Streaming orthogonal prediction filter in $t$ -$x$ domain for random noise attenuation

introduction

Random noise in seismic data comes from many sources, such as wind motion and poorly planted geophones. Prediction filters (PFs) have been applied in seismic data processing for decades, and have proved their effectiveness for random noise attenuation. The PF has different coefficients from prediction-error filters (PEFs), which include extra causal time-prediction coefficients. The different prediction filtering methods, varying from $f$ -$x$ deconvolution (Canales, 1984) to $t$ -$x$ prediction filters (Claerbout, 1992; Abma and Claerbout, 1995), play an important role in random noise attenuation. However, seismic signals are fundamentally nonstationary, and stationary PFs/PEFs still fail in the presence of nonstationary events even if filtering can be done either by ``patching'' or breaking data into overlapping windows. Different regularization methods (Fomel, 2009; Curry, 2003; Crawley, 1999; Liu and Chen, 2013; Liu et al., 2015) help PFs/PEFs estimate the nonstationary coefficients corresponding to the underdetermined autoregression problems.

Most of the nonstationary PFs/PEFs use iterative or recursive approaches to calculate their coefficients. This leads to high computational costs, especially in the storage of variable coefficients (Ruan et al., 2015). Recently, a streaming PEF (Fomel and Claerbout, 2016) was proposed to solve this problem. This method updates the PEF coefficients incrementally as new data arrive. This method reduces the computational cost of the streaming PEF to a single convolution. Moreover, the exact inversion of the streaming PEF makes missing data interpolation straightforward.

In this paper, we propose an adaptive PF method based on streaming and orthogonalization (Chen and Fomel, 2015) to attenuate random noise in nonstationary seismic data. The proposed method is able to characterize the nonstationarity on both time and space axes. The streaming element makes the proposed method a convenient and fast denoising approach. The application of orthogonalization further strengthens its ability in random noise attenuation. Numerical tests using synthetic and field data demonstrate the effectiveness of the proposed SOPF method.

Streaming orthogonal prediction filter in $t$ -$x$ domain for random noise attenuation