Reinvigorating the wavelet transform: A versatile topol for modern seismic imaging

Recent advances in ocean-bottom node acquisition and GPU-enabled computing have established inversion-based methods such as Least-Squares Migration (LSM) and Full Waveform Inversion (FWI) as key tools for high-resolution seismic imaging. However, extending these workflows to higher frequencies and multi-parameter settings introduces persistent challenges, including noise amplification, slow convergence, high computational cost, and severe parameter cross-talk. This study revisits wavelet transform methods as an integral component of the imaging process rather than a pre- or post-processing tool. Exploiting their multiscale, localized, and directional characteristics, we embed wavelet representations directly within inversion workflows to improve scalability, efficiency, and image quality. Applications include wavelet-domain gradient conditioning, adaptive image-domain LSM via Hessian filtering, and practical Hessian-based preconditioning for FWI. We further extend this framework to multi-parameter FWI through a wavelet-domain block Hessian inversion strategy, enabling explicit decoupling of parameter sensitivities without relying on conventional heuristics such as reparameterization or staged inversion. Results from synthetic and field examples, including the Atlantis dataset, demonstrate accelerated convergence, enhanced image fidelity, and substantial reduction of cross-talk. These results position the wavelet transform as a scalable and unifying toolkit for next-generation inversion-driven seismic imaging.