Gaussian beam migration in exploration seismology: methods, advantages and implementation

Migration methods are fundamental to seismic imaging. Generally, seismic migration imaging methods can be categorized in pre-stack and post-stack techniques that are based on either wave-equation or ray-theory principles. Key methods include Kirchhoff Migration, a ray-theory-based approach; wave-equation-based techniques such as Reverse Time Migration (RTM); and Gaussian Beam Migration (GBM), which combines the flexibility of ray theory with the accuracy of wave-equation methods and is getting more attention recently. The GBM methods include two implementations: the frequency domain and the space-time domain. In the construction of the reverse wavefield, the frequency-domain GBM employs ray-tracing methodology to compute the wavefield; by utilizing the kinematic characteristics of the seismic wavefield, it discretizes the computational domain into equal angular segments, thereby reducing computational iterations for imaging points located at greater offsets from the virtual source (receiver point). In contrast, the space-time-domain GBM incorporates the wavefield extrapolation approach derived from RTM, accounting for the dynamic characteristics of the seismic wavefield; it enhances the imaging accuracy of migration results through direct computation of the wavefield information at each imaging point, albeit at the cost of increased computational time. This review firstly traces the development of GBM methods, which progresses from acoustic to viscous, elastic and anisotropic media, and from simple horizontal surface to complex geological structures. It also explores the evolution from Gaussian beam to focused beam and Fresnel beam. A complex multi-layer model is then used to display the imaging differences between the frequency-domain and space-time-domain GBM methods. To enhance readers’ comprehension, a vertical transversely isotropic field dataset is employed to demonstrate the application of GBM methods to real-world datasets, highlighting the advantage of incorporating the actual mechanical properties of subsurface media. Finally, we quantitatively compare the computational efficiency of different methods under three classic scenarios, and accordingly provide application-oriented concrete recommendations.