Least-squares migration can mitigate the limitation of finite seismic acquisition, balance the subsurface illumination and improve the resolution of the image, but it requires many iterations of migration and demigration to obtain the desired subsurface reflectivity model. The efficiency and accuracy of migration and demigration operators are crucial for applying the iterative migration algorithm. We proposed a new approach by utilizing the Gaussian beam as the wavefield extrapolating operator for least-squares migration, denoted as least-squares Gaussian beam migration. Our method combines the advantages of the least-squares migration and the efficiency of the Gaussian beam propagator. This approach is implemented in the common-shot gather domain with a repeated use of dynamic-length complex-valued Green’s function tables to further accelerate the computation. The numerical examples illustrate that the proposed approach can be used to obtain amplitude-balanced images and slightly widened subsurface imaging coverage and to improve the spatial resolution of the migration result.
Since the traditional ray-based migration approaches are efficient, this kind of migration is widely applied for the industrial production. However, the traditional ray-based migration approaches are accompanied with some drawbacks, such as multi-arrivals problem, irregular amplitude at caustics and influence of shadows. In order to overcome the problems of multi-arrivals and caustics, Gaussian beam was introduced into seismic as a tool for imaging, denoted as Gaussian beam migration (Hill, 1990; Hale, 1992a; Hale, 1992b; Alkhalifah, 1995; Hill, 2001; Gray, 2005; Gray and Bleistein, 2009; Popov et al., 2010; Yue et al., 2012, Zheng et al., 2013). Conventional migration operator is usually considered as the adjoint of the corresponding forward modeling operator (Bleistein, 1987; Claerbout, 1992). However, this approximation would produce artifacts and aliases caused by finite bandwidth source signature, limited acquisition aperture, sparse sampling and gaps in the data. Tarantola (1984, 2005) regarded the migration is the first iteration in the inversion. Schuster (1993) and Nemeth et al. (1999) were committed to estimate the image of reflectivity model that modeled data best fit the observed data in the leastsquares sense. This kind of migration is denoted as leastsquares migration (LSM). According to the migration operator, LSM could be classified as least-squares Kirchhoff migration (Cole and Karrenbach, 1997; Nemeth et al., 1999; Duquet et al., 2000; Fomel et al., 2002; Liu et al., 2005; Wang et al., 2013), least-squares one-way wave equation migration (Kühl and Sacchi, 2003; Tang, 2009; Kaplan et al., 2010) and least-squares reverse-time migration (Wong et al., 2011; Dai et al., 2012; Dai et al., 2013; Zhang et al., 2013; Zhang and Schuster, 2014).