Noniterative multiple attenuation methods: Linear inverse solutions to nonlinear inverse problems

摘要

It is now well established that the relationship between data without free-surface multiples (i.e., primaries) and data containing free-surface multiples (i.e., the actual recorded data) is nonlinear. As with most nonlinear inverse problems, solutions to the problem of constructing primaries from recorded data (or attenuating free-surface multiples) are either iterative or in the form of a series with an infinite number of terms. The drawbacks of these solutions are that they are computationally very expensive and often unstable especially when compared to linear solutions like predictive deconvolution or f-k filtering. However, most linear solutions contain unrealistic assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. Fortunately, there are exceptions to this assertion. We are going to present a linear and noniterative solution to the problem of attenuating free-surface multiples which is as accurate as the iterative nonlinear solutions. This linear solution aims at attenuating free-surface multiples for ocean-bottom seismic (OBS) data. Besides the theoretical interest in finding linear solutions to a nonlinear inverse problem, this linear solution is fast, stable, and robust compared to the nonlinear solutions.