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.
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