Applications of least-squares pre-stack depth migration in complex geology around the world

Abstract

Pre-stack depth migration has been an industrial imaging standard for decades, starting from the adoption of Kirchhoff migration in the early Nineties to the emergence of reverse-time migration (RTM) in the late 2000s. These algorithms map the recorded seismic reflection energy from a surface location to a subsurface location, through either a ray-based travel-time table or a waveequation-based propagation engine. In principle, by combining high-fidelity migration algorithms and accurate subsurface velocity models, we can achieve the ultimate goals of seismic imaging: the correct positioning and focusing of the seismic reflectivity of the subsurface geological structures. In reality, however, there are several challenges and issues that need to be addressed before we are able to achieve such an objective, not to mention the fact that most of the time we do not record all subsurface reflections sufficiently owing to limited coverage and sampling of the seismic recording spread. We can consider recorded seismic data to be the result of forward modelling experiments through subsurface structures. To image the reflectivity of the subsurface, we need to reverse the forward wave-propagation effects with an inverse of the forward modelling operator. Essentially, this is an inversion process. However, conventional imaging algorithms are formulated as adjoint operators rather than as true inverses (Claerbout, 1992). This approximation caused image degradation due to irregular and aliased acquisition sampling, limited receiver coverage, noise, and inhomogeneous or poor illumination caused by complex overburden. As a result, standard pre-stack depth migration algorithms suffer from migration artifacts with uncancelled swings, limited bandwidth, and distorted amplitude on subsurface reflectors (Gray, 1997). This is true even for stateof-the-art imaging technology such as RTM (Baysal et al., 1983; Zhang and Zhang, 2009).