Damped Dreamlet Representation for Exploration Seismic Data Interpolation and Denoising

Abstract

The dreamlet (drumbeat-beamlet) transform can provide us an efficient method to represent physical wavefield, because the dreamlet basis satisfies automatically the wave equation, which is a distinctive feature different from mathematical basis, such as Fourier and curvelet. It can obtain an estimation of true signal from the observed noisy data by abandoning those insignificant components in the dreamlet domain. However, we have found that a more accurate estimation can be achieved by a damped version of the dreamlet representation. We have theoretically derived the damped dreamlet representation and given its geometric interpretation and analysis. Two applications of the proposed method have been explored in this paper: seismic random noise suppression and seismic data interpolation. Various examples demonstrate that the damped dreamlet representation-based technique has a superior performance compared with the mathematical-basis-based representation and rank-reduction-based techniques.