Coherence index and curvelet transformation for denoising geophysical data.

Geophysical data contain stochastic noise that may mask their useful content. For example, ground roll (GR) is a coherent noise that is present in seismic data. Thus, such data are usually a mixture of useful information and useless coherent noise. The latter masks the relevant geologic information that seismic records contain, and its removal has always been a problem of fundamental importance. We propose a denoising method based on the curvelet transformation (CT), a multiscale transformation with strong directional character that provides an optimal representation of objects that have discontinuities along their edges. An algorithm is presented for processing and denoising of geophysical data. As an example, we apply the method to seismic images that are contaminated with the GR noise. First, the coherence index (CI), which represents a measure of the amount of energy contained in the most coherent modes of Karhunen-Lòeve transform for any given segment of the data, is computed. The contaminated region of the data is then identified as the maximum region of the 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 noncontaminated region. It is also significantly more efficient computationallty than the previous methods. The use of the method is demonstrated by its application to synthetic, as well as actual, seismic data for hydrocarbon reservoirs.