Denoising for full-waveform inversion with expanded prediction-error filters

Low-frequency data of less than 5 Hz are essential to the convergence of full-waveform inversion (FWI) toward a useful solution. They help to build the velocity model low wavenumbers and reduce the risk of cycle skipping. In marine environments, low-frequency data are characterized by a low signal-tonoise ratio (S/N) and can lead to erroneous models when inverted, especially if the noise contains coherent components. Often, field data are high-pass filtered before any processing step, sacrificing weak but essential signal for FWI. We have denoised the low-frequency data using prediction-error filters that we estimate from a high-frequency component with a high S/N. The constructed filter captures the multidimensional spectrum of the high-frequency signal. We expand the filter' axes in the time-space domain to compress its spectrum tow, the low frequencies and wavenumbers. The expanded filter becomes a predictor of the target low-frequency signal, and we incorporate it in a minimization scheme to attenuate noise. To account for data nonstationarity while retaining the simplicity of stationary filters, we divide the data into nonoverlapping patches and linearly interpolate stationary filters at each data sample. We apply our method to synthetic stationary and non-stationary data, and we find that it improves the FWI results initialized at 2.5 Hz using the Marmousi model. We also demonstrate that the denoising attenuates nonstationary shear energy recorded by the vertical component of ocean-bottom nodes.