Iterative deblending with multiple constraints based on shaping regularization |

where is the blended data, is the blending operator, and is the unblended data. The formulation of has been introduced in Mahdad (2012) in detail. When considered in time domain, corresponds to blending different shot records onto one receiver record according to the shot schedules of different shots. Deblending amounts to inverting equation 1 and recovering from .

Because of the ill-posed property of this problem, all inversion methods require some constraints.

Chen et al. (2014a) proposed a general iterative deblending framework via shaping regularization Fomel (2007,2008). The iterative deblending is expressed as:

where is the shaping operator, which provides some constraints on the model, and is the backward operator, which approximates the inverse of . The shaping regularization framework offers us much freedom in constraining an under-determined problem by allowing different types of constraints. In this paper, the backward operator is simply chosen as , where is a scale coefficient closely related with the blending fold, and stands for the adjoint operator of (or the pseudo-deblending operator). For example, can be optimally chosen as in a two-source dithering configuration Chen et al. (2014a); Mahdad (2012). In the next two sections, I will first introduce the conventional way for choosing the and then propose a novel way for designing the .

Iterative deblending with multiple constraints based on shaping regularization |

2015-09-15