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.

Figure 1

A typical synthetic seismic image containing ground-roll noise [15].

Figure 2

Demarcating the noisy region. Points A and B1 are the starting points, and B2 is the final point, which in this study is set to be the lower-right corner of the seismic image. We use $l,k$ instead of $I,J$ throughout the paper.

Figure 3

Normalized coherence index (CI), calculated by the KL transform. Higher CI corresponds to the coherent noise region.

Figure 4

(a) The demarcated region of the data shown in Fig. 1, corresponding to the maximum of CI in Fig. 3. (b) The denoised image of part of the data shown in (a), using the curvelet transform. (c) The noise removed from the image in (a).

Figure 5

(a) Synthetic seismic data with GR noise (courtesy of Geokinetics). (b) The denoised image of the data in (a). In this case we used the CT to denoise the entire image, but, as shown in the figure, some of the useful data have also been removed from the image. (c) The data removed from the image in (a). (d) The denoised image using the proposed method. In this image only the coherent sections, corresponding to the high values of the CI, have been denoised.

Figure 6

The computed coherence index CI for the seismic data of Fig. 5.

Figure 7

Actual seismic data for an oil reservoir in southern Iran with GR noise.

Figure 8

The computed coherence index CI for the seismic data of Fig. 7.

Figure 9

(a) The demarcated region of the data shown in Fig. 7, corresponding to the maximum of CI in Fig. 8. (b) The denoised image of part of data shown in (a), using the curvelet transform method. (c) The data removed from (a).

Figure 10

Actual seismic data, one shot with the GR noise, for a shallow oil reservoir (courtesy of Geokinetics).

Figure 11

The computed coherence index CI for the entire image shown in Fig. 10.

Figure 12

(a) Demarcating and denoising, (a) upper part and (b) lower part of the image for the seismic data shown in Fig. 10.