Inversion-Based Time-Domain Inverse $Q$ -Filtering for Seismic Resolution Enhancement

Seismic wave will suffer from resolution loss during its propagation in subsurface media, which is caused by the earth filtering effect. Inverse Q-filtering (IQF) is an essential scheme for eliminating earth filtering effect and enhancing temporal resolution. In this letter, IQF is achieved by solving a time-domain inverse problem whose corresponding forward model is established based on the idea of seismic migration, i.e., extrapolating the unfiltered record (the detected signal if there is no earth filtering effect) from surface downward to each time-depth point and then adopting imaging condition to obtain the attenuated record. We express this migration-based forward model as a matrix-vector equation and construct the objective function of inversion-based time-domain IQF (ITIQF). Instead of adopting frequency-domain incomplete amplitude compensation operator for the purpose of antinoise, we propose three transform-domain sparse regularization strategies, including wavelet-based constraint, curvelet-based constraint, and double constraint (a combination of wavelet- and curvelet-based constraints). Solvers of these constrained ITIQF methods are provided according to convex optimization theory. We demonstrate the superior performance of ITIQF scheme via both synthetic and field data examples.