Source wavefield reconstruction based on an implicit staggered-grid finite-difference operator for seismic imaging

Reverse time migration and full waveform inversion involve the crosscorrelation of two wavefields,propagated in the forward-and reverse-time directions,respectively.As a result,the forward-propagated wavefield needs to be stored,and then accessed to compute the correlation with the backward-propagated wavefield.Boundary-value methods reconstruct the source wavefield using saved boundary wavefields and can significantly reduce the storage requirements.However,the existing boundary-value methods are based on the explicit finite-difference(FD)approximations of the spatial derivatives.Implicit FD methods exhibit greater accuracy and thus allow for a smaller operator length.We develop two(an accuracy-preserving and a memory-efficient)wavefield reconstruction schemes based on an implicit staggered-grid FD(SFD)operator.The former uses boundary wavefields at M layers of grid points and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield for a(2M+2)th-order implicit SFD operator.The latter applies boundary wavefields at N layers of grid points,a linear combination of wavefields at M–N layers of grid points,and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield(0≤N<M).The required memory of accuracy-preserving and memory-efficient schemes is(M+1)/M and(N+2)/M times,respectively,that of the explicit reconstruction scheme.Numerical results reveal that the accuracy-preserving scheme can achieve accurate reconstruction at the cost of storage.The memory-efficient scheme with N=2 can obtain plausible reconstructed wavefields and images,and the storage amount is 4/(M+1)of the accuracy-preserving scheme.

Target-oriented Q-compensated reverse-time migration by using optimized pure-mode wave equation in anisotropic media

Research on seismic anisotropy and attenuation plays a significant role in exploration geophysics. To enhance the imaging quality for complicated structures, we develop several effective improvements for anisotropic attenuation effects in reverse-time migration (Q-RTM) on surface and vertical seismic profiling (VSP) acquisition geometries. First, to suppress pseudo-shear wave artifact and numerical instability of the commonly used anisotropic pseudo-acoustic wave equations, an optimized pure P-wave dispersion relation is derived and the corresponding pure-mode wave equation is solved by combining the finite-difference and Possion methods. Second, a simplified anisotropic pure-mode visco-acoustic wave equation (PVAWE) based on standard linear solid model is established. Third, a time-dispersion correlation strategy is applied to improve the modeling accuracy. Fourth, we extend a target-oriented scheme to anisotropic attenuated modeling and imaging. Instead of the conventional wavefield modeling and RTM, the proposed approach can extract available wavefield information near the target regions and produce high imaging resolution for target structures. Last, both anisotropic surface and VSP Q-RTMs are executed by combining optimized PVAWE, time-dispersion correlation and target-oriented algorithm. Modeling examples demonstrate the advantages of our schemes. Moreover, our modified Q-compensated imaging workflow can be regarded as a supplement to the classical anisotropic RTM.