Optimized approximation for constitution of constant Q viscoelastic media in time domain seismic wave simulation

Taking into account viscoelastic damping effect of media with constant Q, the error of the synthetic waveform can be effectively reduced in seismic wave simulation. In term of time domain finite difference or finite element method for wave simulation, the generalized standard linear body (GSLS), consisted of several standard linear bodies (SLS) connected in parallel, is used to approximate the constitution of viscoelastic media. Via increasing the number of SLS, the accuracy of simulation can be effectively improved but simultaneously increasing the amount of both computational work and memory by times. It is not available yet a general instruction for the choices of the number of SLS in viscoelastic wave simulation, which is the main focus of this paper. The factors that impact on the GSLS approximation error are firstly analyzed with the parameter of GSLS fitted by a nonlinear optimization approach. Via clarifying that the error depends on the bandwidth but not the specific value of upper and lower limits of frequency interval, the feasibility of deriving such an instruction is illustrated. Moreover, for given bandwidth and the given number of SLS used in GSLS, the accuracy of synthetic waveform simulation is demonstrated to be impacted by both the factor of the ratio of wave propagation distance to the interested wavelength in simulation and the factor of the Q value of the media. Incorporating of the two factors, the table for optimal choice of the SLS number for medium with different Q value is established by using a generally applied criterial for measurement of time-frequency goodness-of-fit of the synthetic and the observed waveform. On basis of the new table, a method of using GSLS with different number of SLS for modelling media with different Q values is proposed to avoid the waste of the computational work and memory or the deterioration of the accuracy of simulation caused by using the same number of SLS in GSLS to approximate media with large spanned Q value, which is usually presented in seismic wave simulation. Finally, the accuracy and the efficiency of new method are validated by numerical tests. The work of this paper could further promote the wide application of viscoelastic wave simulation in forward problem and in inverse problem using full waveform inversion technique.