The Research Of Q And Transmission Compensation In Reverse Time Migration

Q and transmission compensation are two indispensable parts in true-amplitude pre-stack depth migration.The viscos cause the amplitude attenuation and phase dispersion during the wavefield propagation.It is difficult to obtain high resolution and amplitude preserved migration images without compensating the viscous effects.Thus,the Q compensating operation is necessary in reverse time migration.The Q compensated reverse time migration consists two parts,the amplitude attenuation and phase dispersion.There are two kinds of viscoacoustic wave equations,the amplitude attenuation and phase dispersion terms decoupled and coupled.For the amplitude attenuation and phase dispersion terms coupled viscoacoustic wave equation,it is only suitable for the one-way wave migration.Only the viscoacoustic wave equations with the amplitude attenuation and phase dispersion terms decouple can be used in reverse time migration.Thus,we improve the decoupled viscoacoustic wave equation,which can be suitable for the small Q values case.Because the new viscoacoustic wave equation is a variable fractional Laplacian viscoacoustic wave equation,and the order of the Laplacian operator varies in space,which can cause strong Gibbs' phenomena during the process of IFT.In this paper,we develop a high-efficiency method for simulating wave propagation by using the least-squares method,which can avoid the Gibbs' phenomena and improve the computation efficiency.The traditional viscoacoustic wave equation based on the standard linear model cannot be used in Q compensated reverse time migration,because the amplitude attenuation and phase dispersion terms are coupled.In frequency wavenumber domain,the first order viscoacoustic wave equation is transformed into a second order viscoacoustic with the amplitude attenuation and phase dispersion decoupled.The numerical calculation indicated that the amplitude and phase dispersion of the new viscoacoustic wave equation is decoupled,which can be used in Q compensated reverse time migration.Besides,it has a high computational efficiency than the variable fractional wave equation.The stability is generally concerned issue in Q compensated reverse time migration.In this paper,we introduce two methods to deal with the instability during the wave propagation.The first method is that the exponential growing wavefield can be replaced by the ratio of different kinds of viscoacoustic wavefields on the premise of non-additional computation amount.In the second method,the wavefields we use are all exponential damping wavefield,with the help of new imaging condition,we obtain the satisfied Q-RTM images.For transmission compensation,the key point is how to obtain the incident angle and its calculation.In this paper the incident angle is calculated by the wavefield propagation direction and the reflector normal direction.In this way,the reflection coefficient and the transmission coefficient can be calculated in the first migration.Then the transmission coefficient is used to compensate the transmission loss in the second reverse time migration.But the calculation amount is huge,in the future how to reduce the calculation amount is the main research contents.