The hybrid absorbing boundary condition for one-step extrapolation and its application in wavefield decomposition-based reverse time migration

Complex traces are popularly used in up/down- and left/right-going wavefield decompositions. The recently developed low-rank one-step method can extrapolate complex wavefields stably and accurately. However, its boundary reflections are difficult to tackle. Traditional perfectly matched layer (PML) or hybrid absorbing boundary conditions (ABCs) cannot be directly applied, and the attenuation ABCs absorb the reflections with low efficiency. We propose novel and efficient hybrid ABCs for the one-step method. A transition area with several layers between the model target area and the boundary edge area is introduced and its wavefields are determined by the weighted combination of the two-way wavefields and Higdon's first-order one-way wavefields to reach a smooth variation. Both the real and imaginary parts of the complex wavefields are processed in this way and the absorption is highly dependent on the layer number of the transition area. The wavefield extrapolated by the low-rank one-step method is intrinsically analytical. We directly decompose the complex wavefields into up-going, down-going, left-going and right-going parts and achieve four decomposed images (up-down, down-up, left-right and right-left) by applying the wavefield decomposition imaging conditions. Numerical examples validate that our proposed hybrid ABCs achieve nearly perfect absorption of the boundary reflections using about 15 transition absorbing layers. Applications of the numerical data and real data demonstrate that the decomposed images effectively suppress the low-frequency noise and show superiority over a single composite image for interpretation.