Denoising of Seismic Data Using Curvelet Transformation: The Effect of on the Content of the Data

Abstract

Abstract Seismic data usually contain stochastic noise, such as the ground roll (GR), a coherent noise. The noise masks the useful content of the data, such as geologic information that seismic records contain. Removal of the noise has always been a problem of fundamental importance. There are already several methods for removing the noise from seismic images, almost all of which have the drawback that they degrade both the noisy and the “unpolluted” regions in seismic images. In addition, seismic data typically contain long-range correlations, characterized by a Hurst exponent H. In this study we propose a novel method for denoising the entire seismic image. The method is based on the curvelet transform (CT), a multiscale transformation with strong directional characters that provides an optimal representation of objects with discontinuities along their edges. We also study the effect of denoising on the Hurst exponent and, hence the long-range correlations that the images contains. Then, to reduce, or eliminate altogether, the impact of denoising on the correlations in the seismic data contain, we propose a denoising method based on the CT and a coherence index (CI) that we introduce in this paper. As an example, we apply the method to seismic images that are contaminated with the GR noise. First, the CI, representing a measure of the amount of energy contained in the most coherent modes of Karhunen-Loeve transform for any given segment of the data, is computed. The contaminated region of the data is then identified as the region with the maximum CI. After demarcating the contaminated segment, the CT is used to eliminate the noise. The method removes the noise with negligible distortion of the data's non-contaminated region. Its computations are also significantly more efficient than those of the previous methods. The use of the method is demonstrated by its application to synthetic, as well as actual seismic data for hydrocarbon reservoirs.