Constructing nearly constant-Q viscoelastic model using the nonlinear optimization method

Key words:  seismic waves  viscoelastic media  quality factor  constant Q model  nonlinear optimization method  forward modeling

Abstract:

Current viscoelastic models have shortage in describing the relation between quality factor Q and frequency. Based on the generalized standard linear body, over-determined system of nonlinear equations was established using the Q formula of viscoacoustic/viscoelastic media and the Levenberg-Marquarat algorithm. The Levenberg-Marquarat algorithm being a nonlinear optimization method was adopted to directly compute the relaxation time to fit the nearly constant Q model. The seismic response of 2D homogeneous model was computed to investigate the effect of viscoelasticity briefly. This method does not involve any approximations or assumptions, so the results are more accurate. The ill-posed problems can also be solved by this method. The fitting and simulation results show that Levenberg-Marquarat algorithm can construct nearly constant Q model more accurately with only two elements. Viscoelasticity has a remarkable effect on the amplitude and frequency spectrum of seismic wave, and should be considered in practical applications.