An optimised one-way wave migration method for complex media with arbitrarily varying velocity based on eigen-decomposition

Abstract

The classical one-way generalised screen propagator (GSP) and Fourier finite-difference (FFD) schemes have limitations in imaging large angles in complex media with substantial lateral variations in wave velocity. Some improvements to the classical one-way wave scheme have been proposed with optimised methods. However, the performance of these methods in imaging complex media remains unsatisfying. To overcome this issue, a new strategy for wavefield extrapolation based on the eigenvalue and eigenvector decomposition of the Helmholtz operator is presented herein. In this method, the square root operator is calculated after the decomposition of the Helmholtz operator at the product of the eigenvalues and eigenvectors. Then, Euler transformation is applied using the best polynomial approximation of the trigonometric function based on the infinite norm, and the propagator for one-way wave migration is calculated. According to this scheme, a one-way operator can be computed more accurately with a lower-order expansion. The imaging performance of this scheme was compared with that of the classical GSP, FFD and the recently developed full-wave-equation depth migration (FWDM) schemes. The impulse responses in media with arbitrary velocity inhomogeneity demonstrate that the proposed migration scheme performs better at large angles than the classical GSP scheme. The wavefronts calculated in the dipping and salt dome models illustrate that this scheme can provide a precise wavefield calculation. The applications of the Marmousi model further demonstrate that the proposed approach can achieve better-migrated results in imaging small-scale and complex structures, especially in media with steep-dipping faults.

Full wavefield migration based on eigen-decomposition propagation operators

“…However, the conventional one-way wave operator used in FWM, such as Phase Shift or Phase Shift Plus Interpolation (PSPI) Migration, has limitations when dealing with strongly inhomogeneous media due to its global velocity approximation (Gazdag and Sguazzero, 1984). To address this, local velocity-based one-way operators have been proposed, which calculate a local homogeneous solution for the velocity at each grid node and can accommodate arbitrarily variant velocity media (Kosloff and Kessler, 1987;Grimbergen et al, 1998;Hammad and Verschuur, 2016;Li and Liu, 2021). In this study, we integrated the one-way wave operator based on eigen decomposition (ED) into the FWMod and FWM framework to make it better suited for heterogeneous media, resulting in improved imaging amplitude and accelerated converage speed.…”

Simulation of acoustic wave based on preserved-amplitude one-way in very low frequency

“…In this paper, the approximation process of one-way wave is firstly derived [8] , the physical meaning of each one-way wave is given, and the simulations are compared for amplitude-preserving one-way wave, conventional one-way wave and twoway wave.…”