Noise attenuation in a low-dimensional manifold

Abstract

We have found that seismic data can be described in a low-dimensional manifold, and then we investigated using a low-dimensional manifold model (LDMM) method for extremely strong noise attenuation. The LDMM supposes the dimension of the patch manifold of seismic data should be low. In other words, the degree of freedom of the patches should be low. Under the linear events assumption on a patch, the patch can be parameterized by the intercept and slope of the event, if the seismic wavelet is identical everywhere. The denoising problem is formed as an optimization problem, including a fidelity term and an LDMM regularization term. We have tested LDMM on synthetic seismic data with different noise levels. LDMM achieves better denoised results in comparison with the Fourier, curvelet and nonlocal mean filtering methods, especially in the presence of strong noise or low signal-to-noise ratio situations. We have also tested LDMM on field records, indicating that LDMM is a method for handling relatively strong noise and preserving weak features.