Reducing Numerical Dispersion with High-Order Finite Difference to Increase Seismic Wave Energy: -

The numerical dispersion of 2D acoustic wave modeling has become an interesting subject in wave modeling in producing better subsurface images. Numerical dispersion is often caused by error accumulation with increased grid size in wave modeling. Wave modeling with high-order finite differences was carried out to reduce the numerical error. This study focused on variations in the numerical order to suppress the dispersion due to numerical errors. The wave equation used in modeling was discretized to higher orders for the spatial term, while the time term was discretized up to the second order, with every layer unabsorbed. The results showed that high-order FD was effective in reducing numerical dispersion. Thus, subsurface layers could be distinguished and observed clearly. However, from the modeling results, the wave energy decreased with increasing distance, so the layer interfaces were unclear. To increase the wave energy, we propose a new source in modeling. Furthermore, to reduce the computational time we propose a proportional grid after numerical dispersion has disappeared. This method can effectively increase the energy of reflected and transmitted waves at a certain depth. The results also showed that the computational time of high-order FD is relatively low, so this method can be used in solving dispersion problems

Reducing Numerical Dispersion with High-Order Finite Difference to Increase Seismic Wave Energy: -

The numerical dispersion of 2D acoustic wave modeling has become an interesting subject in wave modeling in producing better subsurface images. Numerical dispersion is often caused by error accumulation with increased grid size in wave modeling. Wave modeling with high-order finite differences was carried out to reduce the numerical error. This study focused on variations in the numerical order to suppress the dispersion due to numerical errors. The wave equation used in modeling was discretized to higher orders for the spatial term, while the time term was discretized up to the second order, with every layer unabsorbed. The results showed that high-order FD was effective in reducing numerical dispersion. Thus, subsurface layers could be distinguished and observed clearly. However, from the modeling results, the wave energy decreased with increasing distance, so the layer interfaces were unclear. To increase the wave energy, we propose a new source in modeling. Furthermore, to reduce the computational time we propose a proportional grid after numerical dispersion has disappeared. This method can effectively increase the energy of reflected and transmitted waves at a certain depth. The results also showed that the computational time of high-order FD is relatively low, so this method can be used in solving dispersion problems

Seismic modeling by optimizing regularized staggered-grid finite-difference operators using a time-space-domain dispersion-relationship-preserving method

The staggered-grid finite-difference (FD) method is widely used in numerical simulation of the wave equation. With stability conditions, grid dispersion often exists because of the discretization of the time and the spatial derivatives in the wave equation. Therefore, suppressing grid dispersion is a key problem for the staggered-grid FD schemes. To reduce the grid dispersion, the traditional method uses high-order staggered-grid schemes in the space domain. However, the wave is propagated in the time and space domain simultaneously. Therefore, some researchers proposed to derive staggered-grid FD schemes based on the time-space domain dispersion relationship. However, such methods were restricted to low frequencies and special angles of propagation. We have developed a regularizing technique to tackle the ill-conditioned property of the symmetric linear system and to stably provide approximate solutions of the FD coefficients for acoustic-wave equations. Dispersion analysis and seismic numerical simulations determined that the proposed method satisfies the dispersion relationship over a much wider range of frequencies and angles of propagation and can ensure FD coefficients being solved via a well-posed linear system and hence improve the forward modeling precision