Study Of Viscoacoustic Simulation And Reverse Time Migration Method Based On Fractional Laplacian Constant-Q Wave Equation

Seismic imaging is an important process in seismic exploration.The reverse time migration method is an imaging technique which can adapt to the complex geological model and play an important role in the exploration.The actual underground medium usually has attenuation effect.Reduced amplitude and distorted dispersion of seismic waves caused by attenuation,always degrades the resolution of migrated images.Therefore,based on the model describing the attenuation property of underground medium,the viscous forward simulation method is developed.To develop the reverse time migration method which can compensate the amplitude and correct the attenuation is of great significance.Based on the Kjartansson's constant-Q model,the time domain viscoacoustic and viscoelastic wave equations with fractional time derivative are deduced in this paper.The wave equations of approximate constant-Q viscoacoustic and viscoelastic waves containing two spatially varying power fractional Laplacian operators are derived by Fourier transform.We introduced an approach based on the Hermite Distributed Approximating Functional(HDAF)method,to implement the fractional Laplacian in the wave equation The amplitude attenuation and phase distortion of seismic wave propagation in viscous medium can be simulated well.Based on the decoupling constant Q viscous acoustic wave equation,the causes of amplitude attenuation and phase distortion of seismic wave imaging in viscous media are discussed in this paper.The decoupling amplitude compensation and phase correction wave field extension operators are derived.Based on the cross-correlation imaging condition,the Qcompensating reverse time migration The resolution of the imaging results can be improved well.