Adaptive rank reduction method for SSA to reconstruct seismic data

Farzaneh Bayati, Daniel O. Trad

Seismic data reconstruction is an important step in seismic data processing that affects the whole processing sequence because many tools for noise attenuation or imaging require the input data to be sampled regularly in space to work properly. It is also important for data acquired on difficult terrain with natural or cultural obstacles which may be missing a large portion of the surface shots and receivers. For plane waves or data with small curvatures, the rank reduction method is a very effective signal reconstructing method One of the advantages of rank reduction methods is simultaneous random noise attenuation and data interpolation. One of its limitations, on the other hand, is that it needs to satisfy the plane wave assumption. To satisfy the plane wave assumption the rank reduction methods need to be applied to local windows. Most of the time it is not easy to find the proper window size because it is hard to decide whether the structure in the local window is linear or not. Moreover, it is hard to approximate the rank of each window. Choosing the wrong rank will lead to a failure because the overestimation of rank remains a significant residual and underestimation of it will cause random noise and distort the signal. In this report, we will apply a method that selects rank automatically for each local window, and then apply the method on a global window. In the adaptive rank reduction method, we want to find the cutoff number that indicates when the contribution from the signal becomes much less than the contribution of the missing traces or random noise. This cutoff number happens at the point where the ratio of two consecutive singular values becomes the largest.