 shows (a) the vertical slice along x=6.8 km and (b) the horizontal slice at the depth of 0.8 km. Since there is no anisotropic parameters available for this model, the anisotropic parameters are set to be zero. Figure 2.13 shows the same slices of the smoothed velocity model as in Figure 2.12. This smooth velocity model is obtained by 3D boxcar smoothing the original model with a window size 200 m along X, Y and Z directions.

The synthetic dataset is migrated with the conventional RTM method and the same slices of the image are shown in Figure 2.14 after high-pass filtering. These images will be treated as the benchmark for comparison. Then the 400 common shots gathers are encoded and stacked together to form 16 supergathers with 25 shots each. The multisource LSRTM method is used to migrate the supergathers. Random time shift and random polarity encoding functions are dynamically used with iterative LSRTM. Figure 2.15 shows the result after 10 iterations for the same slices as in Figure 2.12. Since the input dataset contains 16 supergathers, according to equation 2.13, the SNR of the LSRTM image is expected to be high. When compared to the conventional sources RTM image in Figure 2.14, the multisource LSRTM image in Figure 2.15 is almost free of crosstalk noise. In a vertical slice, the conventional RTM image shows strong amplitudes for the reflectors above the salt body, but in the LSRTM image, the same reflectors are of similar amplitudes along X direction. In the horizontal slice, the arc around x=2km and y=2km is barely visible in the conventional RTM image (Figure 2.14(b)), but it is well illuminated in the multisource LSRTM image (Figure 2.15(b)).

The LSRTM image is expected to exhibit higher resolution compared to conventional RTM. By careful examination, the reflector on top of the salt body is more clearly delineated in the LSRTM image due to the resolution improvement. In terms of compuational cost, the LSRTM method for Figure 2.15 enjoys a speedup $\frac{400}{2*16*10}=1.25$ . Compared to conventional RTM, multisource LSRTM can produce migration images of better quality with similar computational cost.

Another important advantage of the least-squares migration is the removal of migration artifacts. However, the above dataset is not aliased because the peak frequency of the wavelet is as low as 5 Hz. Therefore, no apparent migration artifacts are observed in the conventional RTM image (Figure 2.14). In order to illustrate the advantage of least-squares migration, the above dataset is decimated to 100 shots with a 1280 m interval along both the X and Y directions, and migrated with conventional RTM. The corresponding images are shown in Figure 2.16. The same 100 shots are then encoded and stacked to form 10 supergathers. These supergathers are migrated with the multisource LSRTM method to generate images in Figure 2.17. In the horizontal slice, the conventional RTM image contains a few streaks along the X direction, but they are not present in the LSRTM image.