Low-rank one-step wave extrapolation for reverse time migration

Abstract

Reverse time migration (RTM) relies on accurate wave extrapolation engines to image complex subsurface structures. To construct such operators with high efficiency and numerical stability, we have developed a one-step wave extrapolation approach using complex-valued low-rank decomposition to approximate the mixed-domain space-wavenumber wave extrapolation symbol. The low-rank one-step method involves a complex-valued phase function, which is more flexible than a real-valued phase function of two-step schemes, and thus it is capable of modeling a wider variety of dispersion relations. Two novel designs of the phase function leads to the desired properties in wave extrapolation. First, for wave propagation in inhomogeneous media, including a velocity gradient term assures a more accurate phase behavior, particularly when the velocity variations are large. Second, an absorbing boundary condition, which is propagation-direction-dependent, can be incorporated into the phase function as an anisotropic attenuation term. This term allows waves to travel parallel to the boundary without absorption, thus reducing artificial reflections at wide incident angles. Using numerical experiments, we revealed the stability improvement of a one-step scheme in comparison with two-step schemes. We observed the low-rank one-step operator to be remarkably stable and capable of propagating waves using large time step sizes, even beyond the Nyquist limit. The stability property can help to minimize the computational cost of seismic modeling or RTM. The low-rank one-step wave extrapolation also handles anisotropic wave propagation accurately and efficiently. When applied to RTM in anisotropic media, the proposed method generated high-quality images.

Pure quasi-P-wave calculation in transversely isotropic media using a hybrid method

“…One family of high resolution algorithms for solving the anisotropic acoustic wave equation free of S-wave artifacts falls under the so-called spectral approach (Etgen & Brandsberg-Dahl 2009;Du et al 2010;Fomel et al 2013;Alkhalifah 2014;Song & Alkhalifah 2013;Wu & Alkhalifah 2014;Sun et al 2016). They are based on approximately separating the space-and wavenumber-dependency of the dispersion relation.…”

Pseudo‐spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

“…Other methods such as the pseudo‐spectral (Kosloff and Baysal ; Sun et al . ), finite‐element (Eriksson and Johnson ), spectral elements (Komatitsech et al . ), discontinuous Galerkin (Chung and Engquist ; De Basabe et al .…”

“…The finite-difference method (FDM) remains the most popular numerical method for seismic modelling because it is robust and relatively simple to implement, and it offers a good balance between accuracy and efficiency (Moczo et al 2007;Yang et al 2010;Virieux et al 2011;Liu 2013). Other methods such as the pseudo-spectral (Kosloff and Baysal 1982;Sun et al 2016a), finite-element (Eriksson * E-mail: 923458778@qq.com and Johnson 1991), spectral elements (Komatitsech et al 2000), discontinuous Galerkin (Chung and Engquist 2006;De Basabe et al 2008), finite-volume (Benjemaa et al 2007), and grid methods (Zhang and Liu 1999) are used to various extent in the geophysical community. Wave propagation simulation has attracted a renewed interest mainly because the so-called (acoustic or elastic) full-wave equation approaches have become a fundamental tool in seismic migration and waveform inversion, considering the new challenges in exploration, especially anisotropy (Operto et al 2009;Lisitsa and Vishnevskiy 2010;Bartolo et al 2015;Cheng et al 2016).…”

The optimized gradient method for full waveform inversion and its spectral implementation

“…A popular approximation to that is given by the perfectly matching layer (PML) boundary condition (Berenger 1994). Similar to Berenger (1994) and Sun et al (2016), we extend the domain and consider a function α(x) equal to zero in the original domain and positive in the extended part. From eq.…”