Seismic data interpolation using nonlinear shaping regularization

Comparison with the traditional methods and limitation discussion

The shaping regularization can be viewed as a general framework for any inversion problem, including the seismic data recovery problem. The normal shaping regularization can be viewed as POCS or IST, which are two most commonly used approaches for interpolating irregularly sampled seismic data in the literature. The faster version shaping regularization can be viewed a breakthrough in accelerating the convergence for the conventional approach. Thus, the comparison between faster and normal shaping regularization corresponds to the a comparison between the proposed approach with other approaches cited in the introduction, such as the POCS approach (Abma and Kabir, 2006).

The traces should be randomly sampled spatially and binned to regular spatial grids. The limitation of the interpolation approaches is that the largest gap between two neighbor traces should not be very large. There also exist a lot of researches in the literature trying to solve this limitation by raising different kinds of sampling approaches, such as Hennenfent and Herrmann (2008) and Herrmann (2010).

Seismic data interpolation using nonlinear shaping regularization