Swell noise attenuation on marine seismic data using variational mode decomposition in an automatic approach

Denoising is an important step in seismic data processing that can improve the results of other processing steps and, consequently, the interpretation of seismic sections. Both land and marine seismic data contain coherent and incoherent noise. Swell noise is one of the noises present in marine seismic data. It has a high amplitude and low frequency band and is observed as vertical bands in marine seismic data. Developing methods that can attenuate swell noise more while causing the least damage to the signal in marine seismic data seems necessary. There are various methods for attenuating swell noise, each with its advantages and limitations. The approach of most denoising methods is to maximize the separation of noise from the signal. Variational mode decomposition (VMD) has shown promising results in seismic denoising by separating different modes of signal and noise. The goal is to obtain a set of intrinsic mode functions (IMFs) and their corresponding center frequencies. The main approach of VMD is to decompose the input signal into a number of sub-signals (modes), which also have sparsity properties while recovering the input signal. Here, the sparsity of each mode is chosen as the bandwidth of that mode. In other words, it is assumed that each mode is more concentrated around the center frequency, which is determined in the decomposition. Another important issue in noise attenuation is that the denoising method should be able to perform the denoising process automatically with minimal user intervention. The proposed denoising algorithm in this paper consists of four steps: decomposition, identification, filtering, and reconstruction. In the first step, the seismic signal is decomposed into its constituent modes using the VMD method. In the second step, the modes contaminated with noise is identified according to the autocorrelation function of the modes, where the higher values of standard deviation of autocorrelation above a predefined measure present noisy modes. In the third step, the noise is removed through a filtering process based on a hard thresholding procedure. In the final step, the constituent modes, including the clean untouched modes, the denoised modes, and the residue, are summed together and the signal is denoised. The proposed algorithm's efficacy is demonstrated through its application to both synthetic and real seismic data. Notably, the method demonstrates superior performance compared to conventional high-pass filtering and time-frquency denoising (TFDN) method, effectively attenuating swell noise while preserving valuable low-frequency seismic information.