HESS VTI model

The multisource LSRTM algorithm is tested for the HESS VTI model decimated to 1800 $\times$ 750 grid points with a grid interval of 10 m; and 1800 geophones are deployed on the surface with one geophone at each grid point and 1800 point sources are evenly distributed on the surface with a source interval of 10 m. The acquisition geometry is fixed spread, as each geophone is activated for each source. A Ricker wavelet with a 12.5 Hz peak frequency is used as the source wavelet. Figure 2.2 shows (a) the P-velocity model, (b) the delta-distribution model and (c) the epsilon-distribution model. The background velocity model in Figure 2.3(a) is generated by recursively convolving the original P-slowness model with the filter [0.25 0.5 0.25] along both the $x$ and $z$ directions. The corresponding relative slowness perturbation model is shown in Figure 2.3(b), which can be thought of as the true reflectivity distribution.

Figure 2.4(a) shows the RTM image for conventional seismic data (each shot gather separately migrated) after high-pass filtering with the same filter which was used as the preconditioner in LSRTM: the image is convolved with a small filter [0.25 0.5 0.25] along both $x$ and $z$ directions recursively for 32 times, then subtracted from the orignal image to give the high-pass filtered image. In this image, most of the reflectors are well delineated except the one below the salt body. However, the problems are: (1) some migration artifacts are still present around the salt body; (2) the amplitudes of reflectors differ significantly from the shallow part to the deep part and (3) the images of the shallow reflectors, especially the water bottom, are of low resolution.

The multisource LSRTM algorithm with linear inversion is then applied to ameliorate these problems. In this example, random source time shifts and random source polarities are used as the encoding functions and are changed at every iteration to suppress crosstalk. All 1800 shot gather are encoded and stacked together to form just one supergather, which is then migrated with just one migration operation. Figure 2.4(b) shows the multisource LSRTM images after 30 iterations of linear inversion. Compared to the conventional RTM image in Figure 2.4(a), the LSRTM image in Figure 2.4(b) shows fewer migration artifacts, more balanced amplitudes, and higher resolution for shallow reflectors. The problem with the multisource LSRTM images is that there are more high-frequency artifacts due to crosstalk noise associated with encoded supergathers.