Statistics-Guided Residual Dictionary Learning for Footprint Noise Removal

Abstract

The footprint noise is a type of coherent noise that arises from the acquisition geometry. The footprint noise is commonly seen in 3-D seismic volumes and greatly affects the amplitude-based processing and interpretation steps in the seismic exploration workflow. Thus, removal of the footprint noise is necessary for warranting a reliable interpretation output of seismic data processing. However, because footprint noise is usually weak and also spatially coherent, it is inevitable to cause damages to useful signals during its removal steps. Here, we propose a dictionary learning (DL)-based method to effectively remove the footprint noise. We design an algorithm framework to effectively learn the dictionary atoms of the signal waveforms and separate the features of the footprint noise from the learned atoms. Considering the special features of the footprint noise in the dictionary atoms, we propose a statistics-guided way to separate the dictionary atoms into footprint-affected and footprint-free atoms. Then, the footprint-affected atoms are processed via a 2-D median filtering step. The combination between the untouched footprint-free atoms and filtered footprint-affected atoms result in a better dictionary of the signal waveforms and the footprint atoms. We use residual DL to encode the input data by a linear combination of signal atoms and footprint atoms. Removal of footprint atoms and their corresponding sparse coefficients leads to a successful footprint removal. We use both 3-D synthetic and field data examples to demonstrate the effectiveness of the proposed method.