Results for wave‐equation migration in the frequency domain using the constant‐density acoustic two‐way wave equation have been compared to images obtained by its one‐way approximation. The two‐way approach produces more accurate reflector amplitudes and provides superior imaging of steep flanks. However, migration with the two‐way wave equation is sensitive to diving waves, leading to low‐frequency artifacts in the images. These can be removed by surgical muting of the input data or iterative migration or high‐pass spatial filtering. The last is the most effective. Iterative migration based on a least‐squares approximation of the seismic data can improve the amplitudes and resolution of the imaged reflectors. Two approaches are considered, one based on the linearized constant‐density acoustic wave equation and one on the full acoustic wave equation with variable density. The first converges quickly. However, with our choice of migration weights and high‐pass spatial filtering for the linearized case, a real‐data migration result shows little improvement after the first iteration. The second, nonlinear iterative migration method is considerably more difficult to apply. A real‐data example shows only marginal improvement over the linearized case. In two dimensions, the computational cost of the two‐way approach has the same order of magnitude as that for the one‐way method. With our implementation, the two‐way method requires about twice the computer time needed for one‐way wave‐equation migration.
Numerical solution of the acoustic wave equation using Raviart–Thomas elements