Least-Squares Gaussian Beam Transform for Seismic Noise Attenuation

We propose a novel seismic noise attenuation approach based on least-squares Gaussian beam transform (LSGBT). Gaussian beam transform uses time-domain Gaussian beam (TGB), which can be characterized by a particular location, arrival time, amplitude, slope, curvature, and width. We implement the local attributes such as beam center, spacing, and width to perform Gaussian beam decomposition. In this approach, we first introduce the plane-wave decomposition (PWD) theory to implement TGB decomposition of noisy seismic data and then apply data reconstruction. Unlike most state-of-the-art algorithms, random noise is attenuated in the process of Gaussian beam reconstruction. In the reconstruction records, the useful events are well preserved simultaneously removing random noise. Comparisons of experimental results on field data using traditional $f$ - $x$ deconvolution (FX Decon) and median filter (MF) methods are also provided, which suggest that our method achieves better denoising performance than FX Decon and MF methods. Taking into account that signal loss is sometimes unavoidable in almost all existing denoising methods. In addition to the signal-to-noise ratio (SNR) measurement, we also use local similarity as an efficient tool to evaluate denoising performance. A group of synthetic and field examples demonstrates the effectiveness of the proposed approach.