Fractional Order Equation Based Attenuation Compensation In Reverse Time Migration

Seismic waves in viscoelastic underground media have the effect of absorption and attenuation,which makes seismic records have problems such as amplitude attenuation and phase distortion.It is difficult to accurately describe the information of deep areas,resulting in reduced imaging resolution.Therefore,compensating amplitude attenuation and phase distortion is particularly important in the process of seismic migration imaging.The migration method closer to the actual medium assumption has become the focus of attention.Q-compensated viscoelastic reverse time migration imaging method takes into account the absorption attenuation law and wave field propagation characteristics of the viscoelastic medium,and performs attenuation compensation during the wave field propagation,which can effectively compensate the attenuation effect and improve the imaging accuracy,which is helpful for oil and gas exploration and development deployment.In this paper,based on the constant Q theory model,the first-order velocity stress equation of decoupled fractional Laplace viscoelastic is derived.Time finite difference method combined with the staggered pseudospectral method is used to realize the numerical simulation of seismic wave field,the propagation law of wavefield in viscoelastic medium is studied.The multi-component viscoelastic wave field contains both longitudinal and transverse wave fields.To avoid the generation of crosstalk between coupled wavefields during imaging,wavefield separation method based on decoupling equation is used to extract the vector longitudinal and transverse wave fields.In conventional Q-compensated reverse-time migration,the high-frequency noise will be exponentially amplified during amplitude compensation,resulting in numerical instability.This paper uses only the dispersion wave field and the viscoelastic wave field to construct a stable compensation operator,which is embedded in the excitation amplitude imaging condition,and the unrelated moments are discarded to improve the ratio stability.The test results of the layer model and the Marmousi model show that the Q-compensated viscoelastic reverse time migration based on the decoupled fractional Laplace viscoelastic first-order velocity stress stress equation can stably compensate the deep structure energy,correct the phase distortion and improve the imaging resolution.