As the underground medium is not completely elastic,seismic waves will experience attenuation during propagation.To accurately simulate this phenomenon,many feasible methods have been proposed by scholars at home and abroad.Through extensive research of domestic and foreign literatures,this paper summarizes and categorizes attenuation models into two main categories:approximate constant Q models based on standard linear solids models and fractional order constant Q models.It also elaborates on the basic principles,current developments,advantages,and disadvantages of these two models for wave equation forward modeling,as well as the progress of high-precision time and space numerical simulation techniques.Among these attenuation models,the fractional order constant Q model can accurately and efficiently describe the absorption and attenuation effects of seismic waves in certain frequency bands,and can decouple the amplitude attenuation and phase distortion during the propagation of seismic waves.Therefore,this paper focuses on the introduction of the fractional-order constant-Q model,and based on this,conducts forward simulation of isotropic viscoelastic wave equation in homogeneous media.It also simulates the propagation of seismic waves in frozen soil layers and analyzes the influence of frozen soil layers on seismic records.Finally,a summary and outlook are provided for the fractional-order viscoelastic wave equation.
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