Optimization of one‐way wave equations

Abstract

The theory of wave extrapolation is based on the square‐root equation or one‐way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square‐root equation represents waves propagating in one direction only.

Optimum split‐step Fourier one‐way operators for seismic modeling and imaging in 3D VTI media

“…Similar work is shown by Lee and Suh [1985] where the optimum coefficients for a continued fraction approximation of the dispersion relation were derived. In the following,W s + is considered.…”

High Resolution/High Fidelity Seismic Imaging and Parameter Estimation for Geological Structure and Material Characterization

“…However, it will bring extra computation cost, so here we focus on the other approach, to optimize the expansion coefficients in the rational functions, which has been studied extensively in the traditional one-way 'phase' propagator (e.g., Lee & Suh, 1985;Ristow & Rühl, 1994;Huang & Fehler, 2000;Xie et al, 2000). For the conventional 45 º FD equation Lee & Suh (1985) proposed a least-squares optimization scheme. Ristow & Rühl (1994) proposed a locally optimized scheme for the Fourier Finite-Difference (FFD) propagator.…”

Salvo: Seismic imaging software for complex geologies

“…Therefore, this operator is approximated by an optimized series which originates from a continued-fraction expansion [8, p. 84] [34, p. 513]. The continued-fraction expansion can be represented by ratios of polynomials [21], and the polynomial coefficients can be optimized for propagation angle [19]. With these approximations, the partial wave equation can be written as and crl and~1 are the expansion coefficients derived by Lee and Suh [19].…”

“…The continued-fraction expansion can be represented by ratios of polynomials [21], and the polynomial coefficients can be optimized for propagation angle [19]. With these approximations, the partial wave equation can be written as and crl and~1 are the expansion coefficients derived by Lee and Suh [19]. These coefficients are listed in Appendix B.1 for reference.…”

“…(3.3), are repeated in Table 11 from Lee and Suh [19]. These coefficients are specifiedin src/include/opt_coefl.inc.…”