Lowrank one-step wave extrapolation for reverse-time migration

Conclusions

We have developed lowrank wave extrapolation using a one-step scheme. The one-step lowrank method appears to be more stable than the two-step method, and exhibits superior stability in numerical experiments. The capability of propagating waves using large time steps can help saving costs when performing modeling, imaging or full waveform inversion tasks. We propose two modifications to the complex phase function, which can be accurately handled by the lowrank one-step approach. First, we show that, when the velocity-gradient term is included in the approximation of the phase function, a higher accuracy can be achieved. Next, we use a one-step scheme to incorporate a propagation-direction-dependent absorbing boundary condition in the wave propagation operator, which reduces artificial reflections at wide-incident angles. Numerical examples using simple models demonstrate the improved accuracy and efficiency of the proposed method. In particular, we apply the lowrank one-step operator to wave extrapolation in 2D TTI media and 3D orthorhombic media, and obtain wavefields free of dispersion artifacts or residual shear-wave artifacts. When lowrank one-step RTM is applied on the BP 2007 TTI benchmark data set, it produces high-quality seismic images.

Lowrank one-step wave extrapolation for reverse-time migration