Chapter 3: Least-squares reverse time migration of marine data with frequency-selection encoding

The random encoding functions used by Romero et al. (2000); Schuster et al. (2011); Krebs et al. (2009) and Dai et al. (2012), cannot be applied to a seismic survey with marine streamer geometry (Huang and Schuster, 2012a; Routh et al., 2011), because the calculated synthetic data are also of fixed spread geometry, but the observed data are of marine streamer geometry. As a remedy, Routh et al. (2011) proposed a cross-correlation based misfit functional to mitigate the effect of recording pattern mismatch. Alternatively, Huang and Schuster (2012a) proposed a frequency-selection encoding strategy for least-squares phase shift migration, which is applicable to marine data.

The frequency-selection encoding strategy can also be applied with least-squares reverse time migration, where the time-domain simulation are performed with a single frequency harmonic source instead of the conventional broadband source. Nihei and Li (2006) proposed to use a time-domain finite-difference method to obtain the single frequency response of a point source in a velocity model. Compared to the conventional frequency domain method, their method has significantly lower arithmetic complexity and storage requirements in the 3D case.

In this chapter, the frequency-selection encoding method is applied with least-squares reverse time migration and tested on the Marmousi2 model to show that LSRTM can produce better images than conventional RTM with comparable cost for marine datasets.