Thresholding in preconditioned full waveform inversion: depth resolution and convergence analysis using the Marmousi model

Abstract The performance of full waveform inversion (FWI), a high-resolution seismic imaging technique, depends not only on the choice of numerical solvers, but also on effective parameterization strategies that guide convergence and improve depth resolution. Among these, optimization methods, particularly those employing preconditioners, play a central role in stabilizing updates and enhancing the efficiency of the inversion process. This study examines how threshold scheduling within a diagonal pseudo-Hessian-based preconditioner affects inversion outcomes in frequency-domain acoustic FWI. Using the synthetic Marmousi model, two strategies are compared under an identical cumulative frequency-continuation schedule: a constant threshold (fixed θ across all multiscale steps), and a variable-threshold strategy in which θ decreases from 10 −1 to 10 −4 from Step 1 to Step 4. This framework enables a controlled investigation of how depth sensitivity and convergence behavior are shaped by threshold selection within a consistent preconditioner formulation. The results indicate that variable thresholding leads to more balanced gradient updates and improved imaging of deep velocity structures, as confirmed by depth-binned RMS/NRMS error analysis, while constant thresholding can bias updates toward shallow zones at larger θ or yield less stable deep behavior at the smallest θ. These results support threshold scheduling as a practical control on depth-dependent conditioning for the Marmousi benchmark under the tested acquisition and frequency band and demonstrate that FWI results can benefit from threshold scheduling and motivate further testing to identify effective schedules for a given dataset and acquisition setting.