Directional Q Compensation Using Sparse Inversion and Preconditioning

The patent extracts and removes the dependency on velocity fields from the Q compensation process. By formulating the problem in the frequency-wavenumber domain and using spectral ratios, the method eliminates the need for velocity field inputs that cause travel time estimation errors, directly addressing the contradiction between measurement precision and reliability.

The patent replaces the conventional mechanical approach of using velocity fields and time-domain filtering with a spectral-domain method. By substituting the velocity field-based mechanical model with frequency-wavenumber domain spectral analysis, the method achieves more accurate travel time estimation without relying on complex velocity field assumptions.

The patent changes the domain parameters from time-domain to frequency-wavenumber domain, enabling selective filtering. By working in the spectral domain, the method can enhance resolution through Q compensation while simultaneously suppressing noise and spatial aliasing by operating on specific frequency and wavenumber components, rather than uniformly amplifying all frequencies as in conventional time-domain methods.

The patent introduces spectral ratios as an intermediary mechanism. By forming ratios of spectral components at different frequencies, the method achieves Q compensation while the spectral domain representation naturally suppresses noise and spatial aliasing, acting as an intermediary that separates signal enhancement from noise amplification.