Numerical Results

The skeletonized least-squares GDM method is tested on synthetic data associated with the 2D SEG/EAGE salt model (see Figure ). These traces were computed by FD solutions to the 2D acoustic wave equation. The data include 162 shot gathers with a peak-frequency of 15 Hz, with 176 traces in each shot gather, the shot and receiver intervals are 97.6 m and 24.4 m, respectively. To save computation time, I down-sampled the traces from 4001 time samples with a time interval of 0.001 to 1001 time samples with a time interval of 0.004 s in each trace.

A simple filtering plus thresholding scheme is used to skeletonize the Green's function. Convolution of the skeletonized traces (early-arrivals windowed with a window length of 5 periods) of both the source-side and the receiver-side Green's functions is computed and the migration kernels are saved to disk.

Figure: The 2D SEG/EAGE velocity model.

Figure: Migration results for all 162 shot gathers of the SEG/EAGE salt model: a) GDM result which is identical to standard RTM image; b) low cut filtered version of a); c) skeletonized least-squares GDM image after 10 iterations.

Figure a shows the migration of the 2D SEG/EAGE data set using the GDM scheme. The shallow structures are contaminated by the large amplitude artifacts due to the strong reflection at the ocean bottom. Artifacts are also clearly noticeable around the up boundary of the salt at 1.5 km. Figure b shows the result after applying a low-cut filter. The major part of the artifacts are removed.

A preconditioned conjugate gradient LSM method is then implemented with Figure a as the starting model. All of the migration kernels are available, so no new simulations are needed to get the updated migration image at each iteration. This is the key point for an efficient implementation of iterative LSM, and the result after 10 iterations is shown in Figure c. These strong artifacts are successfully eliminated by the least-squares iterations. Compared to Figure b, the structure below the salt dome and faults are more clearly resolved in Figure c. This is demonstrated in Figure , which shows zoom views of Figure b and Figure c.