Q-Constrained Time-Varying Wavelets Estimation

Estimating time-varying wavelets and the quality factor Q of a viscoelastic medium are two important tasks in seismology. Previous studies conducted these two tasks separately. For time-varying wavelets estimation, several time windows are used to segment reflectivity series and seismic traces. Different wavelets are independently estimated from these segmented data. There are no physical constraints for time-varying wavelets, which can lead to overparameterization issues and estimation errors. Estimated neighbouring wavelets can suffer from unphysical variation. In this paper, we propose a Q-constrained time-varying wavelets estimation method. The time-varying wavelets are modelled using only three parameters, reference frequency ω0, fractional value μ and quality factor Q, based on the generalized seismic wavelets equation and the constant-Q model. There are two advantages of this proposed method: (1) it solves the overparameterization issue by adding a Q constraint; (2) it simultaneously estimates time-varying wavelets and Q of the studied viscoelastic medium. We tested the proposed method using a numerical case study. The estimated Q is 98.60% close to the true Q. The estimated time-varying wavelets match well with true wavelets with normalized root mean squared error (NRMSE) as 0.054.