Attenuation-compensated reverse time migration based on the stereo-modeling operator

Abstract

The viscosity in the subsurface is ubiquitous. Prestack reverse time migration (RTM) based on the viscoacoustic wave equation is an accurate imaging method to compensate attenuation. The resolution of an imaging result highly depends on the accuracy of the wave equation solution. We extend the nearly analytic center difference (NACD) method to a viscoacoustic wave equation to compensate seismic attenuation. The NACD method can achieve fourth-order accuracy in the time and space domain. We use the pressure and its gradients to approximate the spatial derivatives based on stereo modeling. Numerical simulations and dispersion analysis demonstrate that our NACD has less numerical dispersion and is more accurate than the Lax-Wendroff correction (LWC) method. Thus, the NACD is less expensive in terms of computational time and storage space. Numerical simulations indicate that the forward modeling of the viscoacoustic wavefield via the NACD is able to obtain more accurate wavefields compared with the conventional LWC method and can accurately simulate the effect of the viscosity on waves in attenuative media. When applied to RTM, the viscous effects of the subsurface can be compensated. Synthetic examples demonstrate that the attenuation-compensated RTM using NACD can obtain an image with higher resolution in attenuative media compared with that using the acoustic RTM. Furthermore, the image determined by the NACD is clearer than that of the LWC method in RTM.