Another way for dealing with the simultaneous-source data is to solve the following equation for directly, which is known as direct imaging of blended data,
Equation 4 can be best solved using a least-squares (LS) based migration approach. More robust LS solvers involve adding constraints of structural coherency when inverting , either in a preconditioned LS formulation (Dai and Schuster, 2011; Chen et al., 2015c) or in a shaping-regularized LS iterative framework (Xue et al., 2014; Fomel, 2007b).
Because of the great success of deblending reported in the literature (Chen, 2015; Zu et al., 2015; Li et al., 2013; Beasley et al., 2012; Mahdad et al., 2011; Abma et al., 2010; Gan et al., 2015b) in the recent years, more and more focus is currently moving towards the direct imaging of blended data, which can be more efficient and can illuminate the surface better (Berkhout et al., 2012; Verschuur and Berkhout, 2011). It is worth mentioning that the deblending step for the massive blended data requires large computational resources (mainly for the parallel processing of a huge number of common receiver gathers) and a long processing period because of the thousands of iterations used for each common receiver gather. If the direct imaging can obtain a good result, we can obtain a big saving in both computational resources and processing period. However, a key aspect for the success of direct imaging is the macro velocity model of subsurface. Either tomography based velocity analysis or Born-approximation wave-equation based velocity inversion, requires an initial acceptable velocity model from the very noisy blended data (Figure 9a shows an example). In the next section, we will introduce a way for obtaining high-resolution and high-fidelity velocity spectrum from blended data, using the recently developed similarity-weighted semblance.