A frequency‐space 2-D scalar wave extrapolator using extended 25-point finite‐difference operator

Finite‐difference frequency‐domain modeling for the generation of synthetic seismograms and crosshole tomography has been an active field of research since the 1980s. The generation of synthetic seismograms with the time‐domain finite‐difference technique has achieved considerable success for waveform crosshole tomography and for wider applications in seismic reverse‐time migration. This became possible with the rapid development of high performance computers. However, the space‐frequency (x,ω) finite‐difference modeling technique is still beyond the capability of the modern supercomputer in terms of both cost and computer memory. Therefore, finite‐difference time‐domain modeling is much more popular among exploration geophysicists. A limitation of the space‐frequency domain is that the recently developed nine‐point scheme still requires that G, the number of grid points per wavelength, be 5. This value is greater than for most other numerical modeling techniques (for example, the pseudospectral scheme). To overcome this disadvantage inherent in space‐frequency domain modeling, we propose a new weighted average finite‐difference operator by approximating the spatial derivative and the mass acceleration term of the wave equation. We use 25 grid points around the collocation. In this way, we can reduce the number of grid points so that G is now 2.5. This approaches the Nyquist sampling limit in terms of the normalized phase velocity.