Seismic wave attenuation, quantified by the quality factor (Q), leads to energy loss and waveform distortion, significantly degrading seismic data quality and resolution. Accurate Q estimation is essential for understanding subsurface properties, particularly in applications such as carbon capture and storage (CCS) and near-surface studies, where attenuation effects are pronounced due to the presence of fluids, gases, or loose soil. Traditional Q tomography methods predominantly rely on spectral-ratio or centroid-frequency shift approaches to account for attenuation effects. However, these methods often face significant limitations, including oversimplified wave propagation assumptions, poor localization in heterogeneous media, and a tendency to produce smeared results, ultimately reducing resolution and accuracy.

To address these challenges, we introduce a novel Q-estimation approach that integrates full-waveform matching for accurate attenuation-effect estimation and compensation during the migration process. The Full Wavefield Migration method is enhanced by incorporating Q into a one-way modeling operator, utilizing full-waveform matching for precise Q estimation, and applying a Random Forest regression constraint to mitigate cross-talk between Q and reflectivity. This approach enables robust and localized Q estimations. Numerical examples demonstrate its effectiveness in accurately retrieving both reflectivity and attenuation models, thereby improving imaging resolution in complex subsurface environments.

Seismic waves traveling through the subsurface experience several forms of attenuation, including geometric spreading, reflection, transmission, and earth attenuation (via the so-called quality factor Q). To achieve high-resolution sub-surface details, it is essential to tackle all types of attenuation resulting from the overburden. Attenuation is associated with dispersion, causing gradual changes in signal shape and strength, leading to a shift of energy towards lower frequencies and potential signal distortion over time. Precisely measuring Q in seismic data is challenging but crucial for accurate subsurface imaging. The primary objective of this study is to explore the role of internal multiples (reflections within subsurface layers) for more accurate Q estimation, although traditional methods remove multiples in advance. Therefore, we utilize the Full Wavefield Migration method, which make use of the Full Wavefield Modeling (FWMod) scheme as its forward engine. This approach encompasses not only geometric spreading, reflectivity and transmission effects but also includes multiple scattering. The FWMod process is structured in a modular manner, where wavefield operators describe propagation and reflection/transmission. Consequently, including Q is relatively straightforward by redefining the propagator. Based on a synthetic data example it is demonstrated that multiples, when integrated into the inversion process, enhance the Q estimation.