Seismic Random Noise Attenuation in the Laplace Domain Using Singular Value Decomposition

We attenuated incoherent seismic noise using singular value decomposition in the Laplace domain. Laplace-domain wavefields are sensitive to small-amplitude noise contaminating the first-arrival signals due to damping in the Laplace transform; this noise is boosted by the Laplace transform, so we need to attenuate the amplified noise in the Laplace domain. We transformed seismic wavefields into the Laplace domain and attenuated noise in the logarithmic wavefields by applying a moving average filter and low-rank approximation using truncated singular value decomposition. The process was very efficient since the number of matrix decomposition was the same as the number of damping coefficients. We removed highly oscillatory random noise from the logarithmic wavefields, and the denoised Laplace-domain wavefields were used in subsequent Laplace-domain full waveform inversions. The inversions of synthetic and field data demonstrated that denoising the Laplace-domain wavefield does not significantly alter the inversion results; however, this approach could reduce the misfit errors and uncertainties from noise.