Full-Path Compensated Least-Squares Reverse Time Migration of Joint Primaries and Different-Order Multiples for Deep-Marine Environment

Abstract

In the deep-marine environment, seismic data contain multiples and are seriously affected by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> attenuation. Multiples have been used in migration to image the shadow zones and improve the resolution. However, the effect of attenuation on multiples is more serious than primaries because multiples have longer propagation paths. Therefore, we compensate the forward-propagated source-side and backward-propagated receiver-side wavefields along all the propagation paths of multiples. To fully use the primaries and multiples, we construct an objective function of least-squares reverse time migration of joint primaries and multiples (LSRTM-J) to update the imaging results by jointly using primaries and different-order multiples. In practice in a seawater medium, seismic waves can hardly be affected by attenuation. To decrease the computational cost, we divide the medium in the deep-marine environment into an acoustic medium part and a viscoacoustic medium part and derive the acoustic–viscoacoustic coupled compensated forward continuation operator, compensated adjoint operator, attenuated demigration operator, and gradient formula of joint primaries and multiples. To eliminate the severe scattering and diffracted noise caused by the strong-reflected irregular seabed interface, we mesh the velocity and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> models into curvilinear grids to perfectly match the seabed structure and realize the proposed viscoacoustic LSRTM-J in the curvilinear domain. Numerical examples on two typical models and a real data test suggest that the proposed method produces images with high SNR, high resolution, balanced amplitude, clear imaging structures, and strong deep region energy, and the total computational cost is the least of the other four conventional methods.