This dissertation addresses the problem of seismic noise attenuation by using inversion. Two types of noise are considered. First, spiky noise, which is attenuated with a robust error measure called the Huber norm. This norm treats small residual with the norm and large residuals with the norm. It is continuous everywhere and can be minimized with a standard gradient-based solver. In this thesis, the well-known quasi-Newton method L-BFGS is used. The Huber norm and the L-BFGS solver are flexible enough to be used in many different situations, such as velocity analysis and regridding of noise bathymetry data. Another powerful application of the Huber norm is adaptive subtraction of surface-related multiples. In this case, weak multiples in the vicinity of strong primaries are better removed with the Huber norm than with .
Second, coherent noise, which is attenuated by making the residual components of any least-squares fitting of contaminated data independent and identically distributed (IID). To achieve this goal, a weighting and a modeling approach are introduced. The weighting approach aims at approximating the inverse data covariance operator (or matrix) with multidimensional prediction-error filters (PEFs). The modeling approach introduces a coherent noise modeling operator inside the inversion. The modeling technique converges usually better than the weighting approach and yields smaller residuals.
One advantage of the weighting approach, however, is that it can be used to
separate non-stationary signal and non-stationary noise with PEFs.
In this case, the separation is called pattern-based because it
involves the multivariate noise and signal spectra that PEFs
approximate. For removal of surface-related multiples, this technique
proves being more robust to modeling inadequacies than adaptive
subtraction with the norm, as exemplified on marine 2-D and
3-D field data examples.