Full-wavefield modeling using a decoupled viscoacoustic wave equation with vector-reflectivity

Abstract

Conventional Q-compensated least-squares reverse time migration generally employs a linearized viscoacoustic modeling operator based on the first‑order Born approximation, which simulates only primary reflections in synthetic data. As a result, it cannot properly match seismic data containing multiples, leading to prominent crosstalk artifacts and reduced image quality. To overcome this limitation, we started with the relaxation function of the generalized standard linearized solid model and derived a viscoacoustic wave equation with vector-reflectivity. This formulation enabled the simulation of full viscoacoustic wavefields that included both primary and multiple reflections, and it could be numerically solved using finite‑difference algorithms. Numerical experiments demonstrated that the wavefields generated using the proposed vector-reflectivity equation were equivalent to those produced using the original variable-density viscoacoustic wave equation. To further investigate the attenuation characterizations, we decoupled the dissipation and dispersion effects in the viscoacoustic wave equation with vector-reflectivity and derived a corresponding decoupled formulation. Numerical experiments demonstrated that the decoupled viscoacoustic wave equation with vector-reflectivity accurately simulated both dissipation and phase-dispersion wavefields. Based on decoupled characteristics and full-wavefield simulation capabilities, the proposed formulation provides an effective linearized forward-modeling engine for Q-compensated least-squares reverse time migration.

Keywords

Attenuation / Generalized standard linearized solid / Vector-reflectivity / Forward modeling

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