Characterization for wave equations in viscoelastic media based on the constant Q property

The constant Q property in viscoelastic media assumes that the quality factor Q does not change with frequency(i.e.,the Q value is independent of the frequency).For seismic waves propagating in viscoelastic media,the wave equation is determined by the viscoelastic media model.Equivalence relations exist between various frequency domain mathematical models and physical rheological models for the constant Q property.Considering two elastic moduli and three attenuation variables,24 kinds of wave equations based on diff erent generalized rheological models are divided into six classes in this study,and the 12 kinds of specifi c representation for the wave equations in the time domain are derived.On the basis of the equivalence relations between the generalized rheological models,the diff erence and equivalence relation between diff erent wave equations are proven and clarifi ed.Results show that the high-order generalized rheological model can accurately characterize the attenuation characteristics of seismic waves and has advantages in characterizing the dispersion characteristics in viscoelastic media.Lastly,the seismic refl ection characteristics caused by the diff erence of Q value are verifi ed by the forward modeling of the constant Q wave equation in this study,thereby providing a theoretical basis for the analysis and inversion of the formation Q value from refl ection seismic data.

Three-dimensional Q structure in Jiashi earthquake region of Xinjiang

3-D S-wave Q structure in Jiashi earthquake region is inverted based on the attenuation of seismic waves recorded from earthquakes in this region in 1998 by the Research Center of Exploration Geophysics (RCEG), CSB, and a rough configuration of deep crustal faults in the earthquake region is presented. First, amplitude spectra of S-waves are extracted from 450 carefully-chosen earthquake records, called observed amplitude spectra. Then, after instrumental and site effect correction, theoretical amplitude spectra are made to fit observed amplitude spectra with nonlinear damped least-squares method to get the observed travel time over Q, provided that earthquake sources conform to Brune's disk dislocation model. Finally, by 3-D ray tracing method, theoretical travel time over Q is made to fit observed travel time over Q with nonlinear damped least-squares method. In the course of fitting, the velocity model, which is obtained by 3-D travel time tomography, remains unchanged, while only Q model is modified. When fitting came to the given accuracy, the ultimate Q model is obtained. The result shows that an NE-trending low Q zone exists at the depths of 10-18 km, and an NW-trending low Q zone exists at the depths of 12-18 km. These roughly coincide with the NE-trending and the NW-trending low velocity zones revealed by other scientists. The difference is that the low Q zones have a wider range than the low velocity zones.