Efficient simultaneous migration of primary and free-surface related multiples using reformulated two-way wave-equation depth extrapolation scheme

The migration of free-surface related multiples can enhance subsurface illumination and improve overall imaging quality. However, this process encounters two main challenges: crosstalk artefacts resulting from the cross-correlation of non-reflection-related wavefields, and the increased computational burden of imaging different orders of multiples. We propose a novel method that simultaneously and efficiently migrates both primary and multiple reflections while mitigating crosstalk artefacts. The method employs a reformulated two-way wave-equation depth extrapolation scheme that simplifies up/down wavefield separation through straightforward summation and subtraction operations at each depth step. Two innovative algorithms are integrated into this scheme: a generalized up/down separation algorithm, and a simultaneous migration algorithm of primary and free-surface-related multiples. The up/down separation algorithm efficiently separates the up- and down-going wavefields into primary wavefield and multiple reflections of various orders at the measurement surface. The simultaneous migration algorithm then pairs these components as two-way quantities, allowing for efficient depth extrapolation using a unified propagator, followed by effective decomposition into corresponding one-way components for imaging. Numerical experiments conducted on synthetic models, including a two-dimensional two-layer model and the Sigsbee 2B model, as well as on real seismic data from a gas hydrates bearing zone, demonstrate that the proposed method simultaneously migrate both primary and multiple reflections with reduced crosstalk artefacts and limited computational overhead.