Seismic Data Interpolation And Denoising Based On Curvelet Transformation

Seismic data interpolation is a crucial step in the seismic processing flow. For instance, unsuccessful interpolation leads to erroneous multiple predictions that adversely affect the performance of multiple elimination, and to imaging artifacts. Successful recovery of a signal from incomplete measurements depends mainly on two factors:(i) how sampling is done (e.g., uniform or non-uniform in the spatial domain), (ii) how compressible the signal is with respect to some prescribed transform (e.g., Fourier, wavelet, curvelet, etc.). In order to enhance seismic images with the available data by removing noise and filling in missing traces, we present two transform-based reconstruction methods that exploits the compressibility of seismic data in the curvelet domain.In chapter 2, we first give an overview of the curvelet transform and its discrete implementation, the fast discrete curvelet transform (FDCT) and the property of curvelet transform.Chapter 3 deals with the reconstruction of spatially-undersampled seismic data with random noise. We start by a brief review of denoising by simply coefficient shrinkage. Recent research has shown that the method of curvelet thresholding can suppress the random noise more effectively and achieve higher signal to noise ratio than the traditional methods and it overcomes the drawback that the conventional filtering approach may affect the effective wave when suppressing noise. In this chapter, we propose a new iterative interpolation idea based on curvelet thresholding to reconstruct seismic data with missing traces. Experiments demonstrate that this method can obtain fine result for both regular and irregular sampled seismic data.In chapter 4, we turn the interpolation problem of coarsely sampled data into a denoising problem and propose a reconstructive method for incomplete seismic data based on this idea. We conclude by showing some reconstruction examples on synthetic and real data sets. Application of this method to interpolation problems on incomplete seismic data demonstrates that one can obtain excellent reconstructed result and effectively attenuate the random noise just as the case when there are no seismic data missing.